Class 12 Physics (Part 1) Chapter 3 Electric Potential

This quiz on ICSE Class 12 Physics Chapter 3: Electric Potential is designed to test students' conceptual understanding and problem-solving skills related to electrostatics. Covering key topics such as electric potential due to a point charge, potential difference, equipotential surfaces, the relationship between electric field and potential, and potential energy of a system of charges, the quiz aims to reinforce both theoretical knowledge and practical applications. It includes a variety of question types—conceptual, numerical, and application-based—to assess comprehension and analytical abilities. This engaging assessment supports learners in mastering the core principles of electric potential, as outlined in the ICSE curriculum.

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Category: Electron-Volt:

1. (A) 1 electron-volt is equal to $1.6 \times 10^{-19}$ joule.
(R) The work done in moving one electron through a potential difference of 1 volt is $1.6 \times 10^{-19}$ joule.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Work Done in Bringing Charges Together

2. Four identical charges $q$ are placed at the corners of a square of side $a$. What is the work required to remove one charge from its position to infinity?

a) $\frac{q^2}{4 \pi \epsilon_0 a} \left( 1 + \frac{1}{\sqrt{2}} \right)$

b) $\frac{q^2}{4 \pi \epsilon_0 a} \left( 2 + \frac{1}{\sqrt{2}} \right)$

c) $\frac{q^2}{4 \pi \epsilon_0 a} \left( 2 + \frac{1}{2} \right)$

d) $\frac{q^2}{4 \pi \epsilon_0 a} \left( 1 + \frac{1}{2} \right)$

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Category: Electric Potential Energy of a System of Charges

3. Two charges $+1 \, \text{C}$ and $-1 \, \text{C}$ are initially placed $1 \, \text{m}$ apart. How much work is needed to reduce their separation to $0.5 \, \text{m}$?

a) $-9 \times 10^9 \, \text{J}$

b) $9 \times 10^9 \, \text{J}$

c) $-4.5 \times 10^9 \, \text{J}$

d) $4.5 \times 10^9 \, \text{J}$

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Category: Continuous Charge Distribution (Area and Volume Integrals)

4. A non-conducting sphere of radius $R$ has a volume charge density $\rho = \rho_0 e^{-r/a}$, where $\rho_0$ and $a$ are constants, and $r$ is the distance from the center. Calculate the total electric potential at the center of the sphere.

a) $\frac{\rho_0 a^2}{ \varepsilon_0} \left[1 - e^{-R/a} \left(1 + \frac{R}{a}\right)\right]$

b) $\frac{\rho_0 R^2}{2 \varepsilon_0} e^{-R/a}$

c) $\frac{\rho_0 a R}{\varepsilon_0} (1 - e^{-R/a})$

d) $\frac{\rho_0 a^3}{\varepsilon_0 R} (e^{R/a} - 1)$

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Category: Potential Difference

5. A charge $q = -2 \text{C}$ is moved from point A (potential $V_A = 10 \text{V}$) to point B (potential $V_B = 5 \text{V}$). Calculate the work done by the external agent.

a) $-10 \text{J}$

b) $5 \text{J}$

c) $10 \text{J}$

d) $-5 \text{J}$

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Category: Potential Due to Point Charges:

6. Two point charges $+Q$ and $-4Q$ are placed 12 cm apart. At what distance from $+Q$ along the line joining them is the electric potential zero?

a) 3 cm

b) 4 cm

c) 2.4 cm

d) 6 cm

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Category: Potential Difference:

7. (A) The potential difference between two points in an electric field is defined as the work done per unit positive charge to move it from one point to another.
(R) Work done in moving a charge depends only on the initial and final positions and not on the path taken.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Calculation of Potential Energy

8. (A) The potential energy of a system of two like charges is positive.
(R) Like charges repel each other, and work must be done to bring them closer.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Equipotential Surfaces:

9. What is the work done to move a charge along an equipotential surface?

a) Positive work is done

b) Negative work is done

c) No work is done

d) Work depends on the path taken

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Category: Electron-Volt:

10. How many electron-volts correspond to $3.2 \times 10^{-18} \, \text{J}$ of energy?

a) $5 \, \text{eV}$

b) $15 \, \text{eV}$

c) $20 \, \text{eV}$

d) $25 \, \text{eV}$

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Category: Definition and Use in Atomic Physics

11. A proton is placed at a distance of $5.29 \times 10^{-11}$ m from an electron. What is the electric potential energy of the system in electron-volts? (Given $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9$ Nm$^2$/C$^2$)

a) $-13.6$ eV

b) $-27.2$ eV

c) $-54.4$ eV

d) $-1.6$ eV

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Category: Torque on Dipole in Electric Field

12. A dipole with moment $p = 3.2 \times 10^{-28} \, \text{C-m}$ is placed in an electric field $E = 8.0 \times 10^4 \, \text{V/m}$. What will be the torque acting on the dipole when it is oriented at $45^\circ$ relative to the field direction?

a) $2.56 \times 10^{-23} \, \text{N-m}$

b) $1.81 \times 10^{-23} \, \text{N-m}$

c) $3.62 \times 10^{-23} \, \text{N-m}$

d) $1.28 \times 10^{-23} \, \text{N-m}$

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Category: Definition and Calculation

13. (A) The electric field intensity at a point is equal to the negative gradient of the electric potential at that point.
(R) The potential decreases in the direction of the electric field, making the gradient negative.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Electric Potential Energy of an Electric Dipole in an Electrostatic Field

14. (A) The potential energy of an electric dipole placed parallel to a uniform electric field is $-pE$.
(R) When the dipole is aligned parallel to the field, the net work done in bringing it from infinity is $-pE$ due to additional displacement of the negative charge.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Electron-Volt (eV)

15. An electron is accelerated through a potential difference of 5 volts. What is the energy gained by the electron in electron-volts?

a) 1 eV

b) 5 eV

c) 10 eV

d) 15 eV

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Category: Calculation of Potential at Points along the Axis and Equatorial Line

16. A dipole with a dipole moment $p = 4 \times 10^{-6} \, \text{C}\cdot\text{m}$ is placed in vacuum. What is the potential at a point P located 1 m away from the dipole on its axial line? ($\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2$)

a) 18 kV

b) 24 kV

c) 36 kV

d) 48 kV

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Category: Definition and Use in Atomic Physics

17. What is the electric potential energy of a system consisting of two charges $+q_1$ and $+q_2$ separated by distance $r$ in vacuum?

a) $\frac{1}{4 \pi \epsilon_0} \frac{q_1 + q_2}{r}$

b) $\frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2}$

c) $\frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r}$

d) $\frac{q_1 q_2}{r^2}$

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Category: Stable and Unstable Equilibrium

18. (A) An electric dipole placed in a uniform electric field is in stable equilibrium when its potential energy is minimum.
(R) The potential energy of an electric dipole in an electric field is given by $U = -pE \cos \theta$, and it attains its minimum value when $\theta = 0^\circ$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Electric Potential Due to an Electric Dipole

19. An electric dipole of moment $p$ is placed at the origin along the x-axis. What is the ratio of the electric potential at points $(3a, 0)$ and $(0, 4a)$ due to this dipole?

a) $\frac{4}{3}$

b) $\frac{16}{9}$

c) Undefined

d) Zero

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Category: Potential Calculation for Multiple Charges

20. Two point charges, +3 µC and -5 µC, are placed 4 m apart on the x-axis. What is the electric potential at a point 2 m from the +3 µC charge and 6 m from the -5 µC charge?

a) $6.0 \times 10^3$ V

b) $-6.0 \times 10^3$ V

c) $21.0 \times 10^3$ V

d) $-21.0 \times 10^3$ V

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Category: Work Done in Rotating Dipole:

21. If an electric dipole with dipole moment $p$ is rotated by $180^\circ$ from its equilibrium position in a uniform electric field $E$, what is the work done?

a) $0$

b) $pE$

c) $2pE$

d) $4pE$

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Category: Electric Potential Energy of an Electric Dipole in an Electrostatic Field

22. How much work is required to rotate an electric dipole from being parallel ($\theta = 0^\circ$) to perpendicular ($\theta = 90^\circ$) to a uniform electric field $\vec{E}$?

a) $0$

b) $pE/2$

c) $pE$

d) $2pE$

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Category: Relation between Electric Field and Potential Gradient

23. What is the unit of potential gradient?

a) Newton per coulomb (\text{N-C}$^{-1}$)

b) Coulomb per second (\text{C-s}$^{-1}$)

c) Volt per metre (\text{Vm}$^{-1}$)

d) Joule per coulomb (\text{J-C}$^{-1}$)

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Category: Potential Difference

24. Two parallel plates separated by 5 mm have a potential difference of 100 V. An electron is released from rest near the negative plate. What is its kinetic energy when it reaches the positive plate? (Charge of electron $e = -1.6 \times 10^{-19} \, C$, mass $m_e = 9.1 \times 10^{-31} \, kg$)

a) $1.6 \times 10^{-19} \, J$

b) $1.6 \times 10^{-17} \, J$

c) $3.2 \times 10^{-17} \, J$

d) $8.0 \times 10^{-18} \, J$

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Category: Stable and Unstable Equilibrium

25. At what angle $\theta$ between the dipole moment and the electric field is the dipole in unstable equilibrium?

a) $0^\circ$

b) $90^\circ$

c) $180^\circ$

d) $270^\circ$

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Category: Continuous Charge Distribution (Area and Volume Integrals)

26. (A) The potential due to a continuous charge distribution is given by $V = \frac{1}{4 \pi \varepsilon_0} \int \frac{dq}{r}$.
(R) This equation replaces summation with integration because the charge distribution is continuous.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Potential Difference:

27. Points X and Y are in a region with a uniform electric field $\vec{E} = 4\,\text{N/C}\;\hat{i}$. The potential at X is $12\,\text{V}$ and at Y is $-8\,\text{V}$. What is the distance between X and Y?

a) $3\,\text{m}$

b) $5\,\text{m}$

c) $8\,\text{m}$

d) $10\,\text{m}$

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Category: Work Done in Rotating an Electric Dipole in an Electric Field

28. (A) The work done in rotating an electric dipole from $\theta_1 = 0^\circ$ to $\theta_2 = 90^\circ$ in a uniform electric field is $pE$.
(R) The torque acting on the dipole at any angle $\theta$ is given by $\tau = pE \sin \theta$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Derivation of the Relation

29. (A) The electric field $E$ at a point is equal to the negative gradient of the electric potential $V$ at that point.
(R) The potential decreases in the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Potential Gradient

30. A charge $q = 2$ C is moved through an electric field where the potential changes uniformly from 10 V to -20 V over 5 m. How much work is done by the electric force during this displacement?

a) 30 J

b) 60 J

c) -60 J

d) -30 J

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Category: Electron-Volt (eV)

31. What is the value of 1 electron-volt (eV) in joules?

a) $1.9 \times 10^{-19} \text{ J}$

b) $1.6 \times 10^{-19} \text{ J}$

c) $1.6 \times 10^{-18} \text{ J}$

d) $3.2 \times 10^{-19} \text{ J}$

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Category: Applications in Point Charges and Dipoles

32. What is the work done to rotate an electric dipole from angle $\theta_1 = 0^\circ$ to $\theta_2 = 90^\circ$ in a uniform electric field $E$?

a) $0$

b) $-pE$

c) $+pE$

d) $2pE$

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Category: Calculation of Electric Potential

33. (A) The electric potential at a point on the equatorial line of an electric dipole is zero.
(R) The potentials due to the positive and negative charges of the dipole cancel each other out on the equatorial line.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Stable and Unstable Equilibrium

34. What is the work done to rotate an electric dipole from stable equilibrium ($\theta = 0^\circ$) to unstable equilibrium ($\theta = 180^\circ$) in an electric field $E$?

a) $pE$

b) $2pE$

c) $-pE$

d) Zero

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Category: Equipotential Surfaces:

35. (A) The work done in moving a charge along an equipotential surface is zero.
(R) The potential difference between any two points on an equipotential surface is zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Work Done in Rotating Dipole:

36. What is the work done in rotating an electric dipole of moment $p$ through an angle $\theta = 90^\circ$ in a uniform electric field $E$ from its equilibrium position?

a) $0$

b) $pE$

c) $2pE$

d) $\frac{pE}{2}$

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Category: Potential Calculation for Multiple Charges

37. Four charges $q_1 = 4 \mu C$, $q_2 = -2 \mu C$, $q_3 = 6 \mu C$, and $q_4 = -8 \mu C$ are placed at the corners of a square of side 2 m. Calculate the total potential energy of the system.

a) -0.445 J

b) -1.234 J

c) 0.567 J

d) -2.345 J

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Category: Electric Dipole:

38. What is the electric potential at a point on the axial line of an electric dipole at distance $r$ from its center when $r \gg l$?

a) $\frac{1}{4 \pi \epsilon_0} \cdot \frac{q l}{r}$

b) $\frac{1}{4 \pi \epsilon_0} \cdot \frac{p}{r^2}$

c) 0

d) $\frac{1}{4 \pi \epsilon_0} \cdot \frac{p}{r^3}$

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Category: Electron-Volt:

39. If a proton is moved through a potential difference of 50 V, what is the work done on the proton in electron-volts?

a) 1 eV

b) 5 eV

c) 50 eV

d) 500 eV

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Category: Electric Potential

40. Two point charges $+q$ and $-q$ are separated by a distance $r$. What is the electrostatic potential energy of the system?

a) $\frac{1}{4 \pi \epsilon_0} \frac{q^2}{r}$

b) $-\frac{1}{4 \pi \epsilon_0} \frac{q}{r^2}$

c) $\frac{1}{4 \pi \epsilon_0} \frac{q}{r^2}$

d) $-\frac{1}{4 \pi \epsilon_0} \frac{q^2}{r}$

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Category: Calculation of Potential at Points along the Axis and Equatorial Line

41. (A) The electric potential at any point on the equatorial line of a dipole is zero.
(R) The distances from both charges of the dipole to any point on the equatorial line are equal, leading to cancellation of potentials.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Potential Difference:

42. (A) The potential difference between two points A and B in an electric field is given by $V_A - V_B = \frac{W}{q_0}$ where W is the work done against the electric force
(R) An external agent must do positive work to move a positive test charge from point A to point B when $V_A > V_B$

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Electric Potential:

43. (A) The electric potential at a point due to a point charge is inversely proportional to the distance from the charge.
(R) The work done in bringing a unit positive test charge from infinity to that point depends on the distance from the charge.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Derivation of the Relation

44. When a test charge \$q_0\$ is moved against an electric field, the work done \$(dW)\$ is given by:

a) \$dW = q_0 E dr\$

b) \$dW = -q_0 E dr\$

c) \$dW = q_0 V dr\$

d) \$dW = -q_0 V dr\$

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Category: Electric Potential due to a Point Charge

45. (A) The electric potential at a point due to a positive point charge decreases as the distance from the charge increases.

(R) The electric potential is inversely proportional to the distance from the point charge.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Perpendicularity of Electric Field to Equipotential Surfaces

46. In a region where the electric potential is given by $V(x) = 3x^2 + 5 \, V$, where $x$ is in meters, what is the electric field at $x = 2 \, m$ and its direction relative to the equipotential surface at that point?

a) 6 V/m, tangent to the surface

b) 12 V/m, perpendicular to the surface

c) -6 V/m, tangent to the surface

d) -12 V/m, perpendicular to the surface

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Category: Electric Potential due to a Group of Point Charges

47. (A) The electric potential at the center of a square formed by four point charges is zero if the algebraic sum of all charges is zero.
(R) Electric potential is a scalar quantity and follows the principle of superposition.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

48 / 600

Category: Torque on Dipole in Electric Field

48. What is the work done to rotate an electric dipole from $\theta = 0^\circ$ to $\theta = 90^\circ$ in a uniform electric field $E$ if its dipole moment is $p$?

a) $pE \sin 90^\circ$

b) $pE \cos 90^\circ$

c) $pE$

d) $2pE$

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Category: Electric Potential Energy of a System of Charges

49. (A) The electric potential energy of a system of three charges $q_1 = +1 \, \text{C}$, $q_2 = -2 \, \text{C}$, and $q_3 = +3 \, \text{C}$ placed at the corners of an equilateral triangle of side $1 \, \text{m}$ is negative.

(R) The net potential energy of a system of charges is determined by the algebraic sum of the potential energies of all pairs, and for unlike charges, the potential energy is negative.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Relation between Electric Field and Electric Potential

50. The electric potential in a region is given by $V(x) = 3x^2 - 4x + 5$ volts, where $x$ is in meters. What is the magnitude of the electric field at $x = 2$ m?

a) 10 V/m

b) 8 V/m

c) 12 V/m

d) 6 V/m

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Category: Unit and Direction of Potential Gradient

51. If the electric field intensity \$E\$ is \$5 \, V \, m^{-1}\$, what is the magnitude of the potential gradient?

a) \$10 \, V \, m^{-1}\$

b) \$2.5 \, V \, m^{-1}\$

c) \$5 \, V \, m^{-1}\$

d) \$0 \, V \, m^{-1}\$

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Category: Potential Gradient

52. The direction of the potential gradient is:

a) Opposite to the direction of the electric field

b) Same as the direction of the electric field

c) Perpendicular to the electric field

d) Along the equipotential surface

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Category: Definition and Formula

53. (A) The potential gradient is a scalar quantity.
(R) The potential gradient is the rate of change of potential with distance and has both magnitude and direction.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

54 / 600

Category: Torque on Dipole in Electric Field

54. (A) When an electric dipole is rotated from $\theta = 60^\circ$ to $\theta = 120^\circ$ in a uniform electric field, the work done is equal to $pE$.
(R) The potential energy of the dipole at $\theta = 120^\circ$ is greater than its potential energy at $\theta = 60^\circ$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Definition and Formula

55. What is the unit of potential gradient?

a) Newton per coulomb

b) Volt per meter

c) Joule per second

d) Coulomb per meter

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Category: Electric Potential Energy of an Electric Dipole in an Electrostatic Field

56. What is the potential energy of an electric dipole when it is placed perpendicular to a uniform electric field $\vec{E}$?

a) $-pE$

b) $0$

c) $+pE$

d) $-2pE$

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Category: Relation between Electric Field and Electric Potential

57. Which of the following is a valid unit for electric field intensity?

a) $J \cdot C^{-1}$

b) $V \cdot m^{-1}$

c) $N \cdot C$

d) $V \cdot s^{-1}$

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Category: Potential Difference

58. Two points A and B are separated by a distance $d$ in a uniform electric field $E$. If a charge $q$ is moved from A to B along the direction of the field, what is the potential difference between A and B?

a) $E \cdot d$

b) $\frac{E}{d}$

c) $E + d$

d) $\frac{d}{E}$

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Category: Physical Interpretation

59. (A) The electric field is zero where the potential gradient is zero.
(R) The electric field is equal to the negative of the potential gradient.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Electron-Volt (eV)

60. (A) The work done in moving an electron through a potential difference of 1 volt is equal to $1.6 \times 10^{-19}$ joules.
(R) 1 electron-volt is defined as the kinetic energy gained by an electron when accelerated through a potential difference of 1 volt.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

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Category: Continuous Charge Distribution (Area and Volume Integrals)

61. A rod of length $L$ has a linear charge density $\lambda = kx$, where $x$ is the distance from one end of the rod. What is the electric potential at a point along the axis of the rod but outside it (at $x = L + a$)?

a) $\frac{k}{4 \pi \varepsilon_0} \left[ (L + a) \ln \left( \frac{a}{L + a} \right) - L \right]$

b) $\frac{k}{4 \pi \varepsilon_0} \left[ (L + a) \ln \left( \frac{L + a}{a} \right) + L \right]$

c) $\frac{k}{4 \pi \varepsilon_0} \left[ (L + a) \ln \left( \frac{a}{L + a} \right) + L \right]$

d) $\frac{k}{4 \pi \varepsilon_0} \left[ (L + a) \ln \left( \frac{L + a}{a} \right) - L \right]$

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Category: Calculation of Electric Potential

62. A dipole with dipole moment $p = 2 \times 10^{-8}$ C-m is placed at the origin. What is the electric potential at a point $(r, \theta) = (4$ m, $60^\circ)$? Assume $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9$ Nm$^2$/C$^2$.

a) 2.8125 V

b) 5.625 V

c) 11.25 V

d) 22.5 V

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Category: Physical Interpretation

63. Which of the following represents the dimensional formula for electric potential?

a) $[W] = M L^2 T^{-2}$

b) $[q] = A T$ \end{itemize} Hence, $[V] = \frac{[W]}{[q]} = \frac{M L^2 T^{-2}}{A T} = M L^2 T^{-3} A^{-1}$

c) $M L^2 T^{-2} A^{-1}$

d) $M L T^{-3} A^{-1}$

e) $M L^2 T^{-3} A^{-1}$

f) $M L^2 T^{-2} A$

64 / 600

Category: Definition and Use in Atomic Physics

64. (A) The electron-volt is a unit of work or energy used in atomic physics.
(R) It represents the kinetic energy gained by an electron when it is accelerated through a potential difference of 1 volt.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

65 / 600

Category: Torque on Dipole in Electric Field

65. What is the torque acting on an electric dipole of moment $p$ placed in a uniform electric field $E$ at an angle $\theta$ with the field?

a) $pE$

b) $pE \cos\theta$

c) $pE \sin\theta$

d) $pE \tan\theta$

66 / 600

Category: Applications in Point Charges and Dipoles

66. What is the electric potential at a point on the equatorial line of an electric dipole?

a) $\frac{1}{4 \pi \varepsilon_0} \frac{p}{r^2}$

b) $\frac{1}{4 \pi \varepsilon_0} \frac{q}{r}$

c) Zero

d) $\frac{1}{4 \pi \varepsilon_0} \frac{2p}{r^2}$

67 / 600

Category: Potential Due to Point Charges:

67. Two charges, $+2 \times 10^{-6}$ C and $-3 \times 10^{-6}$ C, are placed 1 m apart. Find the potential at a point midway between them.

a) -18 kV

b) 18 kV

c) -36 kV

d) 36 kV

68 / 600

Category: Work Done in Rotating an Electric Dipole in an Electric Field

68. What is the torque acting on an electric dipole of moment $p$ placed at an angle $\theta = 180^\circ$ in a uniform electric field $E$?

a) $pE$

b) $-pE$

c) Zero

d) $2pE$

69 / 600

Category: Relation between Electric Field and Electric Potential

69. The electric field intensity $E$ is related to the potential gradient as:

a) $E = \frac{dV}{dr}$

b) $E = -V$

c) $E = -\frac{dV}{dr}$

d) $E = V \cdot dr$

70 / 600

Category: Work Done by External Agent

70. Three charges $+q$, $-q$, and $+q$ are placed at the vertices of an equilateral triangle of side length $a$. What is the work done by an external agent to bring another charge $-2q$ from infinity to the centroid of the triangle?

a) $\frac{\sqrt{3}kq^2}{a}$

b) $\frac{2\sqrt{3}kq^2}{a}$

c) $\frac{3\sqrt{3}kq^2}{a}$

d) Zero

71 / 600

Category: Energy Stored in Electric Field

71. A region has an electric field of $5 \times 10^3 \, \text{V/m}$. What is the energy density in this field? (Given: $\epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m}$)

a) $1.11 \times 10^{-4} \, \text{J/m}^3$

b) $5.55 \times 10^{-5} \, \text{J/m}^3$

c) $2.22 \times 10^{-4} \, \text{J/m}^3$

d) $8.85 \times 10^{-7} \, \text{J/m}^3$

72 / 600

Category: Work Done in Rotating an Electric Dipole in an Electric Field

72. What is the work done in rotating an electric dipole of moment $p$ by an angle $\theta = 90^\circ$ from its equilibrium position in a uniform electric field $E$?

a) $-pE$

b) Zero

c) $pE$

d) $2pE$

73 / 600

Category: Physical Interpretation

73. (A) The work done in moving a charge along an equipotential surface is zero.
(R) The electric field lines are always perpendicular to the equipotential surfaces.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

74 / 600

Category: Definition and Calculation

74. What is the definition of electric potential gradient?

a) Rate of change of electric current with distance

b) Rate of change of charge with time

c) Rate of change of electric potential with distance

d) Rate of change of electric field with time

75 / 600

Category: Electric Potential due to a Group of Point Charges

75. Four charges $+q, +q, -q$ and $-q$ are placed at the four corners of a square of side $2a$. How much work is required to bring a fifth charge $+Q$ from infinity to the center of the square?

a) $\frac{4kqQ}{a\sqrt{2}}$

b) $-\frac{4kqQ}{a\sqrt{2}}$

c) Zero

d) $\frac{2kqQ}{a}$

76 / 600

Category: Relation between Electric Field and Potential Gradient

76. (A) The electric field points in the direction of decreasing potential.
(R) The electric field $\vec{E}$ is equal to the negative gradient of the potential, i.e., $\vec{E} = -\nabla V$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

77 / 600

Category: Electric Potential due to a Group of Point Charges

77. Three point charges $+2q$, $-3q$, and $+4q$ are placed at distances 1 m, 2 m, and 3 m respectively from a point P. What is the net electric potential at P?

a) $\frac{1}{4\pi \varepsilon_0} \frac{7q}{6}$

b) $\frac{1}{4\pi \varepsilon_0} \frac{11q}{6}$

c) $\frac{1}{4\pi \varepsilon_0} \frac{9q}{6}$

d) $\frac{1}{4\pi \varepsilon_0} \frac{13q}{6}$

78 / 600

Category: Potential Difference

78. In a region where the electric potential varies as $V(x) = 3x^2 + 4x - 1$ (where $V$ is in volts and $x$ is in meters), determine the direction and magnitude of the force acting on a proton placed at $x = 2 \, m$.

a) $2.56 \times 10^{-18} \, N$ in $+x$ direction

b) $2.56 \times 10^{-18} \, N$ in $-x$ direction

c) $1.28 \times 10^{-18} \, N$ in $+x$ direction

d) $1.28 \times 10^{-18} \, N$ in $-x$ direction

79 / 600

Category: Work Done in Bringing Charges Together

79. A charge $q_1 = 5 \times 10^{-9} \, \text{C}$ is fixed at the origin. Another charge $q_2 = 3 \times 10^{-9} \, \text{C}$ is moved from a distance of $6 \, \text{cm}$ to $5 \, \text{cm}$ towards $q_1$. Calculate the work done during this process.

a) $2.25 \times 10^{-7} \, \text{J}$

b) $4.49 \times 10^{-7} \, \text{J}$

c) $6.74 \times 10^{-7} \, \text{J}$

d) $8.99 \times 10^{-7} \, \text{J}$

80 / 600

Category: Formulae for Point Charge and Negative Charge

80. (A) The potential at a point due to two equal and opposite charges $+q$ and $-q$ separated by a distance $d$ on the equatorial line is zero for all points.
(R) The potential is a scalar quantity and the algebraic sum of contributions from $+q$ and $-q$ cancels out at every point on the equatorial line.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

81 / 600

Category: Relation between Electric Field and Potential Gradient

81. What is the relation between electric field intensity $E$ and potential gradient $\frac{dV}{dr}$?

a) $E = \frac{dV}{dr}$

b) $E = -dV \cdot dr$

c) $E = -\frac{dV}{dr}$

d) $E = V \cdot dr$

82 / 600

Category: Equipotential Surfaces:

82. What is the angle between the electric field and an equipotential surface?

a) $0^\circ$

b) $45^\circ$

c) $90^\circ$

d) $180^\circ$

83 / 600

Category: Calculation of Potential at Points along the Axis and Equatorial Line

83. A point P is located at a distance $r$ from the center of a dipole, where $r \gg l$. If the angle between the position vector of P and the dipole axis is $\theta$, what is the potential at P?

a) $\frac{1}{4\pi\epsilon_0} \frac{p \sin \theta}{r^2}$

b) $\frac{1}{4\pi\epsilon_0} \frac{p \cos \theta}{r^2}$

c) $\frac{1}{4\pi\epsilon_0} \frac{p \tan \theta}{r^2}$

d) $\frac{1}{4\pi\epsilon_0} \frac{p}{r^2}$

84 / 600

Category: Energy Stored in Electric Field

84. If the electric field inside a parallel-plate capacitor is doubled, how does the stored energy change?

a) Decreases by half

b) Doubles

c) Quadruples

d) Remains the same

85 / 600

Category: Electric Potential Energy of an Electric Dipole in an Electrostatic Field

85. (A) The potential energy of an electric dipole in an electric field is minimum when the dipole moment $\vec{p}$ is aligned parallel to the field $\vec{E}$.
(R) The potential energy of an electric dipole in an electric field is given by $U = -\vec{p} \cdot \vec{E}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

86 / 600

Category: Unit and Direction of Potential Gradient

86. In a region of space, the electric potential is given by $V = 3x^2 - 4y + 5z$ volts. What is the magnitude and direction of the electric field at the point (1, 2, 3)?

a) $-6\hat{i} + 4\hat{j} - 5\hat{k},\, \sqrt{77}\, \text{V/m}$

b) $6\hat{i} - 4\hat{j} + 5\hat{k},\, \sqrt{87}\, \text{V/m}$

c) $-6\hat{i} - 4\hat{j} + 5\hat{k},\, \sqrt{67}\, \text{V/m}$

d) $6\hat{i} + 4\hat{j} - 5\hat{k},\, \sqrt{97}\, \text{V/m}$

87 / 600

Category: Physical Interpretation

87. If 1 joule of work is done to move a test charge of 1 coulomb from infinity to a point in the electric field, what is the electric potential at that point?

a) 2 volts

b) 0.5 volts

c) 1 volt

d) 10 volts

88 / 600

Category: Work Done by External Agent

88. (A) The work done by an external agent to move a charge $+q$ from infinity to a point in an electric field is always positive.
(R) The potential at infinity is taken as zero, and the work done equals the change in potential energy of the system.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

89 / 600

Category: Work Done in Rotating Dipole:

89. (A) The work done in rotating an electric dipole from $\theta = 0^\circ$ to $\theta = 180^\circ$ in a uniform electric field is equal to the change in its potential energy.
(R) The potential energy of an electric dipole in a uniform electric field is given by $U = -pE \cos \theta$ and the work done is $W = pE (1 - \cos \theta)$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

90 / 600

Category: Definition and Formula

90. The electric potential at a point $(x, y, z)$ is given by $V = 5xy - 3z^2$. What is the direction of the electric field at the point $(1, 2, 1)$?

a) Along $-10\hat{i} + 5\hat{j} - 6\hat{k}$

b) Along $-10\hat{i} - 5\hat{j} + 6\hat{k}$

c) Along $10\hat{i} + 5\hat{j} - 6\hat{k}$

d) Along $10\hat{i} - 5\hat{j} + 6\hat{k}$

91 / 600

Category: Electron-Volt:

91. Which of the following correctly defines 1 electron-volt?

a) Energy of one proton moving through 1 volt potential difference

b) Energy of one electron moving through 1 volt potential difference

c) Energy of one coulomb charge moving through 1 volt potential difference

d) Energy of one neutron moving through 1 volt potential difference

92 / 600

Category: Electric Potential:

92. A charge of 5 C is moved from point A to point B in an electric field, and the work done is 25 J. What is the potential difference between points A and B?

a) 0.2 V

b) 1 V

c) 5 V

d) 125 V

93 / 600

Category: Electric Potential

93. Which of the following is true about equipotential surfaces?

a) The electric field is parallel to the surface.

b) The potential varies linearly across the surface.

c) No work is needed to move a charge along the surface.

d) The surface must be spherical in shape.

94 / 600

Category: Work Done in Rotating Dipole:

94. (A) The work done in rotating an electric dipole from $\theta = 0^\circ$ to $\theta = 90^\circ$ in a uniform electric field is $pE$.
(R) The torque acting on the dipole at any angle $\theta$ is given by $\tau = pE \sin \theta$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

95 / 600

Category: Superposition of Potentials

95. For a continuous charge distribution with volume charge density $\rho$, how is the potential at a point calculated?

a) $\frac{1}{4\pi\epsilon_0} \int_V \frac{\rho}{r} \, dr$

b) $\frac{1}{4\pi\epsilon_0} \int_V \frac{\rho \, dV}{r}$

c) $\frac{1}{4\pi\epsilon_0} \int_V \rho \, dV$

d) $\frac{1}{4\pi\epsilon_0} \int_V r \rho \, dV$

96 / 600

Category: Electric Potential Due to an Electric Dipole

96. An electric dipole with moment $\vec{p} = p\hat{i}$ is placed at the origin. At a point $(r, \theta) = (5m, 60^\circ)$, the electric potential is proportional to:

a) $\frac{1}{r^2}$

b) $\frac{\cos\theta}{r^2}$

c) $\frac{\sin\theta}{r^2}$

d) $\frac{\tan\theta}{r^2}$

97 / 600

Category: Electron-Volt:

97. What is the value of 1 electron-volt in joules?

a) $1.6 \times 10^{-16}$ joules

b) $1.6 \times 10^{-17}$ joules

c) $1.6 \times 10^{-18}$ joules

d) $1.6 \times 10^{-19}$ joules

98 / 600

Category: Definition and Calculation

98. What is the correct expression for the electric field $E$ in terms of potential gradient?

a) $E = \frac{dV}{dr}$

b) $E = -\frac{d^2 V}{dr^2}$

c) $E = \frac{d^2 V}{dr^2}$

d) $E = -\frac{dV}{dr}$

99 / 600

Category: Work Done in Rotating Dipole:

99. A dipole of moment $6 \times 10^{-28} \, \text{C-m}$ experiences maximum torque when placed in an electric field at certain orientation. How much work is required to rotate it through $45^\circ$ from this position if the field strength is $5 \times 10^4 \, \text{V/m}$?

a) $1.06 \times 10^{-23} \text{J}$

b) $1.5 \times 10^{-23} \text{J}$

c) $2.12 \times 10^{-23} \text{J}$

d) $3.0 \times 10^{-23} \text{J}$

100 / 600

Category: Electric Potential due to a Group of Point Charges

100. Four charges $+q$, $+2q$, $-3q$, and $+4q$ are placed at the corners of a square with side length $a$. Calculate the work done to bring a test charge $Q$ from infinity to the center of the square.

a) $\frac{4kqQ \sqrt{2}}{a}$

b) $\frac{2kqQ}{a}$

c) $\frac{kqQ \sqrt{2}}{a}$

d) Zero

101 / 600

Category: Electric Potential:

101. (A) The electric potential at a distance $r$ from a point charge $q$ is given by $V = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r}$.
(R) The work done in bringing a unit positive test charge from infinity to a point in the electric field depends on the path taken.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

102 / 600

Category: Electric Potential

102. (A) The surface of a conductor in electrostatic equilibrium is always an equipotential surface.

(R) Inside a conductor, the electric field is zero in electrostatic equilibrium.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

103 / 600

Category: Conversion to Joules

103. A point charge of $+2 \mu C$ is placed in air. What is the work done in bringing a test charge of $+1 nC$ from infinity to a point 2 m away?

a) $9 \times 10^{-9}$ J

b) $4.5 \times 10^{-6}$ J

c) $9 \times 10^{-6}$ J

d) $18 \times 10^{-6}$ J

104 / 600

Category: Conversion to Joules

104. An electron is accelerated through a potential difference of 2 V. What is its kinetic energy in joules?

a) $1.6 \times 10^{-19}$ J

b) $3.2 \times 10^{-19}$ J

c) $4.8 \times 10^{-19}$ J

d) $6.4 \times 10^{-19}$ J

105 / 600

Category: Perpendicularity of Electric Field to Equipotential Surfaces

105. (A) The electric field $\vec{E}$ is always perpendicular to an equipotential surface because no work is done in moving a charge along such a surface.
(R) If the electric field were not perpendicular to the equipotential surface, there would be a component of $\vec{E}$ parallel to the surface, causing work to be done when moving a charge along the surface.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

106 / 600

Category: Energy Stored in Electric Field

106. An electric dipole of moment $p = 6 \times 10^{-30} \, \text{C-m}$ is initially aligned parallel to a uniform electric field $E = 500 \, \text{V/m}$. How much work is required to rotate the dipole through $180^\circ$?

a) $3 \times 10^{-27} \, \text{J}$

b) $6 \times 10^{-27} \, \text{J}$

c) $1.5 \times 10^{-27} \, \text{J}$

d) $12 \times 10^{-27} \, \text{J}$

107 / 600

Category: Spacing between Surfaces in Strong and Weak Fields

107. Two equipotential surfaces in a uniform electric field are separated by a distance $d$. If the electric field strength is doubled while keeping the potential difference between the surfaces the same, how does the separation between the surfaces change?

a) It becomes four times smaller

b) It becomes half

c) It doubles

d) It remains the same

108 / 600

Category: Formulae for Point Charge and Negative Charge

108. Three point charges $q_1 = +2 \mu C$, $q_2 = -3 \mu C$, and $q_3 = +1 \mu C$ are placed at distances $r_1 = 2 m$, $r_2 = 4 m$, and $r_3 = 6 m$ respectively from a point P. Calculate the net electric potential at point P. Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, Nm^2/C^2$.

a) $1.25 \times 10^3 V$

b) $3.75 \times 10^3 V$

c) $-2.5 \times 10^3 V$

d) $5.0 \times 10^3 V$

109 / 600

Category: Relation between Electric Field and Electric Potential

109. Which of the following statements about equipotential surfaces is FALSE?

a) They are always spherical in shape.

b) No work is done in moving a charge along them.

c) The electric field is perpendicular to them.

d) They cannot intersect each other.

110 / 600

Category: Electric Potential Due to an Electric Dipole

110. A point P is located at a distance $r$ from an electric dipole at an angle $\theta = 60^\circ$. The potential at point P is proportional to:

a) $\frac{1}{r}$

b) $\frac{1}{r^2}$

c) $r$

d) $r^2$

111 / 600

Category: No Work Done on Equipotential Surfaces

111. An electric dipole with moment $\vec{p}$ is rotated from an angle $\theta_1 = 0^\circ$ to $\theta_2 = 90^\circ$ in a uniform electric field $\vec{E}$. What is the work done by the external agent during this rotation?

a) Zero

b) $pE$

c) $2pE$

d) $-pE$

112 / 600

Category: SI Unit and Dimensions

112. A dipole with moment $p = 5 \times 10^{-30} \text{ C m}$ is placed in an external electric field $E = 200 \text{ V/m}$ at an angle of $60^\circ$. What is its potential energy?

a) $-5 \times 10^{-28} \text{ J}$

b) $-2.5 \times 10^{-28} \text{ J}$

c) $-1 \times 10^{-27} \text{ J}$

d) $-7.5 \times 10^{-28} \text{ J}$

113 / 600

Category: Equipotential Surfaces

113. In a region of space, the equipotential surfaces are found to be parallel planes separated by unequal distances. What can be inferred about the electric field in this region?

a) The electric field is uniform in both magnitude and direction.

b) The electric field has a constant direction but varying magnitude.

c) The electric field is zero everywhere.

d) The electric field changes direction but has a constant magnitude.

114 / 600

Category: Definition and Calculation

114. What is the relation between electric field intensity ($E$) and potential gradient ($\frac{dV}{dr}$)?

a) $E = \frac{dV}{dr}$

b) $E = - \frac{dV}{dr}$

c) $E = \frac{1}{\frac{dV}{dr}}$

d) $E = \frac{dr}{dV}$

115 / 600

Category: Definition and Use in Atomic Physics

115. A point charge of $+2 \times 10^{-9}$ C is placed in vacuum. What is the electric potential at a distance of 0.5 m from the charge?

a) 9 V

b) 18 V

c) 36 V

d) 72 V

116 / 600

Category: Stable and Unstable Equilibrium

116. How much work is required to rotate an electric dipole from its unstable equilibrium position to a position where it is perpendicular to the electric field?

a) $0$

b) $-pE$

c) $+pE$

d) $2pE$

117 / 600

Category: Calculation of Electric Potential

117. Three charges $q_1 = 1 \mu$C, $q_2 = -2 \mu$C, and $q_3 = 3 \mu$C are placed at the vertices of an equilateral triangle with side length $a = 1$ m. Calculate the total electric potential energy of the system. Assume $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9$ Nm$^2$/C$^2$.

a) -0.045 J

b) -0.090 J

c) 0.045 J

d) 0.090 J

118 / 600

Category: Perpendicularity of Electric Field to Equipotential Surfaces

118. Two equipotential surfaces with potentials $V_1 = 10 \, V$ and $V_2 = 20 \, V$ are separated by a distance of $1 \, m$. What is the magnitude of the electric field between them, and what is its direction relative to the surfaces?

a) 10 V/m, parallel to the surfaces

b) 10 V/m, at 45° to the surfaces

c) 10 V/m, perpendicular to the surfaces

d) 20 V/m, perpendicular to the surfaces

119 / 600

Category: Potential Calculation for Multiple Charges

119. Three point charges $q_1 = 2 \mu C$, $q_2 = -3 \mu C$, and $q_3 = 5 \mu C$ are placed at the vertices of an equilateral triangle of side 4 m. Calculate the electric potential at the centroid of the triangle.

a) 12.345 kV

b) 15.588 kV

c) 10.234 kV

d) 8.765 kV

120 / 600

Category: Definition and Use in Atomic Physics

120. What is the value of 1 electron-volt (eV) in joules?

a) $3.2 \times 10^{-19}$ J

b) $1.6 \times 10^{-19}$ J

c) $6.4 \times 10^{-19}$ J

d) $9.1 \times 10^{-31}$ J

121 / 600

Category: Electric Potential:

121. If the potential difference between two equipotential surfaces separated by 0.1 m is 50 V, what is the magnitude of the electric field between them?

a) 0.5 V/m

b) 50 V/m

c) 500 V/m

d) 5000 V/m

122 / 600

Category: Relation between Electric Field and Electric Potential

122. A point charge produces an electric potential $V$ at a distance $r$. If the distance is doubled, how does the electric field $E$ change?

a) It becomes half

b) It becomes four times

c) It becomes one-fourth

d) It remains unchanged

123 / 600

Category: Relation between Electric Field and Electric Potential

123. Two parallel plates separated by 5 mm have a potential difference of 100 V between them. If the potential decreases uniformly from the positive to the negative plate, what is the electric field strength between the plates?

a) 10,000 V/m

b) 15,000 V/m

c) 20,000 V/m

d) 25,000 V/m

124 / 600

Category: Electric Potential due to a Group of Point Charges

124. A uniformly charged ring of radius $R$ has total charge $Q$. What is the electric potential at a point on its axis at a distance $x$ from its center?

a) $\frac{kQ}{R^2 + x^2}$

b) $\frac{kQ}{\sqrt{R^2 - x^2}}$

c) $\frac{kQ}{\sqrt{R^2 + x^2}}$

d) $\frac{kQ}{x^2}$

125 / 600

Category: Applications in Point Charges and Dipoles

125. What is the electric potential at a point on the axial line of an electric dipole at distance $r$ from its center?

a) $\frac{1}{4 \pi \varepsilon_0} \frac{q}{r}$

b) $\frac{1}{4 \pi \varepsilon_0} \frac{p}{r^2}$

c) Zero

d) $\frac{1}{4 \pi \varepsilon_0} \frac{p}{r^3}$

126 / 600

Category: Torque on Dipole in Electric Field

126. (A) The work done in rotating an electric dipole from $0^\circ$ to $180^\circ$ in a uniform electric field is $2pE$.
(R) The potential energy of the dipole is given by $U = -pE \cos \theta$, and the work done equals the change in potential energy.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

127 / 600

Category: Calculation of Potential Energy

127. Three charges $-1 \, \text{mC}$, $+2 \, \text{mC}$, and $-3 \, \text{mC}$ are placed along a straight line at distances of $1 \, \text{m}$ from each other. Calculate the total potential energy of the system.

a) $\frac{17}{4 \pi \varepsilon_0} \, \text{J}$

b) $-\frac{15}{8 \pi \varepsilon_0} \, \text{J}$

c) $\frac{5}{4 \pi \varepsilon_0} \, \text{J}$

d) $-\frac{17}{8 \pi \varepsilon_0} \, \text{J}$

128 / 600

Category: Calculation of Potential at Points along the Axis and Equatorial Line

128. What is the potential at a point on the axis of an electric dipole with dipole moment $p$ at a distance $r$ from its center, where $r >> l$?

a) $\frac{1}{4\pi\epsilon_0} \frac{p}{r}$

b) $\frac{1}{4\pi\epsilon_0} \frac{p}{r^2}$

c) $\frac{1}{4\pi\epsilon_0} \frac{p}{r^3}$

d) 0

129 / 600

Category: Electric Potential due to a Group of Point Charges

129. A thin ring of radius $R$ carries a uniformly distributed charge $Q$. What is the electric potential at a point on the axis of the ring at distance $x$ from its center?

a) $\frac{kQ}{R + x}$

b) $\frac{kQ}{\sqrt{R^2 + x^2}}$

c) $\frac{kQ}{R^2 + x^2}$

d) $\frac{kQx}{R^2}$

130 / 600

Category: Relation between Electric Field and Potential Gradient

130. (A) The electric field at a point is always directed from higher potential to lower potential.
(R) The electric field intensity is equal to the negative of the potential gradient.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

131 / 600

Category: Electric Potential due to a Point Charge

131. What is the electric potential at a distance $r$ from a point charge $+q$ in a medium of dielectric constant $K$?

a) $\frac{1}{4 \pi \epsilon_0} \frac{q}{r}$

b) $\frac{1}{4 \pi \epsilon_0 K} \frac{q}{r^2}$

c) $\frac{1}{4 \pi \epsilon_0 K} \frac{q}{r}$

d) $\frac{1}{4 \pi \epsilon_0 K} \frac{q^2}{r}$

132 / 600

Category: Derivation of the Relation

132. The potential difference between two points A and B with potentials \$V\$ and \$V - dV\$ respectively is:

a) \$dV\$

b) \$-dV\$

c) \$2V - dV\$

d) \$V + dV\$

133 / 600

Category: Electric Potential:

133. A point charge $q = 5 \, \mu C$ is placed at the origin. What is the electric potential at a distance of 2 meters from the charge? Assume $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \, \text{N m}^2 \, \text{C}^{-2}$.

a) 11.25 kV

b) 22.5 kV

c) 45 kV

d) 5.625 kV

134 / 600

Category: Electric Potential Energy of an Electric Dipole in an Electrostatic Field

134. An electric dipole of moment $p = 3 \times 10^{-9}\, \text{C}\cdot\text{m}$ is aligned parallel to an electric field of strength $200\, \text{N/C}$. How much work must be done to rotate it through $60^\circ$ against the field?

a) $6 \times 10^{-7}\, \text{J}$

b) $3 \times 10^{-7}\, \text{J}$

c) $0$

d) $-3 \times 10^{-7}\, \text{J}$

135 / 600

Category: No Work Done on Equipotential Surfaces

135. Why are electric field lines always perpendicular to equipotential surfaces?

a) Because equipotential surfaces repel electric field lines

b) To ensure the electric field is uniform

c) So that no work is done when a charge moves along the surface

d) Because electric field lines cannot intersect each other

136 / 600

Category: General Formula for Potential at any Point

136. (A) The electric potential at a point due to a uniformly charged spherical shell is the same as if all the charge were concentrated at its center.
(R) For points outside the shell, the behavior of the potential follows the inverse distance law, but for points inside the shell, the potential remains constant.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

137 / 600

Category: Electric Potential due to a Group of Point Charges

137. (A) The electric potential at a point due to multiple point charges is the algebraic sum of potentials due to each individual charge.
(R) Electric potential is a scalar quantity.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

138 / 600

Category: Stable and Unstable Equilibrium

138. For an electric dipole in an external electric field, at what angle $\theta$ is the potential energy zero?

a) $0^\circ$

b) $45^\circ$

c) $90^\circ$

d) $180^\circ$

139 / 600

Category: Definition and Calculation

139. The electric potential in a region is given by $V(x,y,z) = 3x^2 - 4xy + yz^2$. What is the magnitude of the potential gradient at point P(1,2,3)?

a) $\sqrt{153}$

b) $\sqrt{163}$

c) $\sqrt{173}$

d) $\sqrt{183}$

140 / 600

Category: Work Done in Rotating an Electric Dipole in an Electric Field

140. When an electric dipole of moment $p$ is rotated from $\theta = 45^\circ$ to $\theta = 135^\circ$ in an electric field $E$, the work done is found to be $W = p E \sqrt{2}$. What is the value of $\sin 45^\circ$ and $\sin 135^\circ$ used in the calculation?

a) $\sin 45^\circ = \frac{1}{\sqrt{2}}, \sin 135^\circ = \frac{1}{\sqrt{2}}$

b) $\sin 45^\circ = \frac{1}{2}, \sin 135^\circ = \frac{1}{2}$

c) $\sin 45^\circ = 1, \sin 135^\circ = 1$

d) $\sin 45^\circ = \frac{\sqrt{3}}{2}, \sin 135^\circ = \frac{\sqrt{3}}{2}$

141 / 600

Category: Definition and Formula

141. The electric field in a region is given by $E = 100x\,\text{V/m}$. The potential difference between points $x = 1\,\text{m}$ and $x = 2\,\text{m}$ is:

a) $50\,\text{V}$

b) $-50\,\text{V}$

c) $150\,\text{V}$

d) $-150\,\text{V}$

142 / 600

Category: Definition and Use in Atomic Physics

142. An electron is accelerated through a potential difference of 500 V. What is the kinetic energy gained by the electron in electron-volts and joules?

a) 250 eV, $4 \times 10^{-17}$ J

b) 500 eV, $8 \times 10^{-17}$ J

c) 1000 eV, $1.6 \times 10^{-16}$ J

d) 500 eV, $1.6 \times 10^{-19}$ J

143 / 600

Category: Electron-Volt (eV)

143. (A) 1 electron-volt is equal to $1.6 \times 10^{-19}$ joule.
(R) The work done in moving an electron through a potential difference of 1 volt is $1.6 \times 10^{-19}$ joule.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

144 / 600

Category: Superposition of Potentials

144. Four point charges $+Q, +2Q, -3Q,$ and $-4Q$ are placed at the corners of a square of side $a$. What is the electric potential at the center of the square?

a) $-\frac{2\sqrt{2}kQ}{a}$

b) $-\frac{4\sqrt{2}kQ}{a}$

c) $\frac{2\sqrt{2}kQ}{a}$

d) Zero

145 / 600

Category: Superposition of Potentials

145. An electric dipole consists of two charges $+q$ and $-q$ separated by a distance $2a$. What is the electric potential at a point on the equatorial line at a distance $r$ from the midpoint of the dipole?

a) $\frac{2kq}{r^2}$

b) $\frac{kqa}{r^3}$

c) Zero

d) $\frac{kq}{r}$

146 / 600

Category: Formulae for Point Charge and Negative Charge

146. Three point charges $q_1 = +1 \, \mu C$, $q_2 = -2 \, \mu C$, and $q_3 = +3 \, \mu C$ are placed at distances 1 m, 2 m, and 3 m respectively from a point P. Calculate the resultant potential at P.

a) $6000 \, V$

b) $9000 \, V$

c) $12000 \, V$

d) $15000 \, V$

147 / 600

Category: Electric Dipole:

147. For an electric dipole with dipole moment $p = 6 \times 10^{-30}$ C-m, what is the electric potential at a point 3 m away from its center along the axial line? Assume $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9$ Nm$^2$/C$^2$.

a) $6 \times 10^{-20}$ V

b) $6 \times 10^{-21}$ V

c) $9 \times 10^{-21}$ V

d) $9 \times 10^{-20}$ V

148 / 600

Category: Work Done during Rotation

148. For a dipole moment $1.6 \times 10^{-19}$ C-m in a field of $10^6$ N/C, what is true when maximum torque is acting?

a) Work done is zero

b) Potential energy equals the work done

c) Potential energy is zero

d) Both torque and work done are maximum

149 / 600

Category: Formulae for Point Charge and Negative Charge

149. What is the potential at a distance of 1 m from a point charge of $+1 \, \mu C$ in vacuum?

a) 90 V

b) 900 V

c) 9000 V

d) 90000 V

150 / 600

Category: Calculation of Potential Energy

150. Three point charges, $q_1 = 1 \, \text{C}$, $q_2 = -2 \, \text{C}$, and $q_3 = 1 \, \text{C}$, are placed at the corners of an equilateral triangle of side length $2 \, \text{m}$. What is the total potential energy of the system?

a) $\frac{2.5}{4 \pi \varepsilon_0} \, \text{J}$

b) $-\frac{1.5}{4 \pi \varepsilon_0} \, \text{J}$

c) $\frac{1.5}{4 \pi \varepsilon_0} \, \text{J}$

d) $-\frac{2.5}{4 \pi \varepsilon_0} \, \text{J}$

151 / 600

Category: Work Done in Bringing Charges Together

151. Three point charges, each of magnitude $q$, are placed at the vertices of an equilateral triangle of side length $a$. What is the total work done to assemble this configuration?

a) $\frac{q^2}{4 \pi \epsilon_0 a}$

b) $\frac{2q^2}{4 \pi \epsilon_0 a}$

c) $\frac{3q^2}{4 \pi \epsilon_0 a}$

d) $\frac{4q^2}{4 \pi \epsilon_0 a}$

152 / 600

Category: Electron-Volt (eV)

152. How many electron-volts (eV) are equal to 3.2 × 10⁻¹⁹ joules?

a) 1 eV

b) 2 eV

c) 4 eV

d) 5 eV

153 / 600

Category: Electron-Volt (eV)

153. Convert 3.2 eV into joules.

a) $4.8 \times 10^{-19} \text{ J}$

b) $5.12 \times 10^{-19} \text{ J}$

c) $6.4 \times 10^{-19} \text{ J}$

d) $7.2 \times 10^{-19} \text{ J}$

154 / 600

Category: Calculation of Electric Potential

154. The electric potential energy of a system of two point charges, each of $+1 \, \mu\text{C}$, separated by 1 m in air is:

a) 4.5 mJ

b) 9 mJ

c) 18 mJ

d) 36 mJ

155 / 600

Category: Definition and Calculation

155. What is the SI unit of electric potential gradient?

a) Newton per coulomb

b) Volt per metre

c) Joule per second

d) Ampere per metre

156 / 600

Category: Work Done by External Agent

156. An electric dipole with moment $p = 3 \times 10^{-30} C \cdot m$ is placed in an electric field of strength $E = 10^5 N/C$ such that it is parallel to the field. What is the potential energy of the dipole?

a) $3 \times 10^{-25} J$

b) $-3 \times 10^{-25} J$

c) $1.5 \times 10^{-25} J$

d) $-1.5 \times 10^{-25} J$

157 / 600

Category: Electric Potential Due to an Electric Dipole

157. (A) The electric potential at any point on the equatorial line of an electric dipole is zero.
(R) The distances from each charge of the dipole to the point on the equatorial line are equal, resulting in equal and opposite potentials that cancel out.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

158 / 600

Category: Definition and Formula

158. What is the relation between electric field $E$ and potential gradient $\frac{dV}{dr}$?

a) $E = \frac{dV}{dr}$

b) $E = -dV \cdot dr$

c) $E = -\frac{dV}{dr}$

d) $E = V \cdot dr$

159 / 600

Category: Conversion to Joules

159. An electron is accelerated through a potential difference of 500 V. What is the kinetic energy gained by the electron in joules?

a) $1.6 \times 10^{-19}$ J

b) $3.2 \times 10^{-16}$ J

c) $8 \times 10^{-17}$ J

d) $5 \times 10^{-15}$ J

160 / 600

Category: Work Done by External Agent

160. A dipole with moment $p = 4 \times 10^{-9}$ Cm is placed in a uniform electric field $E = 5 \times 10^4$ N/C. The dipole is initially perpendicular to the field and then rotated to align parallel to it. What is the work done by an external agent in this process?

a) $1 \times 10^{-4}$ J

b) $2 \times 10^{-4}$ J

c) $4 \times 10^{-4}$ J

d) $8 \times 10^{-4}$ J

161 / 600

Category: Work Done in Rotating an Electric Dipole in an Electric Field

161. An electric dipole of moment $p = 5 \times 10^{-30}$ C-m is rotated from $\theta = 30^\circ$ to $\theta = 120^\circ$ in a uniform electric field of strength $E = 10^6$ V/m. The work done in this process is:

a) $4.33 \times 10^{-24}$ J

b) $6.83 \times 10^{-24}$ J

c) $8.66 \times 10^{-24}$ J

d) $1.00 \times 10^{-23}$ J

162 / 600

Category: General Formula for Potential at any Point

162. Three point charges $q_1 = +2 \, \mu C$, $q_2 = -3 \, \mu C$, and $q_3 = +4 \, \mu C$ are placed at distances 1 m, 2 m, and 3 m respectively from a point $P$. Calculate the net potential at $P$. ($\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, Nm^2/C^2$)

a) $10.5 \, kV$

b) $16.5 \, kV$

c) $20.5 \, kV$

d) $25.5 \, kV$

163 / 600

Category: General Formula for Potential at any Point

163. A circular ring of radius $R$ carries a uniform linear charge density $\lambda$. What is the electric potential at the center of the ring?

a) $\frac{\lambda}{4 \pi \varepsilon_0 R}$

b) $\frac{\lambda}{2 \varepsilon_0}$

c) $\frac{\lambda R}{2 \varepsilon_0}$

d) $\frac{\lambda}{4 \varepsilon_0}$

164 / 600

Category: Equipotential Surfaces:

164. In a region with a non-uniform electric field, two equipotential surfaces $V_1$ and $V_2$ ($V_2 > V_1$) are separated by distances $d_1$ and $d_2$ in regions where the electric field is $E_1$ and $E_2$, respectively. If $d_1 < d_2$, which relationship between $E_1$ and $E_2$ must hold?

a) $E_1 = E_2$

b) $E_1 < E_2$

c) $E_1 > E_2$

d) Cannot be determined without knowing exact potentials.

165 / 600

Category: Calculation of Electric Potential

165. A charge $q_0 = 2$ C is moved from point $A$ to point $B$ in an electric field, and the work done is $W = 10$ J. What is the potential difference between points $A$ and $B$?

a) 5 V

b) 10 V

c) 20 V

d) 2.5 V

166 / 600

Category: Calculation of Potential Energy

166. Three identical charges of $5 \, \mu\text{C}$ each are placed at the corners of an equilateral triangle with side length $2 \, \text{m}$. What is the potential energy of this system?

a) $\frac{7.5 \times 10^{-11}}{4 \pi \varepsilon_0} \, \text{J}$

b) $\frac{7.5 \times 10^{-11}}{8 \pi \varepsilon_0} \, \text{J}$

c) $\frac{15 \times 10^{-12}}{4 \pi \varepsilon_0} \, \text{J}$

d) $\frac{25 \times 10^{-12}}{8 \pi \varepsilon_0} \, \text{J}$

167 / 600

Category: Unit and Direction of Potential Gradient

167. In which direction does the potential gradient point relative to the electric field \$
vec{E}\$?

a) Same direction as \$ vec{E}\$

b) Perpendicular to \$ vec{E}\$

c) Opposite direction to \$ vec{E}\$

d) At a 45-degree angle to \$ vec{E}\$

168 / 600

Category: Potential Difference

168. (A) The potential difference between two points in an electric field is a scalar quantity.
(R) Potential difference is defined as the work done per unit charge, and work is a scalar quantity.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

169 / 600

Category: Potential Gradient

169. If the potential at a point is given by $V = 50x^2$ (where $x$ is in metres), what is the potential gradient along the $x$-axis at $x = 2$ m?

a) 50 V/m

b) 100 V/m

c) 200 V/m

d) 400 V/m

170 / 600

Category: Electric Potential

170. What are the dimensions of electric potential?

a) $[M L T^{-3} A^{-1}]$

b) $[M L^2 T^{-2} A]$

c) $[M L^2 T^{-3} A^{-1}]$

d) $[M L^{-1} T^{-2} A]$

171 / 600

Category: Relation between Electric Field and Electric Potential

171. For two parallel plates with potentials $V_1$ and $V_2$ separated by distance $d$, the electric field $E$ between them is given by:

a) $E = \frac{V_1 + V_2}{d}$

b) $E = \frac{d}{V_1 - V_2}$

c) $E = \frac{V_1 - V_2}{d}$

d) $E = \frac{V_2 - V_1}{d}$

172 / 600

Category: Perpendicularity of Electric Field to Equipotential Surfaces

172. Two equipotential surfaces cannot intersect because:

a) The electric field would cancel out at the intersection.

b) The potential would become infinite at the intersection.

c) It would violate the definition of a single-valued potential function.

d) The surfaces would merge into one.

173 / 600

Category: Definition and Calculation

173. Which of the following is the unit of potential gradient?

a) $\text{Vm}$

b) $\text{Vm}^{-2}$

c) $\text{JC}^{-1}$

d) $\text{Vm}^{-1}$

174 / 600

Category: Work Done during Rotation

174. (A) The work done in rotating an electric dipole from equilibrium to $180^\circ$ in a uniform electric field is equal to the change in potential energy of the dipole.
(R) The potential energy of a dipole at angle $\theta$ with the field is given by $U = -pE \cos \theta$, and the work done equals the difference in potential energy between initial and final positions.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

175 / 600

Category: Work Done in Rotating Dipole:

175. An electric dipole of moment $p$ is rotated from $\theta_1 = 30^\circ$ to $\theta_2 = 60^\circ$ in a uniform electric field $E$. What is the work done during this rotation?

a) $pE \left(1 - \frac{\sqrt{3}}{2}\right)$

b) $pE \left(\frac{\sqrt{3} - 1}{2}\right)$

c) $pE \left(\frac{1}{2}\right)$

d) $pE \left(1 + \frac{\sqrt{3}}{2}\right)$

176 / 600

Category: Definition and Formula

176. What is the definition of potential gradient in an electric field?

a) Rate of change of electric charge with distance

b) Rate of change of electric current with time

c) Rate of change of electric potential with distance

d) Rate of change of magnetic field with time

177 / 600

Category: Potential Difference:

177. A free negative charge is placed in an electric field where the potential decreases along the positive x-direction. In which direction will the charge naturally move?

a) Positive x-direction

b) Negative x-direction

c) Perpendicular to the x-direction

d) Will remain stationary

178 / 600

Category: Spacing between Surfaces in Strong and Weak Fields

178. (A) In a region where the equipotential surfaces are closer together, the electric field is stronger.
(R) The spacing between equipotential surfaces is inversely proportional to the electric field strength as given by $dr \propto \frac{1}{E}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

179 / 600

Category: Electric Potential due to a Point Charge

179. (A) The electric potential at the midpoint between two equal and opposite point charges $+q$ and $-q$ separated by a distance $2r$ is zero.
(R) The electric potential due to a point charge follows the principle of superposition.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

180 / 600

Category: Definition and Formula

180. The electric field is related to the potential gradient as:

a) $E = \frac{dV}{dr}$

b) $E = -dV/dr$

c) $E = \nabla V$

d) $E = -\nabla V$

181 / 600

Category: Energy Stored in Electric Field

181. (A) The potential energy of an electric dipole aligned parallel to a uniform electric field is minimum.
(R) The potential energy of an electric dipole in a uniform electric field is given by $U = -pE \cos \theta$ and is minimum when $\theta = 0^\circ$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

182 / 600

Category: Stable and Unstable Equilibrium

182. (A) A dipole placed in a uniform electric field is in stable equilibrium when its potential energy is minimum.
(R) The work done to rotate the dipole from stable equilibrium position ($\theta = 0^\circ$) to unstable equilibrium position ($\theta = 180^\circ$) is equal to the change in potential energy of the dipole.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

183 / 600

Category: Relation to Electric Field

183. The electric potential at a point due to a point charge $q$ is given by $V = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r}$. What is the magnitude of the electric field at a distance $r$ from the charge?

a) $\frac{1}{4 \pi \varepsilon_0} \frac{q}{r}$

b) $\frac{1}{4 \pi \varepsilon_0} \frac{q}{r^3}$

c) $\frac{1}{4 \pi \varepsilon_0} \frac{q}{r^2}$

d) $\frac{1}{4 \pi \varepsilon_0} q r$

184 / 600

Category: Derivation of the Relation

184. A positive test charge $q_0$ is moved from point A to point B in a non-uniform electric field. The electric potential at A is $V$ and at B is $V + \Delta V$, where $\Delta V > 0$. If the displacement vector between A and B is $\Delta r$ (aligned with the field), what is the correct expression for the work done by an external agent against the electric force?

a) $-q_0 E \Delta r$

b) $q_0 E \Delta r$

c) $-q_0 \Delta V$

d) $q_0 \Delta V$

185 / 600

Category: Continuous Charge Distribution (Area and Volume Integrals)

185. A circular disk of radius $R$ carries a surface charge density $\sigma = \sigma_0 \left(1 - \frac{r}{R}\right)$, where $\sigma_0$ is a constant and $r$ is the radial distance from the centre of the disk. Find the electric potential at a point located on the axis of the disk at a distance $z$ from its centre.

a) $\frac{\sigma_0}{2 \varepsilon_0} \left[ \sqrt{R^2 + z^2} - z - \frac{R}{2} \ln\left(\frac{\sqrt{R^2 + z^2} + R}{z}\right) \right]$

b) $\frac{\sigma_0}{2 \varepsilon_0} \left[ \sqrt{R^2 + z^2} - \frac{R}{2} \right]$

c) $\frac{\sigma_0}{4 \varepsilon_0} \left[ \sqrt{R^2 + z^2} - z \right]$

d) $\frac{\sigma_0 R}{2 \varepsilon_0} \sqrt{1 + \left(\frac{z}{R}\right)^2}$

186 / 600

Category: Conditions for Potential Difference

186. An external agent does 10 J of work to move a test charge of +2 C from point A to point B in an electric field. What is the potential difference between points B and A?

a) 2.5 V

b) 5 V

c) 10 V

d) 20 V

187 / 600

Category: Work Done in Rotating Dipole:

187. A dipole of moment $p$ is placed in a uniform electric field $E$ such that it aligns perpendicular to the field ($\theta = 90^\circ$). What is its potential energy?

a) $-pE$

b) $pE$

c) $0$

d) $2pE$

188 / 600

Category: Perpendicularity of Electric Field to Equipotential Surfaces

188. What is true about equipotential surfaces?

a) The electric potential varies linearly along the surface.

b) Work is done when moving a charge between two points on the surface.

c) The electric field has a component parallel to the surface.

d) The electric potential is constant at every point on the surface.

189 / 600

Category: Definition and Formula

189. Two charges $+q_1$ and $-q_2$ are placed at a distance $r$ apart. The work done in moving $-q_2$ to a new position where the distance between the charges becomes $2r$ is:

a) $\frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{2r}$

b) $-\frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{2r}$

c) $\frac{3}{8\pi\epsilon_0} \frac{q_1 q_2}{r}$

d) $-\frac{3}{8\pi\epsilon_0} \frac{q_1 q_2}{r}$

190 / 600

Category: Stable and Unstable Equilibrium

190. What is the potential energy of an electric dipole when it is in stable equilibrium in an electric field $E$?

a) $+pE$

b) $-pE$

c) $\frac{pE}{2}$

d) Zero

191 / 600

Category: Definition and Formula

191. (A) The potential gradient in an electric field is always directed opposite to the electric field intensity vector.
(R) The electric field intensity at a point is equal to the negative potential gradient in that direction.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

192 / 600

Category: Superposition of Potentials

192. Four point charges $+q$, $-q$, $+2q$, and $-2q$ are placed at the corners of a square of side length $a$. What is the net electric potential at the center of the square?

a) $\frac{4q}{4\pi \epsilon_0 a}$

b) $\frac{2q}{4\pi \epsilon_0 a \sqrt{2}}$

c) $0$

d) $\frac{q}{4\pi \epsilon_0 a \sqrt{2}}$

193 / 600

Category: Physical Interpretation

193. If the electric potential at a certain point decreases uniformly at the rate of $10 \, V/m$ along a straight line, what is the magnitude of the electric field in that direction?

a) $0 \, V/m$

b) $5 \, V/m$

c) $10 \, V/m$

d) $20 \, V/m$

194 / 600

Category: No Work Done on Equipotential Surfaces

194. A charge $q$ is moved along a circular path around a fixed point charge $Q$. If the radius of the circular path is $r$, what is the work done by the electric field during this motion?

a) $qQ / r$

b) $2\pi r \cdot qE$

c) Zero

d) $qV_B - qV_A$

195 / 600

Category: Potential Difference

195. A charge $q = -2 \times 10^{-6} \, C$ is moved from point A to point B in a uniform electric field of magnitude $E = 500 \, V/m$. The displacement vector $\vec{d}$ from A to B makes an angle of $60^\circ$ with the electric field. If the work done by the external agent is $5 \times 10^{-4} \, J$, what is the distance between points A and B?

a) 0.5 m

b) 1 m

c) 2 m

d) 4 m

196 / 600

Category: Perpendicularity of Electric Field to Equipotential Surfaces

196. (A) The electric field is always perpendicular to equipotential surfaces.
(R) There is no potential gradient parallel to the surface, so the electric field component along the surface must be zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

197 / 600

Category: Work Done in Rotating an Electric Dipole in an Electric Field

197. (A) The work done in rotating an electric dipole from $\theta = 0^\circ$ to $\theta = 180^\circ$ in a uniform electric field $E$ is equal to the change in potential energy of the dipole.

(R) The potential energy of an electric dipole in a uniform electric field is given by $U = -\vec{p} \cdot \vec{E}$, and the work done is the integral of torque over angular displacement.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

198 / 600

Category: Work Done during Rotation

198. A dipole of moment $p$ is aligned at an angle $\theta = 90^\circ$ with a uniform electric field $E$. What is its potential energy at this position?

a) $-p E$

b) $0$

c) $p E$

d) $2 p E$

199 / 600

Category: SI Unit and Dimensions

199. (A) The SI unit of electric field can be expressed in both \text{N C$^{-1}$} and \text{V m$^{-1}$}.
(R) The electric field is related to the potential difference by the relation $E = -\frac{dV}{dr}$, where $E$ is the electric field, $V$ is the potential, and $r$ is the distance.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

200 / 600

Category: Potential Calculation for Multiple Charges

200. (A) The electric potential at the center of a square due to four equal point charges placed at its corners is zero if the charges have alternating signs.
(R) The electric potential is a scalar quantity and adds algebraically.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

201 / 600

Category: Definition and Use in Atomic Physics

201. If the potential difference between two parallel plates is 10 V and the separation between them is 2 m, what is the magnitude of the electric field between the plates?

a) 2.5 V/m

b) 5 V/m

c) 20 V/m

d) 10 V/m

202 / 600

Category: Definition and Formula

202. What is the relation between electric field intensity $E$ and potential gradient $\frac{dV}{dr}$?

a) $E = \frac{dV}{dr}$

b) $E = -\frac{dV}{dr}$

c) $E = \frac{dr}{dV}$

d) $E = -\frac{dr}{dV}$

203 / 600

Category: Electric Potential Due to an Electric Dipole

203. (A) The electric potential at any point on the equatorial line of an electric dipole is zero.
(R) The distances from the two charges of the dipole to any point on the equatorial line are equal and the potentials due to them cancel each other.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

204 / 600

Category: SI Unit and Dimensions

204. The electric potential at a distance of 2 m from a point charge is 10 V. What will be the potential at a distance of 4 m from the same charge?

a) 2.5 V

b) 5 V

c) 10 V

d) 20 V

205 / 600

Category: Properties of Equipotential Surfaces

205. What happens to the work done when a charge is moved between any two points on an equipotential surface?

a) Work done is positive

b) Work done is negative

c) No work is done

d) Work done depends on the path taken

206 / 600

Category: Potential Gradient

206. The electric field intensity $\vec{E}$ is related to the potential gradient as:

a) $\vec{E} = \nabla V$

b) $\vec{E} = -\nabla V$

c) $\vec{E} = \frac{dV}{dr}$

d) $\vec{E} = \frac{\partial V}{\partial x} \hat{i}$

207 / 600

Category: Derivation of the Relation

207. In a region of space, the electric potential varies as $V(x) = 10x^2 - 5x + 2$ (where $V$ is in volts and $x$ is in meters). What is the magnitude and direction of the electric field at $x = 1\,\text{m}$?

a) $15\,\text{V/m}$, along $+x$ direction

b) $-15\,\text{V/m}$, along $-x$ direction

c) $25\,\text{V/m}$, along $+x$ direction

d) $-25\,\text{V/m}$, along $-x$ direction

208 / 600

Category: Equipotential Surfaces:

208. Which of the following statements about equipotential surfaces is FALSE?

a) Work done in moving a charge on an equipotential surface is zero.

b) Electric field lines are always perpendicular to equipotential surfaces.

c) The potential gradient is non-zero along the surface.

d) Closer spacing of equipotential surfaces indicates a stronger electric field.

209 / 600

Category: Work Done in Rotating Dipole:

209. An electric dipole with moment $p = 5 \times 10^{-29} \, \text{C-m}$ is placed in a uniform electric field $E = 10^6 \, \text{V/m}$. What work must be done to rotate it from an angle of $60^\circ$ to $120^\circ$ relative to the field direction?

a) $2.5 \times 10^{-23} \text{J}$

b) $5 \times 10^{-23} \text{J}$

c) $7.5 \times 10^{-23} \text{J}$

d) $10 \times 10^{-23} \text{J}$

210 / 600

Category: General Formula for Potential at any Point

210. A square sheet (side 4m) lies in xy-plane with charge density $\sigma = x+y \, C/m^2$. A line charge $\lambda = 2y \, C/m$ runs along z-axis from z=0 to z=4m. Find potential at point (2,2,2)m if all other potentials are zero at infinity.

a) $2.84 \times 10^{10} V$

b) $2.56 \times 10^{10} V$

c) $2.72 \times 10^{10} V$

d) $2.91 \times 10^{10} V$

211 / 600

Category: Calculation of Potential Energy

211. What is the electric potential energy of two point charges, $q_1 = 2 \, \text{C}$ and $q_2 = -3 \, \text{C}$, placed $1 \, \text{m}$ apart?

a) $\frac{6}{4 \pi \varepsilon_0} \, \text{J}$

b) $-\frac{6}{4 \pi \varepsilon_0} \, \text{J}$

c) $\frac{12}{4 \pi \varepsilon_0} \, \text{J}$

d) $-\frac{12}{4 \pi \varepsilon_0} \, \text{J}$

212 / 600

Category: Potential Difference:

212. In an electric field, a free positive charge moves from:

a) Higher potential to lower potential

b) Lower potential to higher potential

c) Along equipotential lines

d) Remains stationary

213 / 600

Category: Electric Potential Due to an Electric Dipole

213. For an electric dipole of moment $p$, what can be said about the electric potential at any point on the equatorial line?

a) It depends on the value of $p$

b) It is maximum near the dipole

c) It decreases with increasing distance

d) It is always zero

214 / 600

Category: Conditions for Potential Difference

214. A free positive charge moves naturally in an electric field from:

a) Lower potential to higher potential

b) Higher potential to lower potential

c) Remains stationary

d) Cannot be determined

215 / 600

Category: No Work Done on Equipotential Surfaces

215. An electron completes one full revolution around a stationary proton in a circular orbit. What is the work done by the electric field during this motion?

a) Positive, because the electron moves against the electric field.

b) Negative, because the electron loses energy due to radiation.

c) Zero, because the potential is the same at the start and end points.

d) Non-zero, because the electron changes direction continuously.

216 / 600

Category: Work Done in Rotating an Electric Dipole in an Electric Field

216. An electric dipole is rotated by $270^\circ$ from its stable equilibrium position in a uniform electric field. If the work done during the first $180^\circ$ rotation is $W$, what is the total work done in the complete $270^\circ$ rotation?

a) $\frac{W}{2}$

b) $W$

c) $\frac{3W}{2}$

d) $2W$

217 / 600

Category: Superposition of Potentials

217. If two point charges $+q$ and $-q$ are placed at distances $r_1$ and $r_2$ from a point $P$, what is the net potential at $P$?

a) $\frac{q}{4\pi\epsilon_0} \left( \frac{1}{r_1} + \frac{1}{r_2} \right)$

b) $\frac{q}{4\pi\epsilon_0} \left( \frac{1}{r_1} - \frac{1}{r_2} \right)$

c) $\frac{q}{4\pi\epsilon_0} \left( \frac{1}{r_1} \cdot \frac{1}{r_2} \right)$

d) $\frac{q}{4\pi\epsilon_0} \left( \frac{1}{r_1} / \frac{1}{r_2} \right)$

218 / 600

Category: Electric Potential Due to an Electric Dipole

218. What is the approximate electric potential at a point P located far away on the axis of an electric dipole with dipole moment $p$ and distance $r$ from its center?

a) $\frac{1}{4 \pi \epsilon_0} \frac{p}{r}$

b) $\frac{1}{4 \pi \epsilon_0} \frac{p}{r^2}$

c) $\frac{1}{4 \pi \epsilon_0} \frac{p}{r^3}$

d) 0

219 / 600

Category: Calculation of Electric Potential

219. Two point charges $q_1 = 2 \mu C$ and $q_2 = -3 \mu C$ are placed 1 m apart in vacuum. What is the electric potential energy of this system?

a) -0.054 J

b) 0.054 J

c) -0.027 J

d) 0.027 J

220 / 600

Category: Electric Potential

220. If the work done to move a charge of 2 C from point A to point B is 10 J, what is the potential difference between points A and B?

a) 20 V

b) 5 V

c) 0.2 V

d) 10 V

221 / 600

Category: No Work Done on Equipotential Surfaces

221. Two equipotential surfaces are separated by a small distance $\Delta r$ in a region where the electric field is uniform and has magnitude $E$. What is the potential difference $\Delta V$ between these two surfaces?

a) $E \Delta r$

b) $-E \Delta r$

c) $E / \Delta r$

d) $-\Delta r / E$

222 / 600

Category: Work Done by External Agent

222. A point charge $Q = 10$ µC is fixed at the origin. A test charge $q = 2$ µC is moved from point A $(2 \text{m}, 0)$ to point B $(4 \text{m}, 0)$. If the work done by an external agent is $-45$ mJ, what is the potential difference $(V_B - V_A)$?

a) $-22.5$ kV

b) $-11.25$ kV

c) $+22.5$ kV

d) $+11.25$ kV

223 / 600

Category: General Formula for Potential at any Point

223. (A) The potential at a point due to a group of point charges is the algebraic sum of potentials due to each individual charge.
(R) Potential is a scalar quantity and follows the principle of superposition.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

224 / 600

Category: General Formula for Potential at any Point

224. (A) The potential at a point due to a continuous charge distribution can be calculated using $V = \frac{1}{4 \pi \epsilon_0} \int \frac{dq}{r}$.
(R) For continuous charge distributions, the principle of superposition is applied by integrating over infinitesimal charge elements.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

225 / 600

Category: Formulae for Point Charge and Negative Charge

225. (A) The potential at a point due to a group of point charges is always positive if all the charges are positive.
(R) Potential is a scalar quantity and adds up algebraically for multiple charges.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

226 / 600

Category: Superposition of Potentials

226. A solid sphere of radius $R$ has a uniform volume charge density $\rho$. What is the electric potential at a point inside the sphere at a distance $r$ from the center ($r < R$)?

a) $\frac{\rho}{3 \epsilon_0} (R^2 - r^2)$

b) $\frac{\rho}{2 \epsilon_0} (R - r)$

c) $\frac{\rho}{6 \epsilon_0} (3R^2 - r^2)$

d) $\frac{\rho}{4 \epsilon_0} (2R^2 - r^2)$

227 / 600

Category: Potential Due to Point Charges:

227. If the potential at a point is 200 V, how much work is done to bring a charge of $0.5 \mu C$ from infinity to this point?

a) 0.1 mJ

b) 0.5 mJ

c) 1 mJ

d) 2 mJ

228 / 600

Category: Electron-Volt (eV)

228. A proton is moved through a potential difference of 10 volts. What is the work done in eV?

a) 1 eV

b) 5 eV

c) 10 eV

d) 20 eV

229 / 600

Category: Definition and Formula

229. A point charge $q$ creates an electric potential $V = \frac{1}{4\pi\epsilon_0}\frac{q}{r}$ at a distance $r$. At what distance from the charge does the magnitude of the electric field equal $100 \, \text{V/m}$, if $q = 1 \, \mu\text{C}$?

a) $3 \, \text{m}$

b) $9.49 \, \text{m}$

c) $30 \, \text{m}$

d) $90 \, \text{m}$

230 / 600

Category: Electron-Volt:

230. If an electron is accelerated through a potential difference of 5 volts, what is its final kinetic energy in joules?

a) $4 \times 10^{-19} \, \text{J}$

b) $8 \times 10^{-19} \, \text{J}$

c) $1.6 \times 10^{-19} \, \text{J}$

d) $5 \times 10^{-19} \, \text{J}$

231 / 600

Category: Electric Potential

231. The electric potential at a point is defined as the work done in moving a unit positive charge from infinity to that point. What is the SI unit of electric potential?

a) Newton

b) Joule

c) Volt

d) Coulomb

232 / 600

Category: Work Done in Bringing Charges Together

232. Three charges, each of magnitude $q$, are placed at the corners of an equilateral triangle of side length $a$. What is the total work done to assemble this configuration?

a) $\frac{1}{4 \pi \epsilon_0} \frac{q^2}{a}$

b) $\frac{3}{4 \pi \epsilon_0} \frac{q^2}{a}$

c) $\frac{1}{4 \pi \epsilon_0} \frac{3q^2}{a^2}$

d) Zero

233 / 600

Category: Electric Dipole:

233. Where does the electric potential due to an electric dipole become zero?

a) At any point on the axial line

b) At any point on the equatorial line

c) Only at infinity

d) At the dipole's midpoint

234 / 600

Category: Work Done by External Agent

234. A charge of $+3 \times 10^{-9} \, \text{C}$ is moved from a point A at potential $50 \, \text{V}$ to point B at potential $120 \, \text{V}$. What is the work done by the external agent?

a) $210 \times 10^{-6} \, \text{J}$

b) $210 \times 10^{-9} \, \text{J}$

c) $70 \times 10^{-9} \, \text{J}$

d) $70 \times 10^{-6} \, \text{J}$

235 / 600

Category: SI Unit and Dimensions

235. An equipotential surface has a potential of $100 \text{ V}$. If the electric field at a point on this surface is $500 \text{ V/m}$, what is the shortest distance to another equipotential surface with potential $150 \text{ V}$?

a) $5 \text{ cm}$

b) $10 \text{ cm}$

c) $20 \text{ cm}$

d) $25 \text{ cm}$

236 / 600

Category: Electron-Volt (eV)

236. An electron is accelerated through a potential difference of 5 volts. What is its kinetic energy in electron-volts (eV)?

a) 1 eV

b) 2 eV

c) 5 eV

d) 10 eV

237 / 600

Category: Electric Potential

237. An external agent moves a charge $+q_0$ from point A (potential $V_A$) to point B (potential $V_B$). If $V_A > V_B$, what is the work done by the electric field on the charge?

a) $q_0 (V_A - V_B)$

b) $-q_0 (V_A - V_B)$

c) $q_0 (V_B - V_A)$

d) $-q_0 (V_B - V_A)$

238 / 600

Category: Electric Potential due to a Point Charge

238. A test charge $+2 \mu C$ is moved from infinity to a point 3 meters away from a point charge of $+6 \mu C$ in a medium with $K = 3$. What is the work done in this process? (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, Nm^2/C^2$)

a) 1 mJ

b) 2 mJ

c) 4 mJ

d) 8 mJ

239 / 600

Category: Potential Difference

239. In an electric field, a free negative charge moves from:

a) Higher potential to lower potential

b) Lower potential to higher potential

c) Along equipotential lines

d) Remains stationary

240 / 600

Category: Equipotential Surfaces:

240. (A) The electric field is always perpendicular to equipotential surfaces at every point.
(R) The work done in moving a charge along an equipotential surface is zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

241 / 600

Category: Formulae for Point Charge and Negative Charge

241. Four charges $q_1 = +1 \mu C$, $q_2 = -2 \mu C$, $q_3 = +3 \mu C$, and $q_4 = -4 \mu C$ are placed at the corners of a square of side 1 m. Calculate the potential at the center of the square. Assume $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, Nm^2/C^2$.

a) $-12.73 \times 10^3 V$

b) $-25.47 \times 10^3 V$

c) $0 V$

d) $50.92 \times 10^3 V$

242 / 600

Category: Continuous Charge Distribution (Area and Volume Integrals)

242. (A) The potential due to a uniformly charged spherical shell at any point inside it is zero because the electric field inside a uniformly charged spherical shell is zero.
(R) The potential at a point inside a uniformly charged spherical shell is obtained by integrating the contributions from all infinitesimal charge elements on the shell, and the net result is zero due to symmetry.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

243 / 600

Category: Unit and Direction of Potential Gradient

243. Which of the following expressions represents the potential gradient if the potential $V$ varies along all three axes ($x$, $y$, $z$)?

a) $\frac{dV}{dx}$

b) $\frac{\partial V}{\partial x} \hat{i}$

c) $\frac{\partial V}{\partial x} + \frac{\partial V}{\partial y} + \frac{\partial V}{\partial z}$

d) $\frac{\partial V}{\partial x} \hat{i} + \frac{\partial V}{\partial y} \hat{j} + \frac{\partial V}{\partial z} \hat{k}$

244 / 600

Category: Equipotential Surfaces

244. Which of the following statements is true regarding the relationship between the electric field and equipotential surfaces?

a) The electric field is tangential to the equipotential surface

b) The electric field is always perpendicular to the equipotential surface

c) The electric field is stronger where equipotential surfaces are farther apart

d) The electric field can intersect equipotential surfaces at any angle

245 / 600

Category: Conditions for Potential Difference

245. (A) A free positive charge always moves from a region of higher potential to a region of lower potential.
(R) The work done by the electric field on a positive charge is negative when it moves from higher to lower potential.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

246 / 600

Category: Electric Potential Energy of an Electric Dipole in an Electrostatic Field

246. An electric dipole with dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$. If the dipole is rotated from an angle $\theta_1 = 0^\circ$ to $\theta_2 = 90^\circ$, what is the work done by the electric field?

a) $pE$

b) $-pE$

c) $0$

d) $2pE$

247 / 600

Category: Electric Potential Energy of an Electric Dipole in an Electrostatic Field

247. (A) The potential energy of an electric dipole is minimum when it is aligned parallel to the uniform electric field.
(R) When a dipole is parallel to the field, no work is done in bringing it from infinity into the field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

248 / 600

Category: Electric Dipole:

248. (A) The electric potential at any point on the equatorial line of an electric dipole is zero.
(R) No work is done in moving a charge along the equatorial line of an electric dipole.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

249 / 600

Category: Calculation of Electric Potential

249. An electric dipole with dipole moment $p = 4 \times 10^{-8}$ C-m is placed at the origin. What is the electric potential at a point on its axis at a distance of 2 m, if the dipole length is negligible compared to this distance?

a) 45 V

b) 90 V

c) 180 V

d) 360 V

250 / 600

Category: Work Done in Rotating an Electric Dipole in an Electric Field

250. An electric dipole of moment $p = 5 \times 10^{-29} \, \text{C-m}$ is rotated from $\theta_1 = 30^\circ$ to $\theta_2 = 150^\circ$ in a uniform electric field $E = 2 \times 10^5 \, \text{V-m}^{-1}$. Calculate the work done.

a) $1.5 \times 10^{-23} \, \text{J}$

b) $1.732 \times 10^{-23} \, \text{J}$

c) $2 \times 10^{-23} \, \text{J}$

d) $2.5 \times 10^{-23} \, \text{J}$

251 / 600

Category: Calculation of Potential at Points along the Axis and Equatorial Line

251. A point P lies on the axis of an electric dipole with dipole moment $p$. If the distance of P from the center of the dipole is $r$ and $r \gg l$, what is the potential at P due to the dipole?

a) Zero

b) $\frac{1}{4\pi\epsilon_0} \frac{p}{r}$

c) $\frac{1}{4\pi\epsilon_0} \frac{p}{r^2}$

d) $\frac{1}{4\pi\epsilon_0} \frac{p}{r^3}$

252 / 600

Category: Work Done in Bringing Charges Together

252. If two charges $+q$ and $-q$ are separated by a distance $a$, what is the work required to double the separation between them?

a) $-\frac{1}{4 \pi \epsilon_0} \frac{q^2}{a}$

b) $-\frac{1}{4 \pi \epsilon_0} \frac{q^2}{2a}$

c) $\frac{1}{4 \pi \epsilon_0} \frac{q^2}{2a}$

d) Zero

253 / 600

Category: General Formula for Potential at any Point

253. The potential at a point due to a system of point charges is calculated by:

a) Multiplying the magnitudes of all charges and dividing by the sum of their distances.

b) Summing the potentials due to each charge with their respective signs and distances.

c) Taking the average of the potentials due to all charges.

d) Considering only the nearest charge and ignoring others.

254 / 600

Category: Relation to Electric Field

254. For two parallel metallic plates with potentials $V_1$ and $V_2$ separated by distance $d$, what is the electric field $E$ between them?

a) $E = \frac{V_1 + V_2}{d}$

b) $E = V_1 - V_2$

c) $E = \frac{V_1 - V_2}{d}$

d) $E = \frac{d}{V_1 - V_2}$

255 / 600

Category: Potential Calculation for Multiple Charges

255. Three point charges $Q_1 = +3 \, \mu C$, $Q_2 = -5 \, \mu C$, and $Q_3 = +7 \, \mu C$ are placed at the vertices of an equilateral triangle with side length $6 \, m$. Calculate the electric potential at the centroid of the triangle.

a) $12 \, \text{kV}$

b) $13 \, \text{kV}$

c) $15 \, \text{kV}$

d) $18 \, \text{kV}$

256 / 600

Category: Relation to Electric Field

256. Which of the following represents the correct unit of electric field intensity in terms of base SI units?

a) kg$\cdot$m/s$^2$

b) kg$\cdot$m$^2$/s$^3$

c) kg$\cdot$m/(s$^3$$\cdot$A)

d) kg$\cdot$s$^3$/A

257 / 600

Category: Continuous Charge Distribution (Area and Volume Integrals)

257. Which equation correctly represents the potential due to a volume charge distribution with density $\rho$?

a) $V = \frac{1}{4 \pi \varepsilon_0} \int \rho \, dr$

b) $V = \frac{1}{4 \pi \varepsilon_0} \int_V \frac{\rho dV}{r}$

c) $V = \rho \int dV$

d) $V = \frac{1}{2 \pi \varepsilon_0} \int \frac{\rho dV}{r}$

258 / 600

Category: Potential Calculation for Multiple Charges

258. Four charges $+q$, $-q$, $+2q$, and $-2q$ are placed at the four corners of a square with side length $L$. What is the electric potential at the center of the square?

a) $\frac{2kq}{L}$

b) $\frac{4kq}{L}$

c) $0$

d) $\frac{kq}{L}$

259 / 600

Category: Energy Stored in Electric Field

259. Three point charges $q_1 = 2 \times 10^{-9} \, \text{C}$, $q_2 = -3 \times 10^{-9} \, \text{C}$, and $q_3 = 4 \times 10^{-9} \, \text{C}$ are placed at the vertices of an equilateral triangle of side $0.1 \, \text{m}$. Calculate the total electrostatic potential energy of the system.

a) $-1 \times 10^{-8} \, \text{J}$

b) $-2 \times 10^{-8} \, \text{J}$

c) $1 \times 10^{-8} \, \text{J}$

d) $-0.5 \times 10^{-8} \, \text{J}$

260 / 600

Category: Electric Dipole:

260. An electric dipole of moment $5 \times 10^{-30}$ C-m is placed in a uniform electric field of $2 \times 10^5$ V/m at an angle of $60^\circ$. What is its potential energy?

a) $-5 \times 10^{-25}$ J

b) $-1 \times 10^{-24}$ J

c) $5 \times 10^{-25}$ J

d) $1 \times 10^{-24}$ J

261 / 600

Category: Equipotential Surfaces

261. How much work is done in moving a charge along an equipotential surface?

a) Depends on the magnitude of the charge

b) Negative work is done

c) Zero work is done

d) Positive work is done

262 / 600

Category: Calculation of Potential Energy

262. Three point charges $-2 \, \mu \text{C}$, $+3 \, \mu \text{C}$ and $-4 \, \mu \text{C}$ are placed at the vertices of an equilateral triangle of side length $0.1 \, \text{m}$. Calculate the total electric potential energy of the system.

a) -0.899 J

b) -1.245 J

c) -0.542 J

d) -1.103 J

263 / 600

Category: Equipotential Surfaces:

263. (A) Equipotential surfaces for a point charge are concentric spheres.
(R) The electric potential due to a point charge depends only on the distance from the charge.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

264 / 600

Category: Electric Potential due to a Group of Point Charges

264. (A) The electric potential at a point due to a group of point charges is the algebraic sum of potentials due to each charge individually.
(R) Electric potential is a scalar quantity and follows the principle of superposition.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

265 / 600

Category: Physical Interpretation

265. A test charge $+q_0$ is moved from infinity to a point $P$ in an electric field where the potential is $V$. The work done by an external agent to move the charge is found to be $W$. If the potential at another point $Q$ is $2V$, how much work would be required to move the same test charge from $P$ to $Q$? Assume no other forces act on the charge.

a) $V q_0$

b) $2V q_0$

c) $-V q_0$

d) $0$

266 / 600

Category: Electric Potential due to a Group of Point Charges

266. A charged ring of radius R has a linear charge density $\lambda$. What is the electric potential at its center?

a) $\frac{\lambda}{\pi \varepsilon_0}$

b) $\frac{\lambda}{2 \varepsilon_0}$

c) $\frac{2\lambda}{\varepsilon_0}$

d) $\frac{\lambda}{4 \varepsilon_0}$

267 / 600

Category: SI Unit and Dimensions

267. What is the SI unit of electric potential?

a) Joule

b) Coulomb

c) Volt

d) Newton

268 / 600

Category: Potential Calculation for Multiple Charges

268. Three charges $q_1 = 5 \, \mu C$, $q_2 = -3 \, \mu C$, and $q_3 = 8 \, \mu C$ are placed at the vertices of an equilateral triangle of side $4 \, m$. Calculate the total electrostatic potential energy of the system.

a) $-2.25 \, \text{mJ}$

b) $2.25 \, \text{mJ}$

c) $-1.50 \, \text{mJ}$

d) $1.50 \, \text{mJ}$

269 / 600

Category: Spacing between Surfaces in Strong and Weak Fields

269. Which of the following statements is true regarding the work done when moving a charge along an equipotential surface?

a) The work done is always positive.

b) The work done depends on the path taken.

c) No work is done in moving the charge.

d) The work done is equal to the charge multiplied by the distance moved.

270 / 600

Category: Electric Potential Energy of a System of Charges

270. Two point charges $q_1 = 5 \, \mu C$ and $q_2 = -10 \, \mu C$ are placed 4 m apart in vacuum. Calculate the electric potential energy of the system.

a) $-112.5 \, \text{J}$

b) $225 \, \text{J}$

c) $-225 \, \text{J}$

d) $112.5 \, \text{J}$

271 / 600

Category: Definition and Formula

271. For two metallic plates with potentials $V_1$ and $V_2$ separated by a distance $d$, the electric field between them is given by:

a) $E = \frac{V_1 + V_2}{d}$

b) $E = V_1 - V_2$

c) $E = \frac{V_1 - V_2}{d}$

d) $E = \frac{d}{V_1 - V_2}$

272 / 600

Category: Work Done during Rotation

272. What is the potential energy of an electric dipole aligned parallel to a uniform electric field $E$?

a) $-2pE$

b) $-pE$

c) $0$

d) $pE$

273 / 600

Category: Definition and Formula

273. A point charge $q$ is placed at the origin. The potential gradient at a distance $r$ from the charge along the x-axis is given by:

a) $\frac{1}{4\pi\epsilon_0} \frac{q}{r}$

b) $-\frac{1}{4\pi\epsilon_0} \frac{q}{r^2}$

c) $\frac{1}{4\pi\epsilon_0} \frac{q}{r^2}$

d) $-\frac{1}{4\pi\epsilon_0} \frac{q}{r}$

274 / 600

Category: Potential Calculation for Multiple Charges

274. (A) The electric potential at the center of a square with four identical charges $q$ placed at its corners is zero if all charges are positive.
(R) The net electric potential due to multiple point charges is the algebraic sum of potentials due to individual charges.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

275 / 600

Category: Relation between Electric Field and Electric Potential

275. A point charge $q = 2 \, \mu\text{C}$ is placed at the origin. What is the potential at a distance $r = 5 \, \text{m}$ from it? (Given: $\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \text{N m}^2/\text{C}^2$)

a) $1800 \, \text{V}$

b) $3600 \, \text{V}$

c) $7200 \, \text{V}$

d) $9000 \, \text{V}$

276 / 600

Category: Electron-Volt:

276. What is the work done in moving an electron across a potential difference of 12 volts, expressed in electron-volts?

a) $6 \, \text{eV}$

b) $8 \, \text{eV}$

c) $10 \, \text{eV}$

d) $12 \, \text{eV}$

277 / 600

Category: Properties of Equipotential Surfaces

277. (A) No work is done in moving a charge between any two points on an equipotential surface.
(R) The potential difference between any two points on the surface is zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

278 / 600

Category: No Work Done on Equipotential Surfaces

278. Which of the following statements about equipotential surfaces is INCORRECT?

a) Electric field lines are always perpendicular to equipotential surfaces.

b) No work is done when a charge moves along an equipotential surface.

c) The spacing between equipotential surfaces is greater where the electric field is stronger.

d) Two equipotential surfaces cannot intersect each other.

279 / 600

Category: Conditions for Potential Difference

279. A free electron is released in an electric field where the potential decreases uniformly from left to right. In which direction will the electron move initially, and what happens to its potential energy?

a) Left; decreases

b) Right; increases

c) Left; increases

d) Right; decreases

280 / 600

Category: Electron-Volt (eV)

280. An electron is accelerated through a potential difference of 250 volts. What is its kinetic energy in electron-volts (eV)?

a) 125 eV

b) 250 eV

c) 375 eV

d) 500 eV

281 / 600

Category: Electric Potential Due to an Electric Dipole

281. The electric potential at an arbitrary point in space due to an electric dipole depends on:

a) Only distance $r$

b) Only dipole moment $p$

c) Distance $r$ and angle $\theta$

d) Dipole moment $p$, distance $r$, and angle $\theta$

282 / 600

Category: Spacing between Surfaces in Strong and Weak Fields

282. A region of space has two equipotential surfaces with a potential difference of 10 V. If the spacing between these surfaces is 5 mm in a strong electric field region, what would be the approximate spacing between them in a weaker electric field region where the electric field strength is half?

a) 20 mm

b) 10 mm

c) 2.5 mm

d) 5 mm

283 / 600

Category: Superposition of Potentials

283. (A) The electric potential at the center of a uniformly charged ring is zero because all infinitesimal charge elements on the ring are equidistant from the center.
(R) The potential due to a point charge varies inversely with distance, and for a continuous charge distribution, the potential is obtained by integrating contributions from all infinitesimal charges.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

284 / 600

Category: Potential Due to Point Charges:

284. Two charges, $+4 \times 10^{-6}$ C and $-1 \times 10^{-6}$ C, are placed 3 m apart. At what distance from the positive charge will the potential be zero?

a) 1.0 m

b) 1.5 m

c) 2.0 m

d) 2.4 m

285 / 600

Category: Relation between Electric Field and Electric Potential

285. (A) The electric field intensity at a point is equal to the negative potential gradient in that direction.
(R) The potential decreases in the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

286 / 600

Category: Potential Calculation for Multiple Charges

286. (A) The electric potential at a point due to two equal and opposite charges placed symmetrically about the point is zero.

(R) The potential contributions from the two charges cancel each other because they are equal in magnitude but opposite in sign.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

287 / 600

Category: Calculation of Potential at Points along the Axis and Equatorial Line

287. Consider a point P on the equatorial line of an electric dipole. What is the electric potential at P?

a) $\frac{1}{4\pi\epsilon_0} \frac{p}{r^2}$

b) Non-zero but depends on angle

c) Zero

d) $\frac{1}{4\pi\epsilon_0} \frac{p}{r}$

288 / 600

Category: Properties of Equipotential Surfaces

288. If an electric field $\overrightarrow{E}$ is not perpendicular to an equipotential surface at some point, what does it imply?

a) The surface has varying potential

b) The electric field is zero

c) The surface is not an equipotential surface

d) The potential gradient is infinite

289 / 600

Category: Work Done in Rotating an Electric Dipole in an Electric Field

289. A dipole of moment $p = 4 \times 10^{-29} \, \text{C-m}$ is placed in an electric field $E = 3 \times 10^5 \, \text{V-m}^{-1}$. What is the change in potential energy when the dipole is rotated from $\theta = 60^\circ$ to $\theta = 120^\circ$?

a) $-1.2 \times 10^{-23} \, \text{J}$

b) $1.2 \times 10^{-23} \, \text{J}$

c) $-2.4 \times 10^{-23} \, \text{J}$

d) $2.4 \times 10^{-23} \, \text{J}$

290 / 600

Category: Equipotential Surfaces:

290. What is an equipotential surface?

a) A surface with varying electric potential

b) A surface where the electric field is zero everywhere

c) A surface where the electric potential is the same everywhere

d) A surface with uniform charge density

291 / 600

Category: Derivation of the Relation

291. (A) The electric field points in the direction of decreasing potential.
(R) The negative sign in $E = -\frac{dV}{dr}$ indicates that the potential decreases in the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

292 / 600

Category: Stable and Unstable Equilibrium

292. An electric dipole of moment $\overrightarrow{p}$ is placed in a uniform electric field $\overrightarrow{E}$. If the dipole is rotated by $90^\circ$ from its stable equilibrium position, what is the potential energy of the dipole at this new position?

a) $-pE$

b) $0$

c) $+pE$

d) $-2pE$

293 / 600

Category: Continuous Charge Distribution (Area and Volume Integrals)

293. What is the general formula for the electric potential $V$ due to a continuous charge distribution?

a) $V = \frac{1}{4 \pi} \int dq$

b) $V = \frac{1}{4 \pi \varepsilon_0} \int \frac{dq}{r}$

c) $V = \int dq / r$

d) $V = \frac{1}{2 \pi \varepsilon_0} \int \frac{dq}{r}$

294 / 600

Category: Conditions for Potential Difference

294. If the work done by an external agent while moving a charge $q_0$ from point A to point B is negative, what does this imply?

a) The external agent did positive work

b) No work was done

c) The work was done by the electric field

d) The charge was stationary

295 / 600

Category: Electric Potential

295. (A) The electric potential at a point is a scalar quantity.
(R) Electric potential depends only on the position of the point in the electric field and not on the path taken to reach that point.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

296 / 600

Category: No Work Done on Equipotential Surfaces

296. (A) The work done in moving a test charge along an equipotential surface is always zero.
(R) The potential difference between any two points on an equipotential surface is zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

297 / 600

Category: Definition and Formula

297. What is the potential gradient in a uniform electric field of magnitude 100 V/m?

a) 10 V/m

b) -100 V/m

c) 100 V/m

d) 200 V/m

298 / 600

Category: Relation between Electric Field and Potential Gradient

298. Two parallel plates separated by $d = 0.01 \, \text{m}$ have a potential difference of $100 \, \text{V}$. The electric field between the plates is uniform. What is the magnitude of the electric field?

a) 100 \, \text{V/m}

b) 1,000 \, \text{V/m}

c) 10,000 \, \text{V/m}

d) 100,000 \, \text{V/m}

299 / 600

Category: Work Done by External Agent

299. (A) The work done by an external agent to rotate an electric dipole from $\theta = 0^\circ$ to $\theta = 180^\circ$ in a uniform electric field is zero.
(R) The potential energy of an electric dipole at $\theta = 0^\circ$ and $\theta = 180^\circ$ is the same.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

300 / 600

Category: Potential Due to Point Charges:

300. Three point charges $+2 \mu C$, $-3 \mu C$, and $+5 \mu C$ are placed at the vertices of an equilateral triangle with side length 10 cm. Calculate the net electric potential at the centroid of the triangle.

a) $1.8 \times 10^5 \, \text{V}$

b) $3.6 \times 10^5 \, \text{V}$

c) $3.6\sqrt{3} \times 10^5 \, \text{V}$

d) $7.2 \times 10^5 \, \text{V}$

301 / 600

Category: Applications in Point Charges and Dipoles

301. A point charge $q$ is placed at a distance $d$ from the center of an electric dipole along its equatorial line. The dipole has a dipole moment $\vec{p}$. At what distance $x$ from the dipole will the net potential be zero?

a) $x = d$

b) $x = \frac{p}{q}$

c) $x = \sqrt{\frac{p}{q}}$

d) No possible finite distance

302 / 600

Category: Applications in Point Charges and Dipoles

302. (A) The potential energy of an electric dipole placed in a uniform electric field is minimum when the dipole moment is aligned parallel to the electric field.
(R) The potential energy of a dipole in an electric field is given by $U = -pE \cos \theta$, which attains its minimum value when $\theta = 0^\circ$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

303 / 600

Category: Electric Potential Energy of a System of Charges

303. The electric potential energy of two charges $q_1 = 2 \, C$ and $q_2 = -3 \, C$ separated by a distance $r$ is given by $U = -\frac{54}{r}$. Find the force between the charges when they are 3 m apart.

a) $-6 \, \text{N}$

b) $6 \, \text{N}$

c) $-18 \, \text{N}$

d) $18 \, \text{N}$

304 / 600

Category: Work Done during Rotation

304. How much work is required to rotate an electric dipole from equilibrium ($\theta = 0$) to $\theta = 180^\circ$ in a uniform electric field $E$?

a) $pE$

b) $-pE$

c) $2pE$

d) $0$

305 / 600

Category: Electric Potential due to a Point Charge

305. A proton moves from point A at potential +250V to point B at potential -150V in a vacuum. If its mass is $m_p$ and charge $e$, what percentage of its initial kinetic energy at A would be converted to electric potential energy when it reaches B?

a) 160\%

b) 62.5\%

c) The entire initial KE gets converted

d) Not determinable without initial velocity

306 / 600

Category: Potential Difference

306. (A) If a positive charge is moved from a point at higher potential to a point at lower potential in an electric field, the work done by the electric force is negative.
(R) The work done by the electric force depends on the direction of movement relative to the field lines and the change in potential.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

307 / 600

Category: Electron-Volt (eV)

307. (A) The kinetic energy of an electron accelerated through a potential difference of 1 volt is equal to $1.6 \times 10^{-19}$ joule.
(R) The work done in moving an electron through a potential difference of 1 volt is defined as 1 electron-volt, which equals $1.6 \times 10^{-19}$ joule.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

308 / 600

Category: Electric Potential due to a Group of Point Charges

308. Three point charges $+Q$, $-2Q$, and $+3Q$ are placed at distances $1 \, \text{m}$, $2 \, \text{m}$, and $3 \, \text{m}$ from a point $P$, respectively. Calculate the net electric potential at point $P$ due to these charges. ($k = \frac{1}{4 \pi \varepsilon_0}$)

a) $\frac{kQ}{6}$

b) $0$

c) $kQ$

d) $-kQ$

309 / 600

Category: Relation between Electric Field and Potential Gradient

309. (A) The electric field intensity at a point is equal to the negative potential gradient at that point.
(R) The potential decreases in the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

310 / 600

Category: Relation to Electric Field

310. (A) The electric field at a point is directed from higher potential to lower potential.

(R) The relation $E = -\frac{dV}{dr}$ implies that the electric field points in the direction of decreasing potential.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

311 / 600

Category: Properties of Equipotential Surfaces

311. In a region with a non-uniform electric field, how are the equipotential surfaces spaced relative to the field strength?

a) Closer where the field is weaker

b) Equally spaced regardless of field strength

c) Farther apart where the field is stronger

d) Closer where the field is stronger

312 / 600

Category: Derivation of the Relation

312. The electric field intensity at a point is given by $E = -\frac{dV}{dr}$. What does the negative sign in this relation signify?

a) The potential increases in the direction of the field.

b) The potential decreases in the direction perpendicular to the field.

c) The potential decreases in the direction of the field.

d) The potential is constant along the direction of the field.

313 / 600

Category: Electric Dipole:

313. An electric dipole with moment $\vec{p} = 5 \times 10^{-12}$ C$\cdot$m is placed at the origin. What is the electric potential at a point P located at position $\vec{r} = (3\hat{i} + 4\hat{j})$ m?

a) $3.6 \times 10^{-4}$ V

b) $8.1 \times 10^{-4}$ V

c) $1.08 \times 10^{-3}$ V

d) $2.16 \times 10^{-3}$ V

314 / 600

Category: Potential Due to Point Charges:

314. A point charge $+5 \times 10^{-6}$ C is placed at a distance of 2 m from point P. Calculate the electric potential at point P.

a) 11.25 kV

b) 22.5 kV

c) 45 kV

d) 90 kV

315 / 600

Category: Calculation of Potential at Points along the Axis and Equatorial Line

315. A dipole with $p = 6 \times 10^{-6} \, \text{C}\cdot\text{m}$ is placed in vacuum. Calculate the potential at a point R located 2 m away at an angle $\theta = 60^\circ$ from the dipole axis. ($\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2$)

a) 3.38 kV

b) 6.75 kV

c) 13.5 kV

d) 27 kV

316 / 600

Category: Definition and Formula

316. (A) The potential gradient is a vector quantity.
(R) The gradient of any scalar field is always a vector.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

317 / 600

Category: Torque on Dipole in Electric Field

317. If an electric dipole of moment $p$ is aligned parallel to a uniform electric field $E$, what is its potential energy?

a) $-pE$

b) $pE$

c) $-\frac{pE}{2}$

d) $0$

318 / 600

Category: Potential Gradient

318. The electric potential in a region is given by $V(x,y,z) = 3x^2 - 4y + 5z$. What is the electric field vector at $(1, 2, -1)$?

a) $-6\hat{i} + 4\hat{j} - 5\hat{k}$ V/m

b) $6\hat{i} - 4\hat{j} + 5\hat{k}$ V/m

c) $3\hat{i} - 4\hat{j} + 5\hat{k}$ V/m

d) $-3\hat{i} + 4\hat{j} - 5\hat{k}$ V/m

319 / 600

Category: Equipotential Surfaces

319. What is an equipotential surface?

a) A surface with varying electric potential

b) A surface where the electric potential is constant everywhere

c) A surface parallel to the magnetic field lines

d) A surface with no electric field

320 / 600

Category: Potential Due to Point Charges:

320. A charge $q = -4 \mu C$ is moved from infinity to a point where the electric potential due to two fixed charges ($+6 \mu C$ and $-9 \mu C$) is $450 \, \text{V}$. What is the work done by the external force?

a) $-1.8 \times 10^{-3} \, \text{J}$

b) $1.8 \times 10^{-3} \, \text{J}$

c) $-4.5 \times 10^{-4} \, \text{J}$

d) $4.5 \times 10^{-4} \, \text{J}$

321 / 600

Category: Relation between Electric Field and Potential Gradient

321. If the potential decreases along the positive x-axis, what is the direction of the electric field?

a) Negative x-direction

b) Positive x-direction

c) Perpendicular to the x-axis

d) No direction, as it is zero

322 / 600

Category: No Work Done on Equipotential Surfaces

322. If the spacing between two equipotential surfaces decreases, what does it indicate about the electric field strength?

a) The electric field strength decreases

b) The electric field strength remains constant

c) The electric field strength increases

d) The electric field becomes zero

323 / 600

Category: Electric Potential Due to an Electric Dipole

323. An electric dipole with dipole moment $p = 4 \times 10^{-6}$ Cm is placed in vacuum. What is the electric potential at a point 1 m away from the dipole along its axis?

a) 18000 V

b) 36000 V

c) 9000 V

d) 45000 V

324 / 600

Category: Properties of Equipotential Surfaces

324. What is the angle between the electric field lines and an equipotential surface at any point?

a) $0^\circ$

b) $45^\circ$

c) $90^\circ$

d) $180^\circ$

325 / 600

Category: Electric Potential Due to an Electric Dipole

325. (A) The electric potential at any point on the equatorial line of an electric dipole is zero.
(R) The distances from the charges $+q$ and $-q$ to any point on the equatorial line are equal, resulting in cancellation of potentials due to each charge.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

326 / 600

Category: Stable and Unstable Equilibrium

326. (A) An electric dipole is in stable equilibrium when its dipole moment is aligned parallel to the external electric field.

(R) In this position, the potential energy of the dipole is minimum.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

327 / 600

Category: No Work Done on Equipotential Surfaces

327. A charge of 5 \mu C is moved from point A to point B on an equipotential surface. What is the work done by the electric field during this motion?

a) 10 J

b) 5 J

c) -5 J

d) 0 J

328 / 600

Category: Electric Potential Energy of a System of Charges

328. What is the electric potential energy of two point charges $+4 \, \text{C}$ and $-2 \, \text{C}$ placed at a distance of $2 \, \text{m}$ in vacuum?

a) $-3.6 \times 10^{10} \, \text{J}$

b) $7.2 \times 10^{10} \, \text{J}$

c) $-1.8 \times 10^{10} \, \text{J}$

d) $3.6 \times 10^{10} \, \text{J}$

329 / 600

Category: Work Done in Bringing Charges Together

329. (A) The work required to assemble four identical charges $q$ at the corners of a square of side length $a$ is $\frac{1}{4 \pi \epsilon_0} \frac{q^2}{a} \left(4 + \sqrt{2}\right)$.
(R) The potential energy of the system is equal to the total work done in bringing each charge from infinity to its position.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

330 / 600

Category: Definition and Formula

330. Two point charges $q_1 = 2 \mu C$ and $q_2 = 4 \mu C$ are placed 3 m apart in vacuum. What is the electric potential energy of the system? (Given $\frac{1}{4\pi\epsilon_0} = 9 \times 10^9$ Nm$^2$/C$^2$)

a) 6 mJ

b) 24 mJ

c) 48 mJ

d) 72 mJ

331 / 600

Category: Derivation of the Relation

331. If the potential difference between two points $A$ and $B$ separated by a distance $dr$ is $dV$, how is the electric field $E$ related to $dV$ and $dr$?

a) $E = \frac{dV}{dr}$

b) $E = -dV dr$

c) $E = \frac{dr}{dV}$

d) $E = -\frac{dV}{dr}$

332 / 600

Category: No Work Done on Equipotential Surfaces

332. (A) No work is done when moving a charge between two points on an equipotential surface.
(R) The potential difference between any two points on an equipotential surface is zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

333 / 600

Category: Work Done in Rotating Dipole:

333. An electric dipole is rotated from $\theta_1 = 60^\circ$ to $\theta_2 = 120^\circ$ in a uniform electric field $E$. What is the work done if the dipole moment is $p$?

a) $-pE$

b) $pE$

c) $0.5pE$

d) $2pE$

334 / 600

Category: Electric Potential:

334. An electric dipole with dipole moment $p = 4 \times 10^{-9} \, \text{C} \cdot \text{m}$ is placed at the origin along the x-axis. What is the electric potential at a point $(3 \, \text{m}, 4 \, \text{m})$?

a) $0.216 \, \text{V}$

b) $0.432 \, \text{V}$

c) $0.864 \, \text{V}$

d) $1.728 \, \text{V}$

335 / 600

Category: Definition and Formula

335. What is the unit of potential gradient?

a) Newton per coulomb (\$Nm^{-1})

b) Joule per coulomb (\$J C^{-1})

c) Coulomb per volt (\$C V^{-1})

d) Volt per metre (\$Vm^{-1})

336 / 600

Category: Spacing between Surfaces in Strong and Weak Fields

336. If the electric field is weak in a certain region, how does this affect the spacing between adjacent equipotential surfaces?

a) The spacing decreases

b) The spacing increases

c) The spacing becomes zero

d) The spacing oscillates

337 / 600

Category: Calculation of Electric Potential

337. The electric potential at a distance of 2 m from a point charge of $+1 \times 10^{-6}$ C is:

a) 2250 V

b) 4500 V

c) 9000 V

d) 18000 V

338 / 600

Category: Electron-Volt:

338. (A) 1 electron-volt is the energy gained by an electron when it moves through a potential difference of 1 volt.
(R) The work done in moving a charge $q$ through a potential difference $V$ is given by $W = qV$, and for an electron with $q = e$, this becomes $W = eV$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

339 / 600

Category: Calculation of Electric Potential

339. Which of the following statements about equipotential surfaces is true?

a) They intersect electric field lines at an angle of 45 degrees

b) The work done to move a charge along them is non-zero

c) They are parallel to electric field lines

d) The electric field is perpendicular to them

340 / 600

Category: Definition and Formula

340. (A) The electric field intensity at a point is equal to the negative of the potential gradient at that point.
(R) The direction of the electric field is always along the direction of decreasing potential.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

341 / 600

Category: No Work Done on Equipotential Surfaces

341. What is the work done in moving a charge of 5 nC between two points on an equipotential surface?

a) 10 J

b) 5 nJ

c) 0

d) Depends on the distance between the points

342 / 600

Category: Energy Stored in Electric Field

342. An electric dipole of moment $p = 5 \times 10^{-29} \, \text{C-m}$ is placed in a uniform electric field of magnitude $E = 1000 \, \text{V/m}$. What is the potential energy of the dipole when it makes an angle of $60^\circ$ with the electric field?

a) $-2.5 \times 10^{-26} \, \text{J}$

b) $-5.0 \times 10^{-26} \, \text{J}$

c) $-1.25 \times 10^{-26} \, \text{J}$

d) $-7.5 \times 10^{-26} \, \text{J}$

343 / 600

Category: Energy Stored in Electric Field

343. An electric dipole with moment $p = 5 \times 10^{-29} \, \text{C-m}$ is placed in a uniform electric field $E = 2000 \, \text{V/m}$. If the dipole makes an angle of $60^\circ$ with the field, what is the potential energy stored in the dipole?

a) $-1 \times 10^{-25} \, \text{J}$

b) $-5 \times 10^{-26} \, \text{J}$

c) $-2.5 \times 10^{-26} \, \text{J}$

d) $-7.5 \times 10^{-26} \, \text{J}$

344 / 600

Category: Conversion to Joules

344. An $\alpha$-particle (charge $+2e$) is accelerated through a potential difference of 2000 V. What is its kinetic energy in joules?

a) $6.4 \times 10^{-16}$ J

b) $1.6 \times 10^{-16}$ J

c) $3.2 \times 10^{-19}$ J

d) $4.0 \times 10^{-18}$ J

345 / 600

Category: SI Unit and Dimensions

345. If the potential difference between two parallel plates is 100 V and the distance between them is 0.05 m, what is the magnitude of the uniform electric field between the plates?

a) 50 V m$^{-1}$

b) 100 V m$^{-1}$

c) 500 V m$^{-1}$

d) 2000 V m$^{-1}$

346 / 600

Category: Conversion to Joules

346. An electric dipole with moment $4 \times 10^{-30}$ C·m is placed in a uniform electric field of $1000$ V/m at an angle of $60^\circ$. What is its potential energy in joules?

a) $-4 \times 10^{-27}$ J

b) $-2 \times 10^{-27}$ J

c) $-1 \times 10^{-27}$ J

d) $-8 \times 10^{-27}$ J

347 / 600

Category: Conversion to Joules

347. What is the energy in joules equivalent to 5 eV?

a) $8 \times 10^{-19}$ J

b) $1.6 \times 10^{-19}$ J

c) $3.2 \times 10^{-19}$ J

d) $5 \times 10^{-19}$ J

348 / 600

Category: Definition and Use in Atomic Physics

348. Two parallel plates have a potential difference of 100 V and are separated by a distance of 0.02 m. What is the magnitude of the electric field between the plates?

a) 2000 V/m

b) 5000 V/m

c) 10000 V/m

d) 20000 V/m

349 / 600

Category: Potential Difference:

349. An electron is released from rest in a uniform electric field directed from left to right. Which statement correctly describes its motion and potential energy change?

a) Accelerates left; potential energy decreases

b) Accelerates right; potential energy increases

c) Accelerates left; potential energy increases

d) Accelerates right; potential energy decreases

350 / 600

Category: Unit and Direction of Potential Gradient

350. (A) The unit of potential gradient is volt per metre ($\text{Vm}^{-1}$).
(R) Potential gradient is defined as the rate of change of potential with distance in an electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

351 / 600

Category: Potential Difference:

351. A charge $q_0 = -2\,\text{C}$ is moved from point A ($V_A = 5\,\text{V}$) to point B ($V_B = 10\,\text{V}$) in an electric field produced by a positive source charge. What is the work done by the external agent during this process?

a) $+30\,\text{J}$

b) $-10\,\text{J}$

c) $+10\,\text{J}$

d) $-30\,\text{J}$

352 / 600

Category: Equipotential Surfaces:

352. Which of the following correctly explains why two equipotential surfaces cannot intersect each other?

a) Intersection would cause infinite electric field strength.

b) It violates energy conservation principles.

c) The electric field would have two distinct directions at the intersection point.

d) Equipotential surfaces can intersect if their potentials are equal.

353 / 600

Category: Work Done in Rotating Dipole:

353. (A) The work done in rotating an electric dipole from its equilibrium position to $90^\circ$ in a uniform electric field is $pE$.
(R) The torque acting on the dipole at any angle $\theta$ is given by $\tau = pE \sin \theta$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

354 / 600

Category: Equipotential Surfaces:

354. Two equipotential surfaces around a point charge are separated by a distance of 2 cm. The electric field between them is 100 N/C. What is the potential difference between these surfaces?

a) 1 V

b) 2 V

c) 5 V

d) 10 V

355 / 600

Category: Electric Potential due to a Group of Point Charges

355. If a point charge $q_1 = +3 \times 10^{-9}$ C is placed at a distance of 2 m from a point P, what is the electric potential at P?

a) 6.75 V

b) 13.5 V

c) 27 V

d) 54 V

356 / 600

Category: Calculation of Potential Energy

356. Two point charges of $4 \, \text{nC}$ and $-6 \, \text{nC}$ are initially $3 \, \text{m}$ apart. If the distance between them is reduced to $1 \, \text{m}$, what is the change in their potential energy?

a) $-\frac{2 \times 10^{-18}}{\pi \varepsilon_0} \, \text{J}$

b) $\frac{4 \times 10^{-18}}{\pi \varepsilon_0} \, \text{J}$

c) $-\frac{4 \times 10^{-18}}{\pi \varepsilon_0} \, \text{J}$

d) $\frac{8 \times 10^{-18}}{\pi \varepsilon_0} \, \text{J}$

357 / 600

Category: Work Done during Rotation

357. A dipole of moment $2 \times 10^{-8}$ C-m is rotated from $\theta = 60^\circ$ to $\theta = 120^\circ$ in a uniform electric field of $10^4$ N/C. What work is required?

a) $1 \times 10^{-4}$ J

b) $2 \times 10^{-4}$ J

c) $3 \times 10^{-4}$ J

d) $4 \times 10^{-4}$ J

358 / 600

Category: Definition and Calculation

358. (A) The electric field intensity at a point is equal to the negative of the potential gradient in that direction.
(R) The negative sign indicates that the potential decreases in the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

359 / 600

Category: Electric Potential

359. A charge of 2 coulombs is moved from point A with potential 10 V to point B with potential 5 V. What is the work done by the external agent?

a) 10 J

b) -10 J

c) 5 J

d) -5 J

360 / 600

Category: Formulae for Point Charge and Negative Charge

360. Two point charges $q_1 = +2 \times 10^{-6}$ C and $q_2 = -1 \times 10^{-6}$ C are placed 40 cm apart. What is the potential at a point midway between them?

a) 90 kV

b) 45 kV

c) 22.5 kV

d) 0 kV

361 / 600

Category: Potential Calculation for Multiple Charges

361. A charge $Q = 4 \, \mu C$ is moved from infinity to a point where the electric potential due to two charges $q_1 = +2 \, \mu C$ and $q_2 = -3 \, \mu C$ is $9 \, kV$. Calculate the work done.

a) $30 \, \text{mJ}$

b) $36 \, \text{mJ}$

c) $42 \, \text{mJ}$

d) $48 \, \text{mJ}$

362 / 600

Category: Relation between Electric Field and Potential Gradient

362. If the electric potential in a region is given by $V(x, y, z) = 3x^2 + 4y - 5z$ volts, what is the electric field at point (2, -1, 3)?

a) $-12\hat{i} - 4\hat{j} + 5\hat{k} \, \text{V/m}$

b) $12\hat{i} + 4\hat{j} - 5\hat{k} \, \text{V/m}$

c) $-6x\hat{i} - 4\hat{j} + 5\hat{k} \, \text{V/m}$

d) $6x\hat{i} + 4\hat{j} - 5\hat{k} \, \text{V/m}$

363 / 600

Category: Physical Interpretation

363. What is the definition of electric potential at a point in an electric field?

a) The force experienced by a unit positive charge

b) The work done in moving a unit positive charge from infinity to the point

c) The energy stored in a unit positive charge

d) The electric field intensity at that point

364 / 600

Category: General Formula for Potential at any Point

364. A solid sphere of radius 1m has volume charge density $\rho = 2r \, C/m^3$ where r is radial distance. Concentric with this is a spherical shell (radius 2m) with uniform surface charge density $\sigma = -1 C/m^2$. Find the potential at r=3m from the common center.

a) $-1.08 \times 10^{11} V$

b) $-1.32 \times 10^{11} V$

c) $-1.45 \times 10^{11} V$

d) $-1.21 \times 10^{11} V$

365 / 600

Category: Potential Gradient

365. The unit of potential gradient is:

a) $J/m$

b) $N/C$

c) $Vm^{-1}$

d) $C/m^2$

366 / 600

Category: Electric Potential Energy of a System of Charges

366. Two point charges $+3 \, C$ and $-4 \, C$ are initially placed 5 m apart. How much work is required to move them 2 m closer?

a) $12.0 \times 10^9 \, J$

b) $14.4 \times 10^9 \, J$

c) $18.0 \times 10^9 \, J$

d) $10.8 \times 10^9 \, J$

367 / 600

Category: Potential Gradient

367. (A) The electric field at a point is the negative gradient of the electric potential at that point.
(R) The potential gradient is a vector quantity whose direction is opposite to the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

368 / 600

Category: Applications in Point Charges and Dipoles

368. At what position(s) around an electric dipole is the electric potential zero?

a) Only at infinity

b) Only at the midpoint between the two charges

c) Anywhere on the equatorial line perpendicular to the dipole axis

d) Nowhere except at the center of the dipole

369 / 600

Category: Equipotential Surfaces:

369. For an isolated point charge $+q$, what is the shape of the equipotential surfaces?

a) Cubical

b) Spherical

c) Planar

d) Cylindrical

370 / 600

Category: Stable and Unstable Equilibrium

370. An electric dipole with moment $p = 5 \times 10^{-29} \, \text{C-m}$ is placed in a uniform electric field $E = 3 \times 10^5 \, \text{V/m}$. If the dipole is rotated from stable equilibrium to unstable equilibrium, what is the work done?

a) $1.5 \times 10^{-23} \, \text{J}$

b) $3.0 \times 10^{-23} \, \text{J}$

c) $4.5 \times 10^{-23} \, \text{J}$

d) $6.0 \times 10^{-23} \, \text{J}$

371 / 600

Category: Electric Potential

371. What is the SI unit of electric potential?

a) Newton

b) Coulomb

c) Volt

d) Joule

372 / 600

Category: Formulae for Point Charge and Negative Charge

372. How much work is required to bring a charge $q = 0.5 \times 10^{-6}$ C from infinity to a point where the electric potential is 120 V?

a) 30 $\mu$J

b) 60 $\mu$J

c) 120 $\mu$J

d) 240 $\mu$J

373 / 600

Category: Relation to Electric Field

373. Two parallel metallic plates are separated by a distance $d = 5 \, \text{cm}$ with potentials $V_1 = 100 \, \text{V}$ and $V_2 = 20 \, \text{V}$. Calculate the electric field between the plates.

a) $2000 \, \text{V/m}$

b) $1600 \, \text{V/m}$

c) $1200 \, \text{V/m}$

d) $800 \, \text{V/m}$

374 / 600

Category: Unit and Direction of Potential Gradient

374. (A) The potential gradient has units of $V \, m^{-1}$.
(R) The potential gradient represents the rate of change of electric potential with distance.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

375 / 600

Category: Spacing between Surfaces in Strong and Weak Fields

375. (A) The spacing between equipotential surfaces is larger in a region where the electric field is stronger.
(R) The electric field strength $E$ is inversely proportional to the spacing between equipotential surfaces for a given potential change.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

376 / 600

Category: Energy Stored in Electric Field

376. (A) The potential energy of an electric dipole aligned parallel to a uniform electric field is $-pE$.
(R) The work done in rotating the dipole from $\theta = 0^\circ$ to $\theta = 180^\circ$ is $2pE$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

377 / 600

Category: Work Done by External Agent

377. A charge of $+2 \mu C$ is moved from point A (potential $V_A = 100 V$) to point B (potential $V_B = 200 V$). What is the work done by the external agent?

a) $1 \times 10^{-5} J$

b) $2 \times 10^{-4} J$

c) $3 \times 10^{-4} J$

d) $4 \times 10^{-5} J$

378 / 600

Category: Equipotential Surfaces

378. (A) The electric field is always perpendicular to an equipotential surface.
(R) No work is done in moving a charge along an equipotential surface.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

379 / 600

Category: Calculation of Potential Energy

379. Four charges are arranged in a square formation with side length $a$. Three charges are $+q$ and one charge is $-q$. Which configuration gives the lowest (most negative) potential energy for the system?

a) All three $+q$ charges at three corners and $-q$ at fourth corner

b) Two $+q$ charges on one side, one $+q$ and $-q$ on opposite side

c) $-q$ at center with three $+q$ charges at three corners

d) Alternate $+q$ and $-q$ around the square

380 / 600

Category: SI Unit and Dimensions

380. If the potential difference between two plates separated by a distance of 2 m is 10 V, what is the magnitude of the uniform electric field between them?

a) 20 V m$^{-1}$

b) 5 V m$^{-1}$

c) 10 V m$^{-1}$

d) 2.5 V m$^{-1}$

381 / 600

Category: Electric Potential Energy of a System of Charges

381. (A) For two point charges of $+1 \, \text{C}$ and $-1 \, \text{C}$ separated by a distance of $1 \, \text{m}$ in vacuum, the electric potential energy of the system is negative.
(R) The negative sign of potential energy indicates that the net force between the charges is attractive.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

382 / 600

Category: Potential Calculation for Multiple Charges

382. A system consists of three charges: $+q$, $-2q$, and $+3q$ placed at the vertices of an equilateral triangle of side $a$. What is the work done to bring a test charge $Q$ from infinity to the centroid of the triangle?

a) $\frac{kqQ}{a}$

b) $\frac{2kqQ\sqrt{3}}{a}$

c) $\frac{3kqQ}{a}$

d) $\frac{kqQ\sqrt{3}}{a}$

383 / 600

Category: Calculation of Electric Potential

383. (A) The electric potential due to a dipole is zero at all points on its equatorial plane.
(R) The work done in moving a test charge along the equatorial plane of a dipole is always zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

384 / 600

Category: Calculation of Potential at Points along the Axis and Equatorial Line

384. What is the electric potential at any point on the equatorial line of an electric dipole?

a) $\frac{1}{4\pi\epsilon_0} \frac{p}{r^2}$

b) $\frac{1}{4\pi\epsilon_0} \frac{2p}{r^2}$

c) Positive and depends on $r$

d) Zero

385 / 600

Category: Electron-Volt:

385. How much energy in joules does an electron acquire when accelerated through a potential difference of 5 volts?

a) $8 \times 10^{-21}$ joules

b) $8 \times 10^{-20}$ joules

c) $8 \times 10^{-19}$ joules

d) $8 \times 10^{-18}$ joules

386 / 600

Category: Torque on Dipole in Electric Field

386. An electric dipole consists of charges $+q$ and $-q$ separated by a distance of $2l$. If the dipole experiences a torque of $8\sqrt{3} \, \text{N-m}$ in an electric field of $10^5 \, \text{N-C}^{-1}$ when placed at $60^\circ$ to the field, what is the value of $q$ if $l = 1 \, \text{cm}$?

a) $2 \times 10^{-3} \, \text{C}$

b) $4 \times 10^{-3} \, \text{C}$

c) $6 \times 10^{-3} \, \text{C}$

d) $8 \times 10^{-3} \, \text{C}$

387 / 600

Category: Calculation of Potential at Points along the Axis and Equatorial Line

387. For a point at a distance $r$ from an electric dipole making an angle $\theta$ with the dipole axis (assuming $r >> l$), what is the expression for the electric potential?

a) $\frac{1}{4\pi\epsilon_0} \frac{p}{r^2}$

b) $\frac{1}{4\pi\epsilon_0} \frac{p \sin \theta}{r^2}$

c) $\frac{1}{4\pi\epsilon_0} \frac{p \cos \theta}{r^2}$

d) $\frac{1}{4\pi\epsilon_0} \frac{2p \cos \theta}{r^2}$

388 / 600

Category: Electric Dipole:

388. (A) The work done in rotating an electric dipole from $\theta = 60^\circ$ to $\theta = 120^\circ$ in a uniform electric field is zero.
(R) The potential energy of an electric dipole in a uniform electric field depends on the angle between the dipole moment vector and the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

389 / 600

Category: Calculation of Electric Potential

389. (A) The electric potential at any point on the equatorial line of a dipole is zero.
(R) The contributions to the potential from the positive and negative charges cancel each other out on the equatorial line.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

390 / 600

Category: Work Done in Rotating an Electric Dipole in an Electric Field

390. A dipole with moment $p = 2 \times 10^{-29}$ C-m is placed in a uniform electric field $E = 5 \times 10^5$ V/m. What is the difference in potential energy between the positions where the dipole is antiparallel ($180^\circ$) and parallel ($0^\circ$) to the field?

a) $1 \times 10^{-23}$ J

b) $2 \times 10^{-23}$ J

c) $4 \times 10^{-23}$ J

d) $5 \times 10^{-23}$ J

391 / 600

Category: Work Done during Rotation

391. (A) The work done to rotate an electric dipole from $\theta = 0^\circ$ to $\theta = 90^\circ$ in a uniform electric field is $pE$.
(R) The torque acting on the dipole at any angle $\theta$ is given by $\tau = pE \sin \theta$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

392 / 600

Category: Equipotential Surfaces

392. What is the angle between the electric field and an equipotential surface?

a) \$0^\circ\$

b) \$45^\circ\$

c) \$90^\circ\$

d) \$180^\circ\$

393 / 600

Category: Electron-Volt (eV)

393. If an electron gains $1.28 \times 10^{-18}$ joules of kinetic energy after being accelerated through a certain potential difference, what is the potential difference in volts?

a) 4 volts

b) 6 volts

c) 8 volts

d) 10 volts

394 / 600

Category: No Work Done on Equipotential Surfaces

394. (A) Moving a charge along an equipotential surface requires no work because the electric field is always zero on such surfaces.
(R) The potential difference between any two points on an equipotential surface is zero, which implies that no work is done in moving a charge between them.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

395 / 600

Category: Work Done during Rotation

395. What is the work done to rotate an electric dipole of moment $p$ through an angle $\theta = 90^\circ$ in a uniform electric field $E$?

a) $pE/2$

b) $pE$

c) $2pE$

d) $0$

396 / 600

Category: Potential Gradient

396. What is the unit of potential gradient?

a) Newton per coulomb

b) Joule per metre

c) Volt per metre

d) Coulomb per volt

397 / 600

Category: Potential Due to Point Charges:

397. (A) The potential at a point due to a positive point charge is positive.
(R) Work must be done by an external agent to bring a unit positive charge from infinity to that point when the potential is positive.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

398 / 600

Category: Perpendicularity of Electric Field to Equipotential Surfaces

398. How does the spacing between equipotential surfaces relate to the strength of the electric field?

a) They are uniformly spaced regardless of field strength.

b) They are farther apart where the field is stronger.

c) They are randomly spaced.

d) They are closer together where the field is stronger.

399 / 600

Category: Applications in Point Charges and Dipoles

399. An electric dipole of dipole moment $p = 3 \times 10^{-6} \, \text{C}\cdot\text{m}$ is placed in a uniform electric field of strength $E = 2 \times 10^3 \, \text{N/C}$. If the dipole is rotated from $\theta_1 = 0^\circ$ to $\theta_2 = 180^\circ$, what is the work done?

a) $0 \, \text{mJ}$

b) $6 \, \text{mJ}$

c) $12 \, \text{mJ}$

d) $24 \, \text{mJ}$

400 / 600

Category: Definition and Use in Atomic Physics

400. (A) The electric potential energy of a system of two like charges decreases as the distance between them increases.
(R) The potential gradient is directly proportional to the electric field intensity.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

401 / 600

Category: Electric Potential Energy of an Electric Dipole in an Electrostatic Field

401. An electric dipole is placed in a uniform electric field such that it is in stable equilibrium. If the dipole moment is doubled and the electric field strength is halved, what will be the new potential energy of the dipole?

a) $-2pE$

b) $-pE$

c) $-0.5pE$

d) $0$

402 / 600

Category: Equipotential Surfaces

402. If the spacing between two adjacent equipotential surfaces decreases, what does this indicate about the electric field strength in that region?

a) The electric field strength increases

b) The electric field strength decreases

c) The electric field strength remains constant

d) The electric field becomes zero

403 / 600

Category: Unit and Direction of Potential Gradient

403. What is the unit of potential gradient?

a) Newton per coulomb

b) Joule per meter

c) Volt per meter

d) Coulomb per newton

404 / 600

Category: Electric Potential Energy of an Electric Dipole in an Electrostatic Field

404. A dipole with a dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$. The dipole is initially aligned perpendicular to the field ($\theta = 90^\circ$). What is the work done to rotate the dipole so that it makes an angle of $180^\circ$ with the field?

a) $-pE$

b) $0$

c) $pE$

d) $2pE$

405 / 600

Category: Conversion to Joules

405. (A) The energy gained by an electron accelerated through a potential difference of 1 V is $1.6 \times 10^{-19}$ J.
(R) $1$ eV is defined as the energy acquired by an electron when it moves through a potential difference of $1$ V.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

406 / 600

Category: Potential Difference:

406. A charge of $2 \, \text{C}$ is moved from point A to point B, where the potential difference between them is $10 \, \text{V}$. What is the work done by the external agent?

a) 5 J

b) 10 J

c) 20 J

d) 40 J

407 / 600

Category: Electric Potential due to a Point Charge

407. What is the work done by an external agent to bring a unit positive charge from infinity to a point at potential $V$?

a) $V$

b) $-V$

c) $V/q$

d) $qV$

408 / 600

Category: Conditions for Potential Difference

408. An external agent moves a $-2 \, \mu\text{C}$ charge from point $A$ ($V_A = 10 \, \text{V}$) to point $B$ ($V_B = 5 \, \text{V}$). What is the work done by the electric field during this process?

a) $+10 \, \mu\text{J}$

b) $-10 \, \mu\text{J}$

c) $-20 \, \mu\text{J}$

d) $+20 \, \mu\text{J}$

409 / 600

Category: Electron-Volt:

409. (A) The energy of a photon with wavelength 620 nm is approximately 2 eV.
(R) The energy $E$ of a photon in eV can be calculated using the formula $E = \frac{1240}{\lambda \text{(nm)}}$ eV.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

410 / 600

Category: Electron-Volt:

410. An electron is accelerated through a potential difference of 10 kV. What is the kinetic energy gained by the electron in electron-volts?

a) 100 eV

b) 1,000 eV

c) 10,000 eV

d) 100,000 eV

411 / 600

Category: Conditions for Potential Difference

411. A free electron is placed in an electric field where point A has a potential of $-10\,V$ and point B has a potential of $-5\,V$. In which direction will the electron naturally move?

a) From point A to point B

b) From point B to point A

c) It will remain stationary

d) The direction depends on the electric field lines

412 / 600

Category: Electric Potential due to a Point Charge

412. (A) The electric potential at a point due to a positive point charge is positive.
(R) Work must be done by an external agent to bring a unit positive charge from infinity to that point in the field of a positive charge.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

413 / 600

Category: Potential Gradient

413. (A) The electric field intensity at a point is equal to the negative of the potential gradient at that point.
(R) The direction of the potential gradient is opposite to the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

414 / 600

Category: Torque on Dipole in Electric Field

414. An electric dipole of dipole moment $\mathbf{p}$ is placed in a uniform electric field $\mathbf{E}$. What is the torque acting on the dipole when it is aligned at an angle $\theta = 30^\circ$ with the electric field?

a) $\frac{pE}{4}$

b) $\frac{pE}{2}$

c) $pE$

d) $2pE$

415 / 600

Category: Potential Difference

415. (A) If a positive charge moves from point A to point B in an electric field, the work done by the electric force is negative.
(R) The potential difference $V_A - V_B$ is positive when a positive charge moves from point A to point B.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

416 / 600

Category: Conditions for Potential Difference

416. A negative charge $-Q$ creates an electric field. Two points, P and Q, are located at distances $r_P$ and $r_Q$ from $-Q$, respectively, where $r_P > r_Q$. Which statement correctly describes the potentials at P and Q?

a) $V_P > V_Q$

b) $V_P < V_Q$

c) $V_P = V_Q$

d) The comparison depends on the value of $Q$

417 / 600

Category: Electric Potential due to a Point Charge

417. A point charge $Q$ is placed at origin in a medium where dielectric constant varies as $K(r) = 1 + ar$ (a is positive constant). What is the potential at distance $R$ from the charge?

a) $\frac{Q}{4\pi\varepsilon_0}[\frac{1+aR}{R^2}]$

b) $\frac{Q}{4\pi\varepsilon_0}[\frac{1}{R(1+aR)}]$

c) $\frac{Q}{4\pi\varepsilon_0}[\frac{1}{R} - \frac{a}{1+aR}]$

d) $\frac{Q}{4\pi\varepsilon_0}[\ln(1+aR)]$

418 / 600

Category: Potential Gradient

418. (A) The potential gradient is a vector quantity pointing in the direction of decreasing potential.
(R) The electric field intensity is equal to the negative of the potential gradient.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

419 / 600

Category: Potential Difference

419. What is the SI unit of potential difference?

a) Coulomb

b) Newton

c) Volt

d) Joule

420 / 600

Category: Torque on Dipole in Electric Field

420. An electric dipole of moment $p = 4.8 \times 10^{-29} \, \text{C-m}$ is placed in a uniform electric field of strength $E = 2.0 \times 10^5 \, \text{V/m}$. What is the work done in rotating the dipole from an angle of $30^\circ$ to $150^\circ$ with respect to the field?

a) $1.66 \times 10^{-23} \, \text{J}$

b) $2.11 \times 10^{-23} \, \text{J}$

c) $4.80 \times 10^{-23} \, \text{J}$

d) $3.32 \times 10^{-23} \, \text{J}$

421 / 600

Category: Conversion to Joules

421. The energy of a particle is $4.8 \times 10^{-19}$ J. What is its energy in electron-volts?

a) 1 eV

b) 2 eV

c) 3 eV

d) 4 eV

422 / 600

Category: Continuous Charge Distribution (Area and Volume Integrals)

422. A circular disc of radius $R$ has a uniform surface charge density $\sigma$. What is the electric potential at a point on the axis of the disc at a distance $z$ from its center?

a) $\frac{\sigma}{4 \varepsilon_0} \left( \sqrt{z^2 + R^2} - z \right)$

b) $\frac{\sigma}{2 \varepsilon_0} \left( \sqrt{z^2 + R^2} - z \right)$

c) $\frac{\sigma}{2 \varepsilon_0} \left( \sqrt{z^2 + R^2} + z \right)$

d) $\frac{\sigma}{4 \varepsilon_0} \left( \sqrt{z^2 + R^2} + z \right)$

423 / 600

Category: Equipotential Surfaces

423. When moving a test charge along an equipotential surface, what is the work done by the electric field?

a) Positive and equal to the charge magnitude

b) Negative and proportional to the distance moved

c) Zero

d) Depends on the direction of movement

424 / 600

Category: Electric Potential Due to an Electric Dipole

424. A point charge $Q$ and an electric dipole of moment $p$ are placed at the origin. At a distance $r$ from the origin, where $r$ is much larger than the dipole length, the ratio of potentials due to the dipole and the point charge is:

a) $\frac{p}{Qr^2}$

b) $\frac{Qr}{p}$

c) $\frac{p}{Qr}$

d) $\frac{Q}{pr}$

425 / 600

Category: Electric Potential Energy of an Electric Dipole in an Electrostatic Field

425. A dipole with dipole moment $\vec{p} = 5 \times 10^{-10}\, \text{C}\cdot\text{m}$ is placed in a uniform electric field of magnitude $100\, \text{N/C}$. What is the potential energy of the dipole when it makes an angle of $180^\circ$ with the field?

a) $-5 \times 10^{-8}\, \text{J}$

b) $5 \times 10^{-8}\, \text{J}$

c) $0$

d) $-2.5 \times 10^{-8}\, \text{J}$

426 / 600

Category: Calculation of Potential at Points along the Axis and Equatorial Line

426. (A) The electric potential at a point on the equatorial line of an electric dipole is zero.
(R) The distances from the two charges of the dipole to any point on the equatorial line are equal, resulting in cancelation of potentials due to equal and opposite charges.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

427 / 600

Category: Physical Interpretation

427. Which of the following physical quantities has the same dimensions as electric potential but is not equivalent to it in terms of SI units?

a) Electromotive force (EMF)

b) Magnetic flux

c) Inductance times current

d) Power

428 / 600

Category: SI Unit and Dimensions

428. What are the dimensions of electric potential?

a) $[M L T^{-3} A^{-1}]$

b) $[M L^2 T^{-2} A^{-1}]$

c) $[M L^2 T^{-3} A^{-1}]$

d) $[M L^2 T^{-2} A^{-2}]$

429 / 600

Category: Relation between Electric Field and Potential Gradient

429. The electric potential in a region is given by $V(x) = 3x^2 - 2x + 1$ (where $V$ is in volts and $x$ is in meters). What is the electric field at $x = 1 \, \text{m}$?

a) 4 \, \text{V/m}, pointing in the positive x-direction

b) 4 \, \text{V/m}, pointing in the negative x-direction

c) 8 \, \text{V/m}, pointing in the positive x-direction

d) 8 \, \text{V/m}, pointing in the negative x-direction

430 / 600

Category: Torque on Dipole in Electric Field

430. (A) When an electric dipole is aligned parallel to a uniform electric field, the torque acting on it is maximum.
(R) The torque $\tau$ on an electric dipole in a uniform electric field is given by $\tau = pE\sin\theta$, where $\theta$ is the angle between the dipole moment and the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

431 / 600

Category: Relation between Electric Field and Electric Potential

431. (A) The electric field $\vec{E}$ points in the direction of decreasing electric potential $V$.
(R) The electric field is proportional to the negative gradient of the electric potential, i.e., $\vec{E} = -\nabla V$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

432 / 600

Category: Work Done in Bringing Charges Together

432. (A) The work done to bring a charge $q$ from infinity to a point where no other charges are present is zero.
(R) The electric potential at a point due to no other charges is zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

433 / 600

Category: Formulae for Point Charge and Negative Charge

433. A point charge $q = +3 \times 10^{-6}$ C is placed at the origin. What is the electric potential at a point 0.5 m away from it? (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2$)

a) 27 kV

b) 54 kV

c) 108 kV

d) 13.5 kV

434 / 600

Category: Calculation of Electric Potential

434. A point charge $q = 5 \mu C$ is placed at the origin. What is the electric potential at a distance of 2 m from it? (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2$)

a) 11250 V

b) 18000 V

c) 22500 V

d) 45000 V

435 / 600

Category: Properties of Equipotential Surfaces

435. (A) Two equipotential surfaces cannot intersect because at any point in space, the electric field has a unique direction.
(R) The electric field is always perpendicular to the equipotential surface and its magnitude depends on the rate of change of potential with distance.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

436 / 600

Category: Electron-Volt:

436. How much energy in joules is equivalent to 5 MeV?

a) $8 \times 10^{-19}$ J

b) $8 \times 10^{-13}$ J

c) $5 \times 10^{-13}$ J

d) $1.6 \times 10^{-13}$ J

437 / 600

Category: Definition and Calculation

437. A non-uniform electric field has potential function $V(r) = \frac{5}{r} - 2r$ where r is in meters. What work must be done against the electric field to move a 3μC charge from r=2m to r=5m?

a) 18.7 μJ

b) 22.5 μJ

c) 27.3 μJ

d) 31.6 μJ

438 / 600

Category: Electric Potential:

438. What is the electric potential at a distance of 2 meters from a point charge of $4 \times 10^{-6}$ C?

a) 9 kV

b) 18 kV

c) 36 kV

d) 72 kV

439 / 600

Category: Spacing between Surfaces in Strong and Weak Fields

439. Why can't two equipotential surfaces intersect each other?

a) It would violate conservation of energy.

b) The electric field would become infinitely large.

c) The potential difference would become zero.

d) The electric field would have two different directions at the intersection point.

440 / 600

Category: Relation between Electric Field and Electric Potential

440. (A) The electric field at a point is equal to the negative gradient of the electric potential at that point.
(R) The potential decreases in the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

441 / 600

Category: Continuous Charge Distribution (Area and Volume Integrals)

441. A solid sphere of radius $R$ has a volume charge density $\rho = \frac{k}{r}$, where $k$ is a constant and $r$ is the distance from the center of the sphere. What is the electric potential at the surface of the sphere due to this charge distribution?

a) $\frac{k R}{\varepsilon_0}$

b) $\frac{k R^2}{\varepsilon_0}$

c) $\frac{k}{2 \varepsilon_0 R}$

d) $\frac{k}{4 \pi \varepsilon_0 R}$

442 / 600

Category: Relation between Electric Field and Potential Gradient

442. The electric potential due to a point charge at a distance $r$ is given by $V = \frac{kq}{r}$. What is the electric field at this point?

a) $\frac{{kq}}{r^2}\hat{r}$

b) $-\frac{{kq}}{r^2}\hat{r}$

c) $\frac{{kq}}{r}\hat{r}$

d) $-\frac{{kq}}{r}\hat{r}$

443 / 600

Category: Unit and Direction of Potential Gradient

443. What is the direction of the potential gradient relative to the electric field?

a) Same as the electric field

b) Perpendicular to the electric field

c) Opposite to the electric field

d) At 45 degrees to the electric field

444 / 600

Category: General Formula for Potential at any Point

444. Three point charges $+5\mu C$, $-3\mu C$ and $+4\mu C$ are placed at the vertices of an equilateral triangle with side length 2 m. A fourth charge $+2\mu C$ is uniformly distributed along a straight wire of length 1 m placed perpendicular to the plane of the triangle at its centroid. What is the net potential at the centroid of the triangle? Assume $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9 Nm^2/C^2$.

a) $1.65 \times 10^7 V$

b) $1.80 \times 10^7 V$

c) $2.12 \times 10^7 V$

d) $1.92 \times 10^7 V$

445 / 600

Category: Unit and Direction of Potential Gradient

445. In a uniform electric field of 200 N/C directed along the positive x-axis, two equipotential surfaces differ in potential by 50 V. What is the separation between these surfaces?

a) 0.15 m

b) 0.20 m

c) 0.25 m

d) 0.30 m

446 / 600

Category: Calculation of Potential Energy

446. (A) The electric potential energy of a system of three charges $q_1$, $-q_2$, and $q_3$ placed at the corners of an equilateral triangle is always positive.
(R) For any configuration, if one charge is negative and the other two are positive, the net potential energy must be negative due to attraction between unlike charges.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

447 / 600

Category: Work Done by External Agent

447. An electric dipole with dipole moment $p = 5 \times 10^{-30} \, \text{C}\cdot\text{m}$ is aligned parallel to an electric field of magnitude $2 \times 10^{5} \, \text{N/C}$. What is its potential energy?

a) $-1 \times 10^{-24} \, \text{J}$

b) $-2 \times 10^{-24} \, \text{J}$

c) $1 \times 10^{-24} \, \text{J}$

d) $2 \times 10^{-24} \, \text{J}$

448 / 600

Category: Electric Potential Energy of a System of Charges

448. Two point charges $+2 \, \mu C$ and $-4 \, \mu C$ are placed 3 m apart in vacuum. What is the electric potential energy of the system?

a) $-30 \, mJ$

b) $-20 \, mJ$

c) $-24 \, mJ$

d) $-15 \, mJ$

449 / 600

Category: Applications in Point Charges and Dipoles

449. (A) The electric potential at a point on the equatorial line of an electric dipole is zero.
(R) The distances from the two charges of the dipole to any point on the equatorial line are equal, resulting in cancellation of potentials.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

450 / 600

Category: Potential Difference

450. A positive test charge $q_0$ is moved from point B to point A in an electric field by an external agent. The work done by the external agent is $W$. What is the potential difference between points A and B?

a) $\frac{W}{q_0}$

b) $\frac{q_0}{W}$

c) $W q_0$

d) $W + q_0$

451 / 600

Category: Electric Potential Energy of a System of Charges

451. (A) The electric potential energy of two like charges is positive.
(R) Like charges repel each other.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

452 / 600

Category: Stable and Unstable Equilibrium

452. A dipole is placed in an electric field $\overrightarrow{E}$ such that it is in stable equilibrium with the field. If the potential energy of the dipole in this position is $-pE$, what will be the work done to rotate the dipole through $180^\circ$ from its initial stable position?

a) $0$

b) $pE$

c) $2pE$

d) $-2pE$

453 / 600

Category: Calculation of Potential Energy

453. (A) A system of three charges ($+q$, $-q$, and $+q$) placed at the vertices of an equilateral triangle will always have a potential energy that is negative for any finite separation distance.
(R) For a stable equilibrium configuration, the potential energy of the system must be minimized.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

454 / 600

Category: Definition and Calculation

454. In a region where potential varies as $V(x,y) = 4x^3y - 5xy^2$, what is the y-component of electric field at point (2,1)?

a) -8 V/m

b) -10 V/m

c) -12 V/m

d) -14 V/m

455 / 600

Category: Potential Difference:

455. (A) When a positive test charge is moved from point A to point B in an electric field produced by a negative source charge, the work done by the external agent is negative.
(R) The potential difference $V_A - V_B$ is positive when moving a positive test charge from point A to point B in the field of a negative source charge.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

456 / 600

Category: Definition and Calculation

456. (A) The electric field intensity at a point is equal to the negative potential gradient at that point.
(R) The potential decreases in the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

457 / 600

Category: Calculation of Potential Energy

457. Two identical charges of $5 \, \mu \text{C}$ each are initially placed $10 \, \text{cm}$ apart. If they are moved to a new separation of $4 \, \text{cm}$, what is the change in their potential energy and the average force required to bring them closer?

a) $\Delta U = 3.37$ J; $F_{avg} = 56.2$ N

b) $\Delta U = 2.81$ J; $F_{avg} = 46.8$ N

c) $\Delta U = 4.15$ J; $F_{avg} = 69.2$ N

d) $\Delta U = 3.92$ J; $F_{avg} = 65.3$ N

458 / 600

Category: Spacing between Surfaces in Strong and Weak Fields

458. A set of equipotential surfaces in a region has potential differences between adjacent surfaces as follows: 5 V, 10 V, and 15 V. The spacing between the first pair of surfaces is 2 cm. If the electric field strength is inversely proportional to the spacing between surfaces, what is the spacing between the third pair of surfaces?

a) 1 cm

b) 3 cm

c) 6 cm

d) 9 cm

459 / 600

Category: Physical Interpretation

459. What is the SI unit of electric potential?

a) Newton (N)

b) Joule (J)

c) Volt (V)

d) Coulomb (C)

460 / 600

Category: Potential Difference:

460. A charge of $-3 \mu C$ is moved from point P (potential $V_P = 20 V$) to point Q (potential $V_Q = 10 V$). Calculate the work done by the external agent.

a) $-30 \mu J$

b) $-15 \mu J$

c) $15 \mu J$

d) $30 \mu J$

461 / 600

Category: Work Done during Rotation

461. An electric dipole with moment $5 \times 10^{-10}$ C-m is rotated from being parallel to antiparallel in a field of 1000 N/C. What is its potential energy change?

a) $-1 \times 10^{-6}$ J

b) $1 \times 10^{-6}$ J

c) $-5 \times 10^{-7}$ J

d) $5 \times 10^{-7}$ J

462 / 600

Category: Relation to Electric Field

462. Which of the following units can also be used to express the electric field intensity?

a) $J \cdot C^{-1}$

b) $V \cdot m^{-1}$

c) $C \cdot N^{-1}$

d) $F \cdot m^{-1}$

463 / 600

Category: Electric Dipole:

463. What is the general formula for the electric potential at a point at distance $r$ from a dipole and angle $\theta$ with the dipole axis?

a) $\frac{1}{4 \pi \epsilon_0} \cdot \frac{p \sin \theta}{r^2}$

b) $\frac{1}{4 \pi \epsilon_0} \cdot \frac{p \cos \theta}{r^2}$

c) $\frac{1}{4 \pi \epsilon_0} \cdot \frac{2p \cos \theta}{r}$

d) $\frac{1}{4 \pi \epsilon_0} \cdot \frac{p}{r^3}$

464 / 600

Category: Superposition of Potentials

464. What is the electric potential at a point due to a single point charge $q$ at a distance $r$?

a) $\frac{1}{4\pi\epsilon_0} \frac{q^2}{r}$

b) $\frac{1}{4\pi\epsilon_0} \frac{q}{r^2}$

c) $\frac{1}{4\pi\epsilon_0} \frac{q}{r}$

d) $\frac{1}{4\pi\epsilon_0} \frac{r}{q}$

465 / 600

Category: Applications in Point Charges and Dipoles

465. (A) The work done to rotate an electric dipole from $\theta = 90^\circ$ to $\theta = 0^\circ$ in a uniform electric field $\vec{E}$ is equal to its potential energy at $\theta = 0^\circ$.
(R) The potential energy of a dipole in an electric field is given by $U = -pE \cos \theta$, and the work done is $W = pE (\cos \theta_1 - \cos \theta_2)$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

466 / 600

Category: Work Done in Bringing Charges Together

466. (A) The total work done to assemble four identical point charges $q$ at the corners of a square of side length $a$ is $\frac{1}{4\pi\epsilon_0} \frac{q^2}{a} \left( 4 + \sqrt{2} \right)$.
(R) The potential energy of the system depends only on the final configuration of the charges and not on the order in which they are assembled.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

467 / 600

Category: Electric Potential Energy of a System of Charges

467. Three point charges $q_1 = 5 \, \mu C$, $q_2 = -10 \, \mu C$, and $q_3 = 20 \, \mu C$ are placed at the vertices of an equilateral triangle with side length 2 m. Calculate the total electrostatic potential energy of the system.

a) $-0.675 \, J$

b) $-0.450 \, J$

c) $-0.900 \, J$

d) $-0.225 \, J$

468 / 600

Category: Relation to Electric Field

468. (A) The electric field is always perpendicular to equipotential surfaces.
(R) No work is done in moving a charge along an equipotential surface.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

469 / 600

Category: Electric Potential

469. (A) The potential difference between two points in an electric field is always zero if the work done in moving a test charge between them is zero.
(R) Equipotential surfaces are those surfaces where the potential difference between any two points on the surface is zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

470 / 600

Category: Relation to Electric Field

470. Two parallel plates have potentials $V_1 = 100 \, V$ and $V_2 = 50 \, V$ respectively, separated by $d = 0.5 \, m$. If a point charge $q = 5 \, \mu C$ moves from plate $V_1$ to $V_2$, what is the change in its potential energy?

a) 250 \, \mu J

b) -250 \, \mu J

c) 500 \, \mu J

d) -500 \, \mu J

471 / 600

Category: Potential Difference:

471. A charge of $+2 \mu C$ is moved from point A to point B in an electric field. The potential difference between A and B is 50 V. What is the work done by the external agent in moving this charge?

a) $0.05 \, mJ$

b) $-0.1 \, mJ$

c) $0.1 \, mJ$

d) $-0.05 \, mJ$

472 / 600

Category: Physical Interpretation

472. A charge of $2 \, \mu C$ is moved from infinity to a point where the electric potential is $50 \, V$. What is the work done by the external agent?

a) $50 \, \mu J$

b) $100 \, \mu J$

c) $150 \, \mu J$

d) $200 \, \mu J$

473 / 600

Category: Definition and Formula

473. (A) The electric field intensity at a point is equal to the negative of the potential gradient at that point.
(R) The potential gradient is a vector quantity directed opposite to the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

474 / 600

Category: Perpendicularity of Electric Field to Equipotential Surfaces

474. (A) The electric field is always perpendicular to an equipotential surface.
(R) No work is done in moving a charge along an equipotential surface.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

475 / 600

Category: Electric Potential:

475. Three point charges $q_1 = 1 \, \mu\text{C}$, $q_2 = -2 \, \mu\text{C}$, and $q_3 = 3 \, \mu\text{C}$ are placed at the vertices of an equilateral triangle of side $1 \, \text{m}$. Calculate the total electric potential energy of the system.

a) $-90 \, \text{mJ}$

b) $-45 \, \text{mJ}$

c) $-22.5 \, \text{mJ}$

d) $-11.25 \, \text{mJ}$

476 / 600

Category: Electric Potential:

476. An electric dipole of moment $p = 5 \times 10^{-8} \, \text{C} \cdot \text{m}$ is placed in a uniform electric field $E = 2 \times 10^3 \, \text{N/C}$ at an angle of $60^\circ$. What is the potential energy of the dipole in this configuration?

a) $-10 \, \mu\text{J}$

b) $-5 \, \mu\text{J}$

c) $5 \, \mu\text{J}$

d) $10 \, \mu\text{J}$

477 / 600

Category: Torque on Dipole in Electric Field

477. An electric dipole is rotated from $\theta_1 = 60^\circ$ to $\theta_2 = 120^\circ$ in a uniform electric field $\mathbf{E}$. What is the work done in this process?

a) $-pE$

b) $0$

c) $pE$

d) $2pE$

478 / 600

Category: Applications in Point Charges and Dipoles

478. The electric potential at a point P located at a distance $r = 5 \, \text{m}$ from the center of an electric dipole with dipole moment $p = 4 \times 10^{-9} \, \text{C}\cdot\text{m}$ is found to be $V = 36 \, \text{V}$. What is the angle $\theta$ between the dipole axis and the line joining the dipole to point P? Assume $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2$.

a) $30^\circ$

b) $60^\circ$

c) $90^\circ$

d) $120^\circ$

479 / 600

Category: Conversion to Joules

479. (A) 1 eV is equal to $1.6 \times 10^{-19}$ J.
(R) The work done in moving one electron through a potential difference of 1 volt is $1.6 \times 10^{-19}$ J.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

480 / 600

Category: Continuous Charge Distribution (Area and Volume Integrals)

480. (A) The potential at any point inside a uniformly charged spherical shell is constant because
(R) The electric field inside a uniformly charged spherical shell is zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

481 / 600

Category: Perpendicularity of Electric Field to Equipotential Surfaces

481. The relation between electric field $\vec{E}$ and potential $V$ is given by:
$\vec{E} = -\nabla V$
What does this imply about the direction of $\vec{E}$ relative to an equipotential surface?

a) Parallel to the surface.

b) Antiparallel to the potential.

c) Perpendicular to the surface.

d) At a 45° angle to the surface.

482 / 600

Category: Definition and Calculation

482. In which direction does the electric field point relative to the potential gradient?

a) Same direction as the potential gradient

b) Perpendicular to the potential gradient

c) Opposite to the potential gradient

d) No specific relation

483 / 600

Category: Derivation of the Relation

483. A point charge $+q$ creates an electric field $E$. The relation between the electric field $E$ and the potential $V$ is given by:

a) $E = \frac{dV}{dr}$

b) $E = -dV \cdot dr$

c) $E = \frac{dr}{dV}$

d) $E = -\frac{dV}{dr}$

484 / 600

Category: Energy Stored in Electric Field

484. (A) The energy density of an electric field in a parallel plate capacitor is directly proportional to the square of the electric field strength.
(R) The energy stored per unit volume in an electric field is given by $u = \frac{1}{2}\epsilon_0 E^2$, where $E$ is the electric field strength.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

485 / 600

Category: Conversion to Joules

485. Two electrons are each accelerated through a potential difference of 300 V. What is their combined kinetic energy in joules?

a) $1.6 \times 10^{-19}$ J

b) $4.8 \times 10^{-17}$ J

c) $9.6 \times 10^{-17}$ J

d) $3.6 \times 10^{-16}$ J

486 / 600

Category: Definition and Formula

486. The electric potential energy of a system of two charges $q_1$ and $q_2$ separated by distance $r$ in vacuum is given by:

a) $U = q_1 q_2 r$

b) $U = \frac{1}{4 \pi \epsilon_0} \frac{q_1 + q_2}{r}$

c) $U = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2}$

d) $U = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r}$

487 / 600

Category: General Formula for Potential at any Point

487. If a point $P$ has contributions from two charges $+q_1$ and $-q_2$ at distances $r_1$ and $r_2$ respectively, the total potential at $P$ is:

a) $\frac{1}{4\pi \varepsilon_0} \left( \frac{q_1}{r_1} + \frac{q_2}{r_2} \right)$

b) $\frac{1}{4\pi \varepsilon_0} \left( \frac{-q_1}{r_1} + \frac{q_2}{r_2} \right)$

c) $\frac{1}{4\pi \varepsilon_0} \left( \frac{q_1}{r_1} - \frac{q_2}{r_2} \right)$

d) Zero because the charges cancel each other out.

488 / 600

Category: Equipotential Surfaces

488. A test charge q$_0$ is moved from point A to point B on an equipotential surface. Another test charge q$_0$ is moved from point C to point D where points C and D lie on different equipotential surfaces. Which of the following correctly compares the work done in these two cases?

a) Work done from A to B is equal to work done from C to D.

b) Work done from A to B is greater than work done from C to D.

c) Work done from A to B is less than work done from C to D.

d) Work done from A to B is zero, but work done from C to D is non-zero.

489 / 600

Category: Unit and Direction of Potential Gradient

489. What is the unit of potential gradient?

a) V/m

b) V m

c) V/m\textsuperscript{2}

d) V\textsuperscript{2}/m

490 / 600

Category: Definition and Formula

490. The electric potential in a region varies along the x-axis as $V = 3x^2 - 4x + 6$ (where $V$ is in volts and $x$ is in meters). What is the magnitude of the electric field at $x = 2$ m?

a) $-10 \, \text{V/m}$

b) $-8 \, \text{V/m}$

c) $8 \, \text{V/m}$

d) $10 \, \text{V/m}$

491 / 600

Category: Work Done in Rotating Dipole:

491. A dipole is rotated from stable equilibrium position to unstable equilibrium position in a uniform electric field. If the dipole moment is $8 \times 10^{-30} \, \text{C-m}$ and electric field strength is $2 \times 10^5 \, \text{V/m}$, what is the net change in potential energy?

a) $-1.6 \times 10^{-24} \text{J}$

b) $0 \text{J}$

c) $1.6 \times 10^{-24} \text{J}$

d) $3.2 \times 10^{-24} \text{J}$

492 / 600

Category: Conditions for Potential Difference

492. A positive test charge $q_0$ is moved from point $B$ to point $A$ in the electric field of a negative source charge. The work done by the external agent is $-4 \, \text{J}$. If the potential at point $B$ is $-8 \, \text{V}$, what is the potential at point $A$?

a) $-4 \, \text{V}$

b) $-12 \, \text{V}$

c) $4 \, \text{V}$

d) $12 \, \text{V}$

493 / 600

Category: Spacing between Surfaces in Strong and Weak Fields

493. Which of the following statements best explains why two equipotential surfaces cannot intersect?

a) They can intersect if the potentials are equal

b) It would imply multiple electric fields at one point

c) The electric flux would cancel out

d) UniqueIt would violate the principle of superposition

494 / 600

Category: Torque on Dipole in Electric Field

494. A dipole of moment $p = 6.0 \times 10^{-30} \, \text{C-m}$ is initially aligned parallel to an electric field $E = 1.5 \times 10^4 \, \text{V/m}$. If it is rotated to an angle of $120^\circ$, what is the change in its potential energy?

a) $-1.35 \times 10^{-25} \, \text{J}$

b) $1.35 \times 10^{-25} \, \text{J}$

c) $-2.70 \times 10^{-25} \, \text{J}$

d) $2.70 \times 10^{-25} \, \text{J}$

495 / 600

Category: Continuous Charge Distribution (Area and Volume Integrals)

495. A solid sphere of radius $R$ has a uniform volume charge density $\rho$. What is the electric potential at a point outside the sphere ($r > R$)?

a) $\frac{\rho R^2}{3 \varepsilon_0 r}$

b) $\frac{\rho R^3}{2 \varepsilon_0 r}$

c) $\frac{\rho R^3}{3 \varepsilon_0 r}$

d) $\frac{\rho R^2}{2 \varepsilon_0 r}$

496 / 600

Category: Electric Potential Energy of an Electric Dipole in an Electrostatic Field

496. A dipole of moment $p=4 \times 10^{-30}$ Cm is rotated from $\theta=60^\circ$ to $\theta=120^\circ$ in a uniform electric field $E=10^6$ N/C. What is the work done during this rotation?

a) $-4 \times 10^{-24}$ J

b) $0$ J

c) $2 \times 10^{-24}$ J

d) $4 \times 10^{-24}$ J

497 / 600

Category: Work Done during Rotation

497. An electric dipole of moment $p$ is rotated from $\theta = 0^\circ$ to $\theta = 60^\circ$ in a uniform electric field $E$. What is the work done during this rotation?

a) $0.25 p E$

b) $0.5 p E$

c) $p E$

d) $2 p E$

498 / 600

Category: Electric Potential due to a Group of Point Charges

498. Three point charges $+q$, $-2q$ and $+3q$ are placed at the vertices of an equilateral triangle of side length $a$. What is the electric potential at the centroid of the triangle? Assume $\frac{1}{4\pi\varepsilon_0} = k$.

a) $\frac{6kq}{a}$

b) $\frac{2kq\sqrt{3}}{a}$

c) $\frac{kq}{a\sqrt{3}}$

d) Zero

499 / 600

Category: Calculation of Potential at Points along the Axis and Equatorial Line

499. For the same dipole as above, what is the potential at a point Q located 1 m away on the equatorial line?

a) 0 V

b) 18 kV

c) 36 kV

d) -36 kV

500 / 600

Category: Work Done in Rotating Dipole:

500. An electric dipole is rotated through $180^\circ$ from its equilibrium position ($\theta = 0^\circ$) in a uniform electric field $E$. The work done is:

a) $pE$

b) $0$

c) $2pE$

d) $-pE$

501 / 600

Category: Spacing between Surfaces in Strong and Weak Fields

501. (A) In a region of strong electric field, the equipotential surfaces are closer together.
(R) The spacing between equipotential surfaces is inversely proportional to the strength of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

502 / 600

Category: Electric Dipole:

502. A dipole of moment $p = 2 \times 10^{-10}$ C$\cdot$m is rotated from $60^\circ$ to $120^\circ$ in a uniform electric field of $E = 10^4$ N/C. Calculate the work done during this rotation.

a) $-2 \times 10^{-6}$ J

b) $1 \times 10^{-6}$ J

c) $2 \times 10^{-6}$ J

d) $4 \times 10^{-6}$ J

503 / 600

Category: Relation between Electric Field and Electric Potential

503. The electric potential in a region is given by $V = 3x^2 + 5y - 2z$. What is the x-component of the electric field at point (2, 1, 4)?

a) $-6 \, \text{V/m}$

b) $-12 \, \text{V/m}$

c) $6 \, \text{V/m}$

d) $12 \, \text{V/m}$

504 / 600

Category: Perpendicularity of Electric Field to Equipotential Surfaces

504. Why is no work done when moving a charge along an equipotential surface?

a) The electric field vanishes on the surface.

b) There is no force acting on the charge.

c) The potential difference between any two points on the surface is zero.

d) The charge moves randomly and cancels out the work.

505 / 600

Category: Work Done during Rotation

505. If an electric dipole is rotated from $\theta = 0^\circ$ to $\theta = 180^\circ$ in a uniform electric field $E$, what is the work done?

a) $p E$

b) $1.5 p E$

c) $2 p E$

d) $4 p E$

506 / 600

Category: Definition and Use in Atomic Physics

506. (A) The electron-volt (eV) is a unit of energy used in atomic physics.
(R) 1 eV is defined as the kinetic energy an electron gains when accelerated through a potential difference of 1 volt.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

507 / 600

Category: Spacing between Surfaces in Strong and Weak Fields

507. If the electric field is strong between two equipotential surfaces, what can be said about their spacing?

a) The spacing is larger

b) The spacing is smaller

c) The spacing remains unchanged

d) The spacing becomes zero

508 / 600

Category: Work Done in Bringing Charges Together

508. Four identical point charges, each of magnitude $q$, are placed at the corners of a square of side length $a$. What is the work required to bring an additional charge $Q$ from infinity to the center of the square?

a) $\dfrac{4qQ}{4 \pi \epsilon_0 a}$

b) $\dfrac{8qQ}{4 \pi \epsilon_0 a}$

c) $\dfrac{4qQ\sqrt{2}}{4 \pi \epsilon_0 a}$

d) $\dfrac{2qQ\sqrt{2}}{4 \pi \epsilon_0 a}$

509 / 600

Category: Physical Interpretation

509. (A) A positive charge placed in an electric field will always move from a region of higher electric potential to a region of lower electric potential.
(R) The direction of movement of a positive charge is determined by the gradient of electric potential, similar to how liquids flow from higher to lower levels.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

510 / 600

Category: Calculation of Potential at Points along the Axis and Equatorial Line

510. (A) The electric potential at any point on the equatorial line of an electric dipole is zero.

(R) The distances of the point from both charges of the dipole are equal, resulting in equal and opposite potentials.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

511 / 600

Category: SI Unit and Dimensions

511. (A) The SI unit of electric potential is volt (V).
(R) Volt is defined as 1 joule per coulomb.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

512 / 600

Category: Potential Due to Point Charges:

512. (A) The electric potential at a point due to two equal positive point charges placed symmetrically about the point is always positive.
(R) Electric potential due to a positive point charge is positive, and the superposition principle allows adding potentials algebraically.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

513 / 600

Category: Electric Potential Energy of an Electric Dipole in an Electrostatic Field

513. What is the potential energy of an electric dipole with dipole moment $\vec{p}$ placed parallel to a uniform electric field $\vec{E}$?

a) $-pE$

b) $0$

c) $+pE$

d) $-2pE$

514 / 600

Category: Conversion to Joules

514. (A) The kinetic energy of an electron accelerated through a potential difference of 5 volts is $8 \times 10^{-19}$ joules.
(R) The work done in moving an electron across a potential difference of $V$ volts is given by $W = eV$, where $e$ is the charge of the electron.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

515 / 600

Category: Electric Potential Due to an Electric Dipole

515. What is the electric potential at any point on the equatorial line of an electric dipole?

a) Maximum

b) Minimum

c) Zero

d) Depends on the angle

516 / 600

Category: Work Done by External Agent

516. (A) The work done by an external agent in moving a charge $q_0$ from infinity to a point with potential $V_B$ is given by $W = q_0 V_B$.
(R) At infinity, the electric potential is considered zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

517 / 600

Category: Relation between Electric Field and Potential Gradient

517. Two parallel plates are separated by a distance of 0.02 m, with potentials of 100 V and 50 V. What is the magnitude of the electric field between the plates?

a) 2000 V/m

b) 2500 V/m

c) 3000 V/m

d) 3500 V/m

518 / 600

Category: Work Done during Rotation

518. (A) The work done in rotating an electric dipole from $\theta_1 = 0^\circ$ to $\theta_2 = 180^\circ$ in a uniform electric field is $W = 2pE$.
(R) The work done in rotating the dipole is given by $W = pE(1 - \cos\theta_2)$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

519 / 600

Category: Definition and Use in Atomic Physics

519. The electric potential in a region is given by $V = 3x^2 + 4y - 5z$ volts. What is the magnitude of the electric field at the point $(1, 1, 1)$?

a) $\sqrt{50}$ V/m

b) $\sqrt{61}$ V/m

c) $\sqrt{77}$ V/m

d) $\sqrt{85}$ V/m

520 / 600

Category: Applications in Point Charges and Dipoles

520. The potential at a point P due to an electric dipole of moment $\vec{p}$ is given by $V = \frac{1}{4 \pi \epsilon_0} \frac{\vec{p} \cdot \vec{r}}{r^3}$. If $\vec{p} = 10^{-29} \, \text{C}\cdot\text{m}$ and $\vec{r}$ is a unit vector making an angle of $45^\circ$ with $\vec{p}$, what is the potential at $r = 1 \, \text{m}$?

a) $9 \times 10^{-20} \, \text{V}$

b) $6.36 \times 10^{-20} \, \text{V}$

c) $4.5 \times 10^{-20} \, \text{V}$

d) $3 \times 10^{-20} \, \text{V}$

521 / 600

Category: Formulae for Point Charge and Negative Charge

521. A point charge $Q = -5 \mu C$ is fixed in space. What is the work done by an external agent to move a test charge $q = +2 \mu C$ from infinity to a point 3 meters away from $Q$? Assume $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, Nm^2/C^2$.

a) $-30 \, mJ$

b) $+30 \, mJ$

c) $-15 \, mJ$

d) $+15 \, mJ$

522 / 600

Category: Potential Difference

522. If the work done to move a charge of $+2$ C from point A to point B is $10$ J, what is the potential difference between A and B?

a) 20 V

b) 5 V

c) 0.5 V

d) 10 V

523 / 600

Category: Definition and Use in Atomic Physics

523. An electron is accelerated through a potential difference of 5 volts. What is the kinetic energy acquired by the electron in joules?

a) $3.2 \times 10^{-19}$ J

b) $4.8 \times 10^{-19}$ J

c) $8.0 \times 10^{-19}$ J

d) $1.6 \times 10^{-18}$ J

524 / 600

Category: Unit and Direction of Potential Gradient

524. For a point charge $q = 10\,\mu\text{C}$, what is the potential gradient at a distance of 5 m from the charge?

a) $-1800\, \text{V/m}$, radially inward

b) $-3600\, \text{V/m}$, radially outward

c) $3600\, \text{V/m}$, radially inward

d) $1800\, \text{V/m}$, radially outward

525 / 600

Category: Work Done in Rotating an Electric Dipole in an Electric Field

525. (A) The work done to rotate an electric dipole from $\theta = 0^\circ$ to $\theta = 90^\circ$ in a uniform electric field is $pE$.
(R) The torque acting on the dipole at any angle $\theta$ is given by $\tau = pE \sin \theta$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

526 / 600

Category: Work Done in Rotating an Electric Dipole in an Electric Field

526. What is the potential energy of an electric dipole of moment $p$ when it is placed perpendicular to a uniform electric field $E$?

a) $-pE$

b) Zero

c) $pE$

d) $2pE$

527 / 600

Category: General Formula for Potential at any Point

527. Two point charges $+q$ and $-q$ are placed at distances $d$ and $2d$ from a point $P$, respectively. What is the net potential at $P$?

a) Zero

b) $\frac{q}{4 \pi \varepsilon_0 d}$

c) $\frac{q}{8 \pi \varepsilon_0 d}$

d) $\frac{-q}{4 \pi \varepsilon_0 d}$

528 / 600

Category: Calculation of Potential Energy

528. For a system of two like charges, what does a positive potential energy indicate?

a) Net attraction between the charges

b) No force between the charges

c) Net repulsion between the charges

d) Stable equilibrium condition

529 / 600

Category: Perpendicularity of Electric Field to Equipotential Surfaces

529. Why is the electric field perpendicular to an equipotential surface?

a) Because the electric field lines are curved.

b) Because the potential gradient parallel to the surface is non-zero.

c) Because the surface is conducting.

d) Because the potential gradient parallel to the surface is zero.

530 / 600

Category: Properties of Equipotential Surfaces

530. Consider two regions in space with different electric field strengths, $E_1$ and $E_2$ where $E_1 > E_2$. How does the spacing between equipotential surfaces compare between these two regions?

a) Spacing is equal in both regions.

b) Spacing is larger in the region with $E_1$.

c) Spacing is smaller in the region with $E_1$.

d) Spacing depends only on the magnitude of $dV$.

531 / 600

Category: Relation to Electric Field

531. (A) The electric field at a point is equal to the negative gradient of the electric potential at that point.
(R) The potential decreases in the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

532 / 600

Category: Equipotential Surfaces

532. (A) The electric field inside a uniformly charged spherical shell is zero because the potential is constant everywhere inside it.
(R) For an equipotential surface, the potential difference between any two points on the surface is zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

533 / 600

Category: Electric Dipole:

533. (A) The electric potential at any point on the equatorial line of an electric dipole is zero.
(R) The contributions to the potential from the two charges of the dipole cancel each other out at all points on the equatorial line.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

534 / 600

Category: Equipotential Surfaces:

534. Consider a point charge $+q$ placed at the origin. A test charge is moved along an equipotential surface of radius $r$. Which of the following statements about the work done and electric field direction is correct?

a) No work is done, and the electric field is tangential to the surface.

b) Work is done, and the electric field is normal to the surface.

c) No work is done, and the electric field is normal to the surface.

d) Work is done, and the electric field is tangential to the surface.

535 / 600

Category: Superposition of Potentials

535. A uniformly charged plate has surface charge density $\sigma$. If a point $P$ is located at a perpendicular distance $d$ from the plate, what is the electric potential at $P$ relative to infinity?

a) $\frac{\sigma d}{2\epsilon_0}$

b) $\frac{\sigma}{2\epsilon_0 d}$

c) $\frac{\sigma d}{\epsilon_0}$

d) Zero

536 / 600

Category: Perpendicularity of Electric Field to Equipotential Surfaces

536. A charge of $5 \, \mu C$ is moved along an equipotential surface in a uniform electric field of strength $100 \, N/C$. What is the work done in moving the charge by $2 \, m$?

a) 1 J

b) 10 J

c) 100 J

d) 0 J

537 / 600

Category: Applications in Point Charges and Dipoles

537. An electric dipole of moment $\vec{p}$ is rotated from $\theta_1 = 60^\circ$ to $\theta_2 = 120^\circ$ in a uniform electric field $E$. If the work done is $W$, what is the magnitude of the dipole moment $p$?

a) $\frac{W}{2E}$

b) $\frac{2W}{E}$

c) $\frac{W}{E}$

d) $\sqrt{\frac{W}{E}}$

538 / 600

Category: Electric Potential Energy of a System of Charges

538. Three charges $+5 \, \mu\text{C}$, $-3 \, \mu\text{C}$, and $+2 \, \mu\text{C}$ are placed at the vertices of an equilateral triangle of side length $3 \, \text{m}$. What is the total potential energy of the system?

a) $-3.3 \times 10^{-2} \, \text{J}$

b) $3.3 \times 10^{-2} \, \text{J}$

c) $-1.1 \times 10^{-2} \, \text{J}$

d) $1.1 \times 10^{-2} \, \text{J}$

539 / 600

Category: Potential Due to Point Charges:

539. The potential at a point P due to a point charge $q = 5 \times 10^{-9}$ C and distance $r = 0.1$ m is:

a) 100 V

b) 250 V

c) 450 V

d) 900 V

540 / 600

Category: General Formula for Potential at any Point

540. What is the electric potential at any point on the equatorial line of an electric dipole?

a) $\frac{1}{4\pi \varepsilon_0} \frac{p}{r}$

b) $\frac{1}{4\pi \varepsilon_0} \frac{p}{r^2}$

c) $\frac{1}{4\pi \varepsilon_0} \frac{2p}{r^3}$

d) Zero

541 / 600

Category: Electric Potential due to a Point Charge

541. If a point charge $-q$ is placed in vacuum ($K = 1$), what is the electric potential at a distance $r$ from it?

a) $\frac{1}{4 \pi \epsilon_0} \frac{q}{r}$

b) $-\frac{1}{4 \pi \epsilon_0} \frac{q}{r}$

c) $\frac{1}{4 \pi \epsilon_0 K} \frac{q}{r}$

d) $-\frac{1}{4 \pi \epsilon_0 K} \frac{q}{r}$

542 / 600

Category: Definition and Formula

542. If the electric potential at a point is given by $V(x) = 4x^2 + 3x + 2$ volts, where $x$ is in meters, what is the electric field at $x = 2$ m?

a) 11 V/m

b) -11 V/m

c) 19 V/m

d) -19 V/m

543 / 600

Category: Potential Difference:

543. What is the potential difference between two points A and B in an electric field if the work done to move a unit positive test charge from B to A is 5 J?

a) 2 V

b) 5 V

c) 10 V

d) 20 V

544 / 600

Category: Conditions for Potential Difference

544. If the work done by an external agent in moving a test charge $q_0$ from point B to point A is $W$, what is the potential difference between A and B?

a) $\frac{q_0}{W}$

b) $\frac{W}{q_0}$

c) $W q_0$

d) $V_B - V_A$

545 / 600

Category: Spacing between Surfaces in Strong and Weak Fields

545. What is the relationship between the magnitude of the electric field and the spacing between equipotential surfaces?

a) Directly proportional

b) Inversely proportional

c) Exponentially related

d) No relation exists

546 / 600

Category: Energy Stored in Electric Field

546. The energy stored per unit volume ($u$) in an electric field is given by:

a) $u = \epsilon_0 E$

b) $u = \frac{1}{\epsilon_0} E^2$

c) $u = \frac{1}{2}\epsilon_0 E^2$

d) $u = 2\epsilon_0 E^2$

547 / 600

Category: Electric Potential:

547. Two charges $q_1 = +3 \, \mu C$ and $q_2 = -4 \, \mu C$ are placed 5 cm apart in vacuum. Calculate the potential energy of the system. Given $\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \, \text{N m}^2 \, \text{C}^{-2}$.

a) -1.08 J

b) -2.16 J

c) -4.32 J

d) -0.54 J

548 / 600

Category: Work Done in Bringing Charges Together

548. What is the work done to bring a charge $q$ from infinity to a point where another identical charge $q$ is already placed at a distance $a$?

a) $\frac{1}{4 \pi \epsilon_0} \frac{q}{a}$

b) $\frac{1}{4 \pi \epsilon_0} \frac{q^2}{a^2}$

c) $\frac{1}{4 \pi \epsilon_0} \frac{q^2}{a}$

d) Zero

549 / 600

Category: Conversion to Joules

549. An electron is accelerated through a potential difference of 500 V. What is the kinetic energy gained by the electron in joules?

a) $3.2 \times 10^{-16}$ J

b) $8.0 \times 10^{-17}$ J

c) $1.6 \times 10^{-19}$ J

d) $5.0 \times 10^{-16}$ J

550 / 600

Category: Potential Due to Point Charges:

550. (A) The net electric potential at a point due to two equal and opposite charges is always zero.
(R) Electric potential is a scalar quantity, and the potentials due to individual charges cancel out when they are equal in magnitude but opposite in sign.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

551 / 600

Category: Formulae for Point Charge and Negative Charge

551. (A) The electric potential at a point due to a negative point charge is negative.
(R) For a negative charge, the potential is given by $V = \frac{1}{4 \pi \varepsilon_0} \frac{-q}{r}$.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

552 / 600

Category: Electron-Volt (eV)

552. A particle has a kinetic energy of $4.8 \times 10^{-19}$ joules. How much is this energy in electron-volts (eV)?

a) 1.5 eV

b) 3.0 eV

c) 4.5 eV

d) 6.0 eV

553 / 600

Category: Derivation of the Relation

553. What is the relationship between electric field \$(E)\$ and electric potential \$(V)\$ in terms of potential gradient?

a) \$E = \frac{dV}{dr}\$

b) \$E = -\frac{dV}{dr}\$

c) \$E = dV \cdot dr\$

d) \$E = -dV + dr\$

554 / 600

Category: Potential Calculation for Multiple Charges

554. Three charges $q_1 = 10 nC$, $q_2 = 20 nC$, and $q_3 = 30 nC$ are brought from infinity to the vertices of an equilateral triangle of side 3 m. Calculate the work done in assembling this configuration.

a) 2.5 $\mu$J

b) 3.3 $\mu$J

c) 4.1 $\mu$J

d) 1.9 $\mu$J

555 / 600

Category: Electric Potential due to a Point Charge

555. A point charge of $-3 \mu C$ is placed in free space ($K = 1$). What is the electric potential at a distance of 1 meter from the charge? (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, Nm^2/C^2$)

a) $-13.5 \, kV$

b) $-27 \, kV$

c) $-54 \, kV$

d) $-108 \, kV$

556 / 600

Category: Properties of Equipotential Surfaces

556. If the electric field in a region is strong, how are the equipotential surfaces spaced relative to each other?

a) Farther apart

b) Closer together

c) Equally spaced

d) Randomly spaced

557 / 600

Category: Work Done by External Agent

557. A system consists of two charges ($+q$ and $-q$) placed at a distance $a$ apart. What is the work done by an external agent to bring a third charge ($+4q$) from infinity to a point P located on the perpendicular bisector of the line joining the two charges at a distance $\frac{a\sqrt{2}}{2}$ from each charge?

a) $\frac{8q^2}{4 \pi \epsilon_0 a}$

b) $\frac{16q^2}{4 \pi \epsilon_0 a \sqrt{2}}$

c) $0$

d) $\frac{4q^2}{4 \pi \epsilon_0 a}$

558 / 600

Category: Work Done by External Agent

558. A charge of $-5 \mu C$ is moved from a point with potential $-50 V$ to infinity. What is the work done by the external agent?

a) $2.5 \times 10^{-4} J$

b) $-2.5 \times 10^{-4} J$

c) $5 \times 10^{-4} J$

d) $-5 \times 10^{-4} J$

559 / 600

Category: Potential Gradient

559. A uniform electric field $E$ exists along the x-axis. The potential at $x = 0$ is $V_0$ and decreases linearly to $V_0 - 100$ V at $x = 2$ m. What is the magnitude of the electric field?

a) 25 V/m

b) 50 V/m

c) 100 V/m

d) 200 V/m

560 / 600

Category: Formulae for Point Charge and Negative Charge

560. A point charge $-2 \, \mu C$ is placed in vacuum. What is the potential at a distance of 2 m from it?

a) $-4500 \, V$

b) $-9000 \, V$

c) $-18000 \, V$

d) $-36000 \, V$

561 / 600

Category: Unit and Direction of Potential Gradient

561. (A) The potential gradient is a scalar quantity because it represents the rate of change of electric potential with distance.
(R) The direction of the potential gradient is always from higher potential to lower potential, similar to the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

562 / 600

Category: Properties of Equipotential Surfaces

562. A charge $q$ is moved along an equipotential surface from point A to point B in the presence of an electric field $\vec{E}$. Which of the following statements correctly describes the work done and the relationship between $\vec{E}$ and the surface?

a) Work done is non-zero, and $\vec{E}$ is tangent to the surface.

b) Work done is zero, and $\vec{E}$ is at $45^\circ$ to the surface.

c) Work done is zero, and $\vec{E}$ is perpendicular to the surface.

d) Work done is non-zero, and $\vec{E}$ is perpendicular to the surface.

563 / 600

Category: Electric Potential:

563. (A) The potential difference between any two points on an equipotential surface is zero.
(R) No work is required to move a test charge along an equipotential surface.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

564 / 600

Category: Definition and Formula

564. The electric potential energy of a system of two charges $q_1$ and $q_2$ placed at a distance $r$ apart is given by:

a) $U = \frac{1}{4 \pi \epsilon_0} \frac{q_1^2}{r}$

b) $U = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2}$

c) $U = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r}$

d) $U = \frac{1}{4 \pi \epsilon_0} \frac{q_1 + q_2}{r}$

565 / 600

Category: Derivation of the Relation

565. (A) The electric field intensity at a point is equal to the negative potential gradient in that direction.
(R) The negative sign signifies that the potential decreases in the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

566 / 600

Category: Superposition of Potentials

566. (A) The potential at a point due to a continuous charge distribution can always be calculated using $V = \frac{1}{4 \pi \epsilon_0} \int \frac{dq}{r}$.
(R) Continuous charge distributions have infinite discrete charges, and superposition principle applies.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

567 / 600

Category: Definition and Formula

567. (A) The electric field intensity at a point is equal to the negative potential gradient at that point.
(R) The potential decreases in the direction of the electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

568 / 600

Category: Properties of Equipotential Surfaces

568. Why is it impossible for two distinct equipotential surfaces to intersect each other?

a) Because equipotential surfaces must be parallel to each other.

b) Because the electric field would vanish at the intersection point.

c) Because intersecting surfaces would imply multiple electric field directions.

d) Because equipotential surfaces can only exist in vacuum.

569 / 600

Category: Relation to Electric Field

569. A non-uniform electric field is given by $E = -\frac{dV}{dx}$ where $V(x) = 3x^2 - 2x + 5$ (in volts). A charge $q = 2 \, \mu C$ is moved from $x = 1 \, m$ to $x = 3 \, m$ along an equipotential surface. What is the work done by the electric field during this displacement?

a) 4 \, \mu J

b) 0 \, J

c) 8 \, \mu J

d) -4 \, \mu J

570 / 600

Category: Continuous Charge Distribution (Area and Volume Integrals)

570. What is the expression for the electric potential $V$ at a point due to a continuous surface charge distribution with charge density $\sigma$?

a) $V = \int \sigma dA$

b) $V = \frac{1}{4 \pi \varepsilon_0} \int_A \frac{\sigma dA}{r^2}$

c) $V = \frac{1}{4 \pi \varepsilon_0} \int_A \frac{\sigma dA}{r}$

d) $V = \frac{1}{2 \pi \varepsilon_0} \int \sigma dA$

571 / 600

Category: Electric Potential due to a Point Charge

571. A point charge of $+5 \mu C$ is placed in a medium with dielectric constant $K = 2$. What is the electric potential at a distance of 2 meters from the charge? (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, Nm^2/C^2$)

a) 5.625 kV

b) 11.25 kV

c) 22.5 kV

d) 45 kV

572 / 600

Category: Work Done in Bringing Charges Together

572. Three point charges, each of magnitude $q$, are placed at the vertices of an equilateral triangle of side length $a$. Calculate the work done in assembling this configuration.

a) $\dfrac{q^2}{4 \pi \epsilon_0 a}$

b) $\dfrac{2q^2}{4 \pi \epsilon_0 a}$

c) $\dfrac{3q^2}{4 \pi \epsilon_0 a}$

d) $\dfrac{4q^2}{4 \pi \epsilon_0 a}$

573 / 600

Category: SI Unit and Dimensions

573. The electric potential $V$ at a point due to a point charge is given by $V = \frac{1}{4 \pi \epsilon_0} \frac{q}{r}$. What are the dimensions of $\epsilon_0$?

a) $[M L^{-3} T^4 A^2]$

b) $[M^{-1} L^{-3} T^4 A^2]$

c) $[M L^3 T^{-4} A^{-2}]$

d) $[M^{-1} L^3 T^{-4} A^{-2}]$

574 / 600

Category: Conditions for Potential Difference

574. (A) When an electron moves from point A (potential $V_A = -5V$) to point B (potential $V_B = +3V$), the work done by the electric field is negative.
(R) For an electron, the direction of motion is from lower to higher potential, and the work done by the electric field is given by $W = q(V_B - V_A)$, where $q$ is negative.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

575 / 600

Category: Work Done in Bringing Charges Together

575. A charge $q_1 = 5 \times 10^{-9}$ C is fixed at a point. Another charge $q_2 = 2 \times 10^{-9}$ C is moved from a distance of 4 cm to 2 cm away from $q_1$. What is the work done in this process?

a) $1.125 \times 10^{-6}$ J

b) $2.25 \times 10^{-6}$ J

c) $4.5 \times 10^{-6}$ J

d) $9 \times 10^{-6}$ J

576 / 600

Category: Electric Potential due to a Point Charge

576. Three point charges $+q$, $-2q$, and $+3q$ are placed at the vertices of an equilateral triangle of side $r$ in a medium with dielectric constant $K$. What is the net work done by an external agent in bringing a test charge $q_0$ from infinity to the centroid of the triangle?

a) $\frac{3qq_0}{4\pi\varepsilon_0 K r}$

b) $\frac{2qq_0\sqrt{3}}{4\pi\varepsilon_0 K r}$

c) $\frac{qq_0}{2\pi\varepsilon_0 K r\sqrt{3}}$

d) $\frac{5qq_0}{4\pi\varepsilon_0 K r\sqrt{3}}$

577 / 600

Category: Relation to Electric Field

577. An electric dipole with dipole moment $p = 10^{-12} \, C \cdot m$ is placed in a uniform electric field $E = 10^3 \, N/C$ at an angle of $60^\circ$. What is the potential energy of the dipole?

a) 5 \times 10^{-10} \, J

b) -5 \times 10^{-10} \, J

c) 10^{-9} \, J

d) -10^{-9} \, J

578 / 600

Category: Physical Interpretation

578. The electric potential in a region of space is given by $V(x, y, z) = 3x^2 + 2xy - z^2$. What is the magnitude of the electric field at the point $(1, 1, 1)$?

a) $6\sqrt{2}$

b) $8\sqrt{2}$

c) $4\sqrt{3}$

d) $10$

579 / 600

Category: Conditions for Potential Difference

579. (A) In a uniform electric field, the potential difference between two points is directly proportional to the distance between them along the direction of the field.
(R) The work done by an external agent in moving a unit positive test charge between two points in a uniform electric field depends on the path taken.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

580 / 600

Category: Relation to Electric Field

580. The electric field intensity $E$ at a point in an electric field is related to the potential gradient by which formula?

a) $E = \frac{dV}{dr}$

b) $E = -\frac{dV}{dr}$

c) $E = \frac{d^2V}{dr^2}$

d) $E = V \cdot dr$

581 / 600

Category: Electric Potential

581. A point charge $+q$ is placed at the origin. What is the radius of the equipotential surface where the potential is $V$?

a) $\frac{1}{4 \pi \epsilon_0} \frac{V}{q}$

b) $\frac{1}{4 \pi \epsilon_0} \frac{q}{V}$

c) $4 \pi \epsilon_0 \frac{q}{V}$

d) $4 \pi \epsilon_0 \frac{V}{q}$

582 / 600

Category: Relation between Electric Field and Potential Gradient

582. A point charge $q = 5 \times 10^{-9} \, \text{C}$ is placed at the origin. The electric potential at a distance $r = 2 \, \text{m}$ from the charge is given by $V = \frac{1}{4 \pi \epsilon_0} \frac{q}{r}$. What is the magnitude of the electric field at this point?

a) 5.625 \, \text{V/m}

b) 11.25 \, \text{V/m}

c) 22.5 \, \text{V/m}

d) 45.0 \, \text{V/m}

583 / 600

Category: Electric Dipole:

583. An electric dipole of moment $p = 1 \times 10^{-8}$ C$\cdot$m is placed at the origin. The potential difference between two points A (axial, distance 2 m) and B (equatorial, distance 2 m) is:

a) 0 V

b) 11.25 V

c) 22.5 V

d) 45 V

584 / 600

Category: Derivation of the Relation

584. A test charge $q_0$ is moved from point $B$ to point $A$ in an electric field $E$. The work done $dW$ by an external agent against the electric field is given by:

a) $dW = q_0 E dr$

b) $dW = -E dr$

c) $dW = -q_0 dr$

d) $dW = -q_0 E dr$

585 / 600

Category: Potential Gradient

585. The relation between electric field intensity $E$ and potential gradient $\frac{dV}{dr}$ is:

a) $E = \frac{dV}{dr}$

b) $E = -\frac{dV}{dr}$

c) $E = \frac{dr}{dV}$

d) $E = -\frac{dr}{dV}$

586 / 600

Category: SI Unit and Dimensions

586. (A) The SI unit of electric potential, volt (V), can be expressed as $1 \text{ V} = 1 \text{ J C}^{-1}$.
(R) Electric potential is defined as the work done per unit charge in bringing a test charge from infinity to a point in an electric field.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

587 / 600

Category: Electric Dipole:

587. What is the electric potential at a point on the equatorial line of an electric dipole?

a) $\frac{1}{4 \pi \epsilon_0} \cdot \frac{p}{r^2}$

b) $\frac{1}{4 \pi \epsilon_0} \cdot \frac{2q}{r}$

c) 0

d) $\frac{1}{4 \pi \epsilon_0} \cdot \frac{p}{r}$

588 / 600

Category: Equipotential Surfaces

588. (A) The work done in moving a charge along an equipotential surface is always zero.
(R) The potential difference between any two points on an equipotential surface is zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

589 / 600

Category: Equipotential Surfaces

589. Consider two equipotential surfaces around a point charge +q with potentials V$_1$ and V$_2$ such that V$_1$ > V$_2$. Which of the following statements is correct regarding the electric field between these surfaces?

a) The electric field is uniform between the two surfaces.

b) The electric field is stronger near V$_1$ than V$_2$.

c) The electric field is weaker near V$_1$ than V$_2$.

d) The electric field is zero between the two surfaces.

590 / 600

Category: Superposition of Potentials

590. A thin non-conducting ring of radius $R$ has a charge $+Q$ uniformly distributed on it. A point $P$ lies on the axis of the ring at a distance $x$ from its center. What is the electric potential at point $P$ due to the ring?

a) $\frac{1}{4\pi \epsilon_0} \frac{Q}{x}$

b) $\frac{1}{4\pi \epsilon_0} \frac{Q}{R}$

c) $\frac{1}{4\pi \epsilon_0} \frac{Q}{\sqrt{x^2 + R^2}}$

d) $\frac{1}{4\pi \epsilon_0} \frac{Q x}{R^2}$

591 / 600

Category: Energy Stored in Electric Field

591. An electric dipole of moment $p = 8 \times 10^{-30} \, \text{C-m}$ is rotated from an angle of $30^\circ$ to $90^\circ$ in a uniform electric field of $500 \, \text{V/m}$. Calculate the work done during this rotation.

a) $4.0 \times 10^{-27} \, \text{J}$

b) $6.928 \times 10^{-27} \, \text{J}$

c) $8.0 \times 10^{-27} \, \text{J}$

d) $5.196 \times 10^{-27} \, \text{J}$

592 / 600

Category: Stable and Unstable Equilibrium

592. The potential energy of a dipole $\vec{p} = (3\hat{i} + 4\hat{j}) \times 10^{-29} \, \text{C-m}$ in an electric field $\vec{E} = (2\hat{i} - \hat{j}) \times 10^5 \, \text{V/m}$ is:

a) $-5 \times 10^{-24} \, \text{J}$

b) $-2 \times 10^{-24} \, \text{J}$

c) $+2 \times 10^{-24} \, \text{J}$

d) $+5 \times 10^{-24} \, \text{J}$

593 / 600

Category: Energy Stored in Electric Field

593. Three point charges $q_1 = 2 \mu\text{C}$, $q_2 = -3 \mu\text{C}$, and $q_3 = 4 \mu\text{C}$ are placed at the vertices of an equilateral triangle of side length $1 \, \text{m}$. What is the total potential energy of the system? ($k = 9 \times 10^9 \, \text{N m}^2/\text{C}^2$)

a) $0.09 \, \text{J}$

b) $-0.09 \, \text{J}$

c) $0.18 \, \text{J}$

d) $-0.18 \, \text{J}$

594 / 600

Category: Superposition of Potentials

594. (A) The potential at a point due to multiple point charges can be calculated by adding the potentials due to each charge individually.
(R) Potential is a scalar quantity, so algebraic addition of individual potentials is valid.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

595 / 600

Category: Electric Potential Energy of a System of Charges

595. Three charges $q_1 = 4 \, \mu C$, $q_2 = 6 \, \mu C$, and $q_3 = -8 \, \mu C$ are placed at the corners of an equilateral triangle with side length 2 m. What is the total potential energy of the system?

a) $-0.252 \, \text{J}$

b) $0.504 \, \text{J}$

c) $0.252 \, \text{J}$

d) $-0.504 \, \text{J}$

596 / 600

Category: Properties of Equipotential Surfaces

596. (A) The work done in moving a charge along an equipotential surface is always zero.
(R) The potential difference between any two points on an equipotential surface is zero.

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

c) Assertion is true, but Reason is false.

d) Assertion is false, but Reason is true.

597 / 600

Category: Potential Due to Point Charges:

597. Two point charges $+2 \mu C$ and $-3 \mu C$ are placed 20 cm apart. The potential at the midpoint between them is:

a) 90,000 V

b) -90,000 V

c) 180,000 V

d) -180,000 V

598 / 600

Category: SI Unit and Dimensions

598. What are the dimensions of electric potential?

a) $[M L T^{-3} A^{-1}]$

b) $[M L^2 T^{-3} A^{-1}]$

c) $[M L^2 T^{-2} A^{-1}]$

d) $[M L^2 T^{-2} A]$

599 / 600

Category: Electric Potential:

599. Which of the following best describes an equipotential surface?

a) A surface where the electric field is zero everywhere

b) A surface where the electric potential is the same at every point

c) A surface where the charge density is uniform

d) A surface where the electric field lines are parallel

600 / 600

Category: Properties of Equipotential Surfaces

600. A charge $q$ is moved from point $A$ to point $B$ on an equipotential surface. What can be said about the work done in this process?

a) Positive work is done

b) Negative work is done

c) Work done depends on the path taken

d) No work is done

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Class 12 Physics (Part 1) Chapter 3 Electric Potential

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