Class 10 Physics Chapter 10 Electro-Magnetism

Key Concept: Lenz’s Law

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to Lenz’s law, the direction of the induced current is such that it opposes the change in magnetic flux causing it. This is represented mathematically by $\mathcal{E} = -N \frac{d\Phi}{dt}$, where the negative sign indicates opposition to the change. The reasoning behind this is rooted in the principle of conservation of energy. When mechanical work is done to move a magnet towards or away from a coil, the induced current flows in a direction that opposes this motion, converting mechanical energy into electrical energy. Therefore, both the Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Permanent Magnet, Electromagnet

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that a permanent magnet cannot be easily demagnetized by switching off the current. This is true because permanent magnets are not dependent on an external current to maintain their magnetism. They retain their magnetic properties due to the material they are made of, which is steel. The Reason explains that permanent magnets are made of steel, which has high retentivity, meaning it retains its magnetization even after the external magnetic field is removed. Since the Reason correctly justifies the Assertion, both the Assertion and Reason are true, and the Reason is the correct explanation of the Assertion.

Key Concept: Soft iron core

d) Inserting a soft iron core into the solenoid
[Solution Description]
Placing a soft iron core inside the solenoid increases the magnetic field strength because soft iron has high magnetic permeability, which concentrates and amplifies the magnetic field lines.

Key Concept: A.C. Generator Principle

c) Operates through electromagnetic induction with coaxial slip rings
[Solution Description]
The A.C. generator converts mechanical energy into electrical energy through electromagnetic induction, where a rotating coil within a magnetic field induces an alternating current.

Key Concept: Transformer principle, turns ratio, power conservation

b) 0.25 A
[Solution Description]
For an ideal transformer, input power equals output power: $P_p = P_s$.
Output power $P_s = E_s \times I_s = 11 \times 5 = 55$ W.
Input power $P_p = E_p \times I_p = 220 \times I_p = 55$ W.
Therefore, $I_p = \frac{55}{220} = 0.25$ A.

Key Concept: Direction of Magnetic Field in Solenoid

d) Using the right-hand thumb rule
[Solution Description]
The direction of the magnetic field inside a solenoid can be determined using the right-hand thumb rule. If the fingers of the right hand curl in the direction of the current flowing through the solenoid, the thumb points in the direction of the magnetic field lines inside the solenoid.

Key Concept: Electromagnet, Permanent Magnet

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.
[Solution Description]
The assertion states that an electromagnet's polarity can be reversed by changing the direction of current in its solenoid, which is true because the polarity depends on the direction of current flow. The reason states that the magnetic field of an electromagnet is temporary and ceases when the current is switched off, which is also correct. However, the reason does not explain why the polarity can be reversed; it only explains the temporary nature of the magnetic field. Thus, both statements are true, but the reason is not the correct explanation for the assertion.

Key Concept: Energy Losses, Efficiency

c) 5 A
[Solution Description]
Given: $E_p = 200$ V, $E_s = 400$ V, $I_p = 10$ A.
For an ideal transformer with no energy loss, $E_p I_p = E_s I_s$.
Solving for $I_s$:
$I_s = \frac{E_p I_p}{E_s} = \frac{200 \times 10}{400} = 5 \text{ A}$
The current in the secondary coil is 5 A.

Key Concept: Right-hand Thumb Rule

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion (A) correctly describes the application of the right-hand thumb rule for determining the direction of the magnetic field around a current-carrying conductor. The reason (R) also correctly states the purpose of the right-hand thumb rule. Moreover, the reason provides the correct explanation for why the assertion is true, as the rule directly links the thumb's direction (current) to the curling of fingers (magnetic field direction).

Key Concept: Lenz’s Law

b) Anticlockwise
[Solution Description]
Lenz's law states that the direction of the induced current will oppose the change causing it. When the magnet moves towards the loop, the magnetic flux through the loop increases. To oppose this increase, the induced current will flow in such a direction that it creates a magnetic field opposite to the magnet's field. Using the right-hand rule, if the north pole of the magnet approaches the loop, the induced current will flow clockwise when viewed from the magnet's side, creating a south pole to repel the approaching north pole.

Key Concept: Transformer - Principle

c) D.C. produces a constant magnetic flux
[Solution Description]
A transformer works on the principle of electromagnetic induction, which requires a changing magnetic flux to induce an e.m.f. in the secondary coil. With a D.C. source, the current is constant, so there is no change in magnetic flux, hence no induced e.m.f. in the secondary coil.

Key Concept: Frequency of a.c. in household supplies

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the frequency of alternating current is determined by the number of polarity changes per second. This is true because frequency is defined as the number of cycles (or complete alternations) per second. The reason states that in India, the standard frequency is 50 Hz, meaning the current changes direction 100 times per second (since each cycle includes both positive and negative peaks). Both statements are true, and the reason correctly explains the assertion.

Key Concept: Force on Conductor, Fleming’s Left-Hand Rule

b) South
[Solution Description]
Apply Fleming’s left-hand rule: Point the forefinger (magnetic field) upwards, middle finger (current) eastward; the thumb gives the direction of force. Here, the force will be directed southward.

Key Concept: Transformer Core Material

b) It minimizes energy losses
[Solution Description]
Soft iron is used in transformer cores because it minimizes energy losses due to hysteresis and eddy currents. The laminated structure further reduces eddy current losses.

Key Concept: Construction of AC generator, Slip rings, Brushes

b) The generator produces direct current instead of alternating current
[Solution Description]
In an AC generator, slip rings allow continuous contact between the rotating coil and the external circuit, maintaining alternating current output. If replaced with a split ring commutator, it would reverse the connection of the coil to the external circuit every half rotation, converting AC output to pulsating DC. The brushes remain stationary while the split rings rotate, reversing polarity periodically.
Step 1: Identify the role of slip rings in AC generators → continuous AC output.
Step 2: Understand split ring commutator function → reverses connections, producing DC.
Step 3: Conclusion: Replacement converts AC to pulsating DC.

Key Concept: Electromagnet vs Permanent Magnet

d) Polarity can be reversed
[Solution Description]
An electromagnet is made of soft iron and produces a temporary magnetic field when current flows through its coil. Its polarity can be reversed by changing the direction of current, and it can be easily demagnetized by switching off the current. A permanent magnet is made of steel, has a fixed polarity, and retains its magnetism unless subjected to extreme conditions. Based on this, the correct statement is that the polarity of an electromagnet can be reversed.

Key Concept: Uses of Electromagnet

b) Electric bell
[Solution Description]
An electromagnet is widely used in an electric bell. The electromagnet attracts the armature when current flows, causing the hammer to strike the gong and produce sound. When the circuit breaks, the electromagnet demagnetizes, and the cycle repeats.

Key Concept: Magnetic Field Magnitude \& Superposition Principle

b) $\frac{\mu_0 I}{\pi d}$
[Solution Description]
Step 1: Magnetic field due to first wire ($I$) on middle wire ($2I$): $B_1 = \frac{\mu_0 I}{2 \pi d}$ (direction towards third wire).
Step 2: Magnetic field due to third wire ($3I$) on middle wire: $B_2 = \frac{\mu_0 (3I)}{2 \pi d}$ (opposite to $B_1$ since currents are in same direction).
Step 3: Net field = $\left|\frac{3\mu_0 I}{2 \pi d} - \frac{\mu_0 I}{2 \pi d}\right| = \frac{\mu_0 I}{\pi d}$ (resultant direction towards first wire).
\fieldset{$\frac{\mu_0 I}{2 \pi d}$}
\fieldset{$\frac{\mu_0 I}{\pi d}$}
\fieldset{$\frac{3\mu_0 I}{2 \pi d}$}
\fieldset{$\frac{5\mu_0 I}{2 \pi d}$}

Key Concept: Faraday's Law of Electromagnetic Induction

c) Electromagnetic induction
[Solution Description]
According to Faraday's Law of Electromagnetic Induction, when there is a change in magnetic flux linked with a conductor, an e.m.f. is induced. This phenomenon is known as electromagnetic induction.

Key Concept: Principle of operation, Energy conversion

c) It operates by force acting on a current-carrying conductor in a magnetic field.
[Solution Description]
The device described is converting electrical energy to mechanical energy, which matches the definition of a DC motor. A DC motor operates on the principle of force acting on a current-carrying conductor placed in a magnetic field. Here, the battery supplies direct current (DC), causing the coil in the motor to rotate due to the interaction between the magnetic field and the current. This rotation demonstrates mechanical energy being produced from electrical energy.

Key Concept: Permanent Magnet

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that steel is used to make permanent magnets due to its high retentivity, which is true. The reason explains that high retentivity allows the material to retain magnetism for a long time, which is also true and correctly explains why steel is used for permanent magnets. Thus, both the assertion and reason are correct, and the reason is the correct explanation of the assertion.

Key Concept: Lenz's Law, Conservation of Energy

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
First, let's analyze the Assertion (A):
- When a magnet moves away from a conducting loop, the magnetic flux through the loop decreases.
- According to Faraday's law, an induced current is generated to oppose this decrease in flux.
Now, examine the Reason (R):
- Lenz’s law states that the induced current will create a magnetic field opposing the change in the original flux. This aligns with conservation of energy, as the system resists the external change.
Conclusion:
Both Assertion and Reason are true, and Reason correctly explains Assertion because the opposition to decreasing flux (Assertion) arises due to Lenz's law (Reason).

Key Concept: Polarity of U-shaped electromagnet

d) Poles get reversed
[Solution Description]
The polarity of the electromagnet depends on the direction of the current. Reversing the current reverses the magnetic field, thereby reversing the poles.

Key Concept: Magnetic effect of current, Direction of magnetic field

d) Assertion is false, but Reason is true.
[Solution Description]
According to Oersted’s experiment, when the current flows from south to north (A to B), the compass needle placed above the wire deflects its north pole towards the west, not the east as stated in the Assertion. Therefore, the Assertion is false. However, the Reason correctly describes the right-hand thumb rule for determining the direction of the magnetic field around a current-carrying wire, which is true. Since the Assertion is false and the Reason is true, the correct option is (d).

Key Concept: Magnetic Field Direction

c) Towards the west
[Solution Description]
According to Oersted’s experiment, when current flows from south to north in a wire placed along the north-south direction, the magnetic field produced around the wire causes the north pole of the compass needle to deflect towards the west when placed just below the wire.

Key Concept: Polarity Determination

b) South pole (S)
[Solution Description]
According to the clock rule:
- Clockwise current at a face indicates a south pole (S).
- Anticlockwise current at a face indicates a north pole (N).
Since the current is clockwise when viewed from the end, this end behaves as a south pole.

Key Concept: Electromagnetic Induction - Faraday's Law and Lenz's Law

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that moving a magnet towards a coil induces a current in the coil, which is true according to Faraday's law of electromagnetic induction. The reason correctly states that Lenz's law determines the direction of this induced current such that it opposes the change in magnetic flux causing it, which is consistent with the principle of conservation of energy. Therefore, both the Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Magnetic field formula

a) It becomes half
[Solution Description]
The magnetic field strength $B$ is inversely proportional to the distance $r$ from the wire ($B = \frac{\mu_0 I}{2 \pi r}$). If $r$ doubles, $B$ becomes half.

Key Concept: Effect of reversing current or field

b) The force reverses its direction
[Solution Description]
According to observations, reversing the direction of the current reverses the direction of the force. Hence, the force will be $-F$, i.e., opposite to the original direction. The magnitude remains the same.

Key Concept: Applicability of Fleming’s Left-Hand Rule

d) Current is parallel to the magnetic field
[Solution Description]
Fleming’s left-hand rule applies only when the current and magnetic field are perpendicular to each other. If the current is parallel to the magnetic field, no force acts on the conductor. Hence, the rule cannot be applied in this case.

Key Concept: Right-hand thumb rule, Multiple conductors

b) Into the plane
[Solution Description]
1. For Conductor A (upward current), the right-hand rule gives a field into the plane at the midpoint.
2. For Conductor B (downward current), the field is also into the plane at the midpoint.
3. Both fields add up, resulting in a stronger field into the plane.

Key Concept: Effective value, RMS value

b) 10 A
[Solution Description]
The RMS value of an alternating current is given by:
$I_{\text{rms}} = \frac{I_0}{\sqrt{2}}$
Here, the peak current ($I_0$) is 14.14 A.
Substituting the value:
$I_{\text{rms}} = \frac{14.14}{\sqrt{2}} = \frac{14.14}{1.414} = 10 \, \text{A}$.
Hence, the RMS current is 10 A.

Key Concept: Fleming’s Right-Hand Rule

b) Magnetic field
[Solution Description]
Fleming’s Right-Hand Rule helps determine the direction of induced current. The thumb points in the direction of motion of the conductor, the forefinger points in the direction of the magnetic field, and the central finger gives the direction of the induced current.

Key Concept: Electromagnet Applications

c) Electric bell
[Solution Description]
According to the syllabus, U-shaped electromagnets are used in gadgets like electric bells, dc motors, ac generators, etc., due to their strong magnetic field in the gap between poles.
Step-by-step explanation:
1. An electric bell uses a U-shaped electromagnet to attract and release the armature repeatedly.
2. The electromagnet creates a magnetic field that pulls the soft iron armature, causing the hammer to strike the gong.
3. The circuit breaks momentarily, demagnetizing the electromagnet and resetting the armature for the next cycle.

Key Concept: Force on a Current-Carrying Conductor

c) Fleming’s Left-Hand Rule.
[Solution Description]
The direction of force on a current-carrying conductor placed in a magnetic field is given by Fleming's Left-Hand Rule. If the forefinger points in the direction of the magnetic field, the middle finger in the direction of current, then the thumb gives the direction of force.

Key Concept: Magnetic Field Strength

c) Reversing the direction of current
[Solution Description]
The magnetic field strength of a U-shaped electromagnet can be increased by increasing the number of turns in the winding or by increasing the current through the solenoid. However, reversing the direction of current only changes the polarity but does not affect the strength of the magnetic field.

Key Concept: Electromagnet vs Permanent Magnet

d) An electromagnet’s magnetic field disappears when the current stops
[Solution Description]
An electromagnet produces a temporary magnetic field when current flows through its coil, while a permanent magnet always produces a magnetic field. The strength of an electromagnet can be changed by altering the current or number of turns in the coil. A permanent magnet cannot have its polarity reversed, unlike an electromagnet.

Key Concept: Field line visualization

b) Concentric circles around the conductor
[Solution Description]
Iron filings align themselves along the direction of the magnetic field lines. For a current-carrying conductor, these field lines form concentric circles around the conductor, as described by the right-hand thumb rule. The filings will thus arrange in circular patterns centered on the conductor.

Key Concept: Comparison with Electromagnet

c) Produces a permanent magnetic field
[Solution Description]
Unlike an electromagnet, which requires an external current to produce a magnetic field, a permanent magnet produces a magnetic field without any external power source. Additionally, a permanent magnet cannot have its polarity reversed easily or change its magnetic field strength.

Key Concept: Frequency, Cycle Duration

c) 50 Hz
[Solution Description]
Frequency ($f$) is the reciprocal of the time period ($T$) for one complete cycle. Given $T = 0.02$ s, $f = 1/T = 1/0.02 = 50$ Hz.

Key Concept: Fleming’s Left-Hand Rule

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that according to Fleming’s left-hand rule, the thumb points in the direction of force when the current (central finger) and magnetic field (forefinger) are known. This is correct as per the rule. The reason explains that the force is perpendicular to both the current and magnetic field directions, which is a fundamental property of electromagnetic forces. The reason correctly explains why the thumb (force) is perpendicular to both the forefinger (magnetic field) and central finger (current) in Fleming’s left-hand rule.
Thus, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Faraday’s First Law

b) Whenever there is a change in magnetic flux linked with the coil
[Solution Description]
Faraday's first law states that an e.m.f. is induced in a coil whenever there is a change in the magnetic flux linked with the coil. The e.m.f. lasts as long as the change in flux continues.

Key Concept: Magnetic Field Due to Current in a Straight Wire

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion (A) is true because the Right-Hand Thumb Rule is indeed used to determine the direction of the magnetic field lines around a current-carrying straight wire. The Reason (R) is also true as it correctly explains the Right-Hand Thumb Rule, relating the direction of current (thumb) to the direction of the magnetic field lines (curled fingers). Moreover, Reason (R) provides the correct explanation for Assertion (A).

Key Concept: A.C. Generator - Principle and Working

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to Faraday's law of electromagnetic induction, the magnitude of the induced e.m.f. in a coil rotating in a magnetic field depends on the rate of change of magnetic flux ($\phi$) linked with the coil. When the plane of the coil is parallel to the magnetic field (θ = 90°), no magnetic flux passes through the coil ($\phi = 0$). However, the rate of change of flux is maximum at this position because the coil is moving perpendicular to the field lines, resulting in the highest induced e.m.f. Therefore, both Assertion and Reason are true, and Reason correctly explains the Assertion.

Key Concept: Multi-concept: Field outside solenoid, right-hand rule

c) Zero.
[Solution Description]
Outside the solenoid, the magnetic field is negligible ($B \approx 0$). The electron's velocity $\vec{v}$ is parallel to the axis, but since $B = 0$, the Lorentz force $F = q(\vec{v} \times \vec{B}) = 0$.
Calculation:
1. $B_{\text{outside}} \approx 0$.
2. Force $F = -e (v \hat{i} \times 0 \hat{j}) = 0$.

Key Concept: Field Variation with Distance \& Current Dependence

c) $\frac{\mu_0 (I_0 + kt)}{2 \pi r}$
[Solution Description]
Step 1: Substitute $I = I_0 + kt$ into $B = \frac{\mu_0 I}{2 \pi r}$.
Step 2: Thus, $B(t) = \frac{\mu_0 (I_0 + kt)}{2 \pi r}$.
Step 3: The field increases linearly with time due to the term $kt$.
\fieldset{$\frac{\mu_0 I_0}{2 \pi r}$}
\fieldset{$\frac{\mu_0 k}{2 \pi r}$}
\fieldset{$\frac{\mu_0 (I_0 + kt)}{2 \pi r}$}
\fieldset{$\frac{\mu_0 (I_0 - kt)}{2 \pi r}$}

Key Concept: Direction reversal, Applications in D.C. Motor

c) Force magnitude remains the same, direction reverses
[Solution Description]
From Fleming's Left-Hand Rule, reversing the current direction reverses the direction of the force. The magnitude remains the same as it depends on $I$, $B$, and $l$.

Key Concept: Split ring commutator, Brushes, DC motor

c) The motor oscillates without completing full rotations
[Solution Description]
The split ring commutator reverses the current direction in the coil every half-rotation to maintain unidirectional torque. If replaced with a continuous ring, the current direction won’t reverse, causing the coil to oscillate around its mean position instead of rotating continuously.
Step 1: Split ring function → reverses current for continuous rotation.
Step 2: Continuous ring → no current reversal, leading to oscillations.
Step 3: Result: Motor fails to rotate continuously.

Key Concept: Force on a Current-Carrying Conductor in a Magnetic Field

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that a current-carrying wire placed perpendicular to a magnetic field experiences a force, determined by Fleming's left-hand rule. This is true as the force $F = I \cdot B \cdot l$ acts perpendicular to both the current and magnetic field directions. The Reason explains that this force arises due to the interaction of the magnetic field produced by the current with the external magnetic field, which is also correct and accurately explains the Assertion. Hence, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Fleming's Left Hand Rule

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion (A) correctly describes Fleming's left hand rule where the thumb gives the direction of force (\textbf{F}), the forefinger gives the direction of the magnetic field (\textbf{B}), and the middle finger gives the direction of current (\textbf{I}). The reason (R) is also true because Fleming's left hand rule is indeed only applicable when the current and magnetic field are perpendicular to each other. Furthermore, the reason correctly explains why the assertion works, as the rule is designed specifically for perpendicular scenarios.

Key Concept: Electric Generators, Induced EMF

c) 288$\pi$ V
[Solution Description]
Peak EMF is given by:
$\epsilon_0 = NAB\omega$
Area A = 0.2 m × 0.3 m = 0.06 m\textsuperscript{2}
Angular frequency ω = 2πf = 2π×60 = 120π rad/s
Calculate peak EMF:
$\epsilon_0 = 50 \times 0.06 \times 0.8 \times 120\pi = 288\pi$ V ≈ 904.78 V

Key Concept: Electromagnet, Current Reversal, AC Operation

c) Magnetic attraction is independent of polarity
[Solution Description]
The working principle of an electric bell relies on magnetic attraction which doesn't depend on polarity:
1) With DC: The electromagnet maintains constant polarity while current flows.
2) With AC: The polarity reverses periodically (50/60 times per second), but the armature is still attracted regardless of polarity.
3) The make-and-break mechanism works similarly in both cases as it depends only on the presence of magnetic field, not its direction.
Thus, the correct reason is that magnetic attraction is independent of polarity.

Key Concept: Faraday's Laws of Electromagnetic Induction, Lenz's Law

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to Faraday's Second Law, the magnitude of the induced e.m.f. is proportional to the rate of change of magnetic flux ($\mathcal{E} = -N \frac{d\phi}{dt}$). Lenz's Law states that the induced current opposes the change in magnetic flux. Therefore, both Assertion and Reason are true, and Reason correctly explains Assertion since the opposition is due to the induced current creating its own magnetic field to counteract the change.

Key Concept: Advantage of AC over DC

b) A.C. can be easily transformed to higher or lower voltages, reducing transmission losses.
[Solution Description]
The syllabus mentions that a.c. can be easily stepped up or down using transformers, reducing energy loss during transmission, unlike d.c., which cannot be transformed efficiently.

Key Concept: Frequency of a.c., Transformer, A.C. Generator

c) Assertion is true, but Reason is false.
[Solution Description]
The Assertion (A) is true because the frequency of the alternating current (a.c.) in household supplies (e.g., 50 Hz or 60 Hz) is indeed determined by the rotational speed of the generator's coil in the power station. The faster the coil rotates, the higher the frequency of the generated a.c.
The Reason (R) is false because transformers do not change the frequency of the alternating current. They only change the voltage level while keeping the frequency unchanged. The transformer operates on the principle of electromagnetic induction and maintains the same frequency in the secondary coil as in the primary coil.
Therefore, Assertion is true, but Reason is false.

Key Concept: Magnetic Field Direction

b) Anticlockwise
[Solution Description]
According to the Right Hand Thumb Rule, if the thumb points in the direction of the current (upward), the fingers curl in the direction of the magnetic field lines. For an upward current, the magnetic field lines are concentric circles in the anticlockwise direction.

Key Concept: Electromagnet vs Permanent Magnet

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that an electromagnet can produce a stronger magnetic field than a permanent magnet, which is true as per the syllabus (Section 10.8). The Reason explains that the strength of an electromagnet’s magnetic field can be adjusted by changing the current in its solenoid, which is also correct (Section 10.9). Furthermore, the Reason directly explains why the Assertion is true since the adjustable current allows for a stronger field. Therefore, both statements are true, and the Reason correctly explains the Assertion.

Key Concept: Oersted's Experiment

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to Oersted’s experiment, when an electric current passes through a conducting wire, it produces a magnetic field around it. This magnetic field exerts a torque on the compass needle, causing it to deflect. Thus, both Assertion (A) and Reason (R) are true, and Reason (R) correctly explains Assertion (A).

Key Concept: Lenz’s Law and Induced Current

a) The solenoid repels the magnet due to the induced current.
[Solution Description]
According to Lenz's law, the direction of the induced current opposes the change causing it. Here, the magnet moves towards the solenoid, so the induced current flows in a direction that creates a magnetic field opposing the incoming magnet. This ensures energy conservation as mechanical work done against the opposing force converts into electrical energy.

Key Concept: Electromagnet vs. Permanent magnet, Retentivity

c) An electromagnet loses its magnetism faster than a permanent magnet
[Solution Description]
Retentivity is the ability of a material to retain its magnetism after the external magnetizing force is removed. An electromagnet is made of soft iron, which has low retentivity, meaning it loses its magnetism quickly when the current is switched off. A permanent magnet is made of steel, which has high retentivity, so it retains its magnetism even after the external magnetizing force is removed.

Key Concept: Fleming’s left hand rule, Force direction

b) Force direction remains the same as if perpendicular
[Solution Description]
Step 1: Fleming’s rule assumes mutual perpendicularity. For non-perpendicular cases, only the perpendicular component ($B \sin\theta$) contributes to force.
Step 2: At 30°, $\sin(30°) = 0.5$, so force magnitude reduces but direction follows the same thumb rule (assuming orthogonal components).
Step 3: The angle changes force magnitude, not its direction relative to the defined axes.

Key Concept: Magnetic Field Due to Current

b) Zero
[Solution Description]
When two parallel wires carry currents in the same direction, the magnetic fields due to each wire at the midpoint are equal in magnitude but opposite in direction (as per the right hand thumb rule). Hence, they cancel each other out, resulting in zero net magnetic field at the midpoint.

Key Concept: Lenz’s Law Direction of Induced Current

b) Opposes the change in magnetic flux
[Solution Description]
Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux producing it. This means the induced current creates its own magnetic field to resist the change causing it.

Key Concept: Magnetic Field Strength, Polarity Reversal

b) Electromagnet because its field strength and polarity can be controlled
[Solution Description]
The problem requires a magnet whose field strength can be changed and its polarity reversed.
1. An electromagnet is made of soft iron and allows adjusting the magnetic field strength by changing the current or number of turns in the coil.
2. It also permits reversing the polarity by reversing the direction of current, unlike a permanent magnet.
3. Thus, an electromagnet satisfies both conditions mentioned in the question.

Key Concept: Step-up Transformer

c) $N_s > N_p$
[Solution Description]
A step-up transformer increases the voltage from primary to secondary coil, which requires more turns in the secondary coil ($N_s > N_p$).

Key Concept: A.C. Generator - Working

b) When the coil is parallel to the magnetic field
[Solution Description]
The induced e.m.f. in an A.C. generator is maximum when the rate of change of magnetic flux linked with the coil is maximum. This occurs when the plane of the coil is parallel to the magnetic field lines, i.e., $\theta = 90^\circ$ or $270^\circ$.

Key Concept: Frequency and Maximum e.m.f.

b) 6.28 V
[Solution Description]
The formula for maximum e.m.f. induced is:
$e_0 = 2\pi n B A N$
Given,
$n = 50 \text{Hz}$,
$B = 0.02 \text{T}$,
$A = 0.01 \text{m}^2$,
$N = 100$ turns.
Substituting the values,
$e_0 = 2\pi \times 50 \times 0.02 \times 0.01 \times 100 = 6.28 \text{V}$

Key Concept: AC source, Soft iron core

c) The magnetic field strength reverses polarity but remains strong.
[Solution Description]
With an AC source, the current direction alternates 50 times per second, causing the polarity of the magnetic field to reverse at the same rate. However, the soft iron core continually aligns with the changing field, maintaining magnetization. Therefore, the average magnetic field strength remains comparable to that of a DC source, despite rapid polarity changes.

Key Concept: Eddy Currents

c) Eddy currents
[Solution Description]
Induction cooktops use electromagnetic induction to generate eddy currents in the metal vessel placed on them. These eddy currents flow in closed loops within the conductor (vessel) due to the changing magnetic field produced by the alternating current in the cooktop's coil. The resistance of the vessel material causes these currents to dissipate energy as heat, thereby heating the vessel.

Key Concept: Applications of Electromagnet

d) The hammer stops striking the gong as the electromagnet loses its magnetism.
[Solution Description]
The electromagnet in an electric bell gets magnetized when current flows through it, attracting the soft iron armature and causing the hammer to strike the gong. When the current is switched off, the electromagnet loses its magnetism, releasing the armature, and the hammer moves back due to the spring strip, stopping the ringing sound.

Key Concept: Electromagnet

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The syllabus states that an electromagnet is made by passing current through a coil wound around soft iron, which becomes magnetized when current flows but loses its magnetism immediately after the current is switched off because soft iron has low retentivity. The Assertion correctly describes this behavior of an electromagnet. The Reason provides the correct explanation for why the Assertion is true, as low retentivity means the material cannot retain magnetism without external current. Hence, both are true and related.

Key Concept: Working Principle

b) Force on a current-carrying conductor in a magnetic field
[Solution Description]
A D.C. motor works on the principle of force acting on a current-carrying conductor placed in a magnetic field, converting electrical energy into mechanical energy.

Key Concept: Force on a Current-Carrying Conductor

c) $BIl$
[Solution Description]
The force on a current-carrying conductor in a magnetic field is given by $F = BIl\sin\theta$. Since the conductor is perpendicular to the magnetic field, $\theta = 90^\circ$ and $\sin(90^\circ) = 1$. Therefore, the force is $F = BIl$.

Key Concept: Transformer Working Principle

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
A transformer works on the principle of electromagnetic induction, which requires a changing magnetic flux to induce an e.m.f. in the secondary coil. A direct current (d.c.) source provides a constant current, resulting in a constant magnetic field. Since there is no change in the magnetic flux linkage with the secondary coil, no e.m.f. is induced. Therefore, both Assertion (A) and Reason (R) are true, and Reason (R) correctly explains Assertion (A).

Key Concept: Induced e.m.f., Frequency, Maximum e.m.f.

b) $40π$ V
[Solution Description]
The formula for maximum e.m.f. is:
$e_0 = 2πnBAN$
Given:
- Rotation frequency, $n = 50 \, \text{Hz}$
- Magnetic field strength, $B = 0.1 \, \text{T}$
- Cross-sectional area, $A = 0.02 \, \text{m}^2$
- Number of turns, $N = 200$
Plugging in the values:
$e_0 = 2π \times 50 \times 0.1 \times 0.02 \times 200$
Step 1: Multiply $2π \times 50 = 100π$
Step 2: Multiply $100π \times 0.1 = 10π$
Step 3: Multiply $10π \times 0.02 = 0.2π$
Step 4: Multiply $0.2π \times 200 = 40π$
Finally, the maximum e.m.f. is $40π \, \text{V}$.

Key Concept: Construction of U-shaped electromagnet, Magnetic polarity, Current direction

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion (A) states that reversing the current direction in the coil of a U-shaped electromagnet reverses the polarity of its poles. This is true because the magnetic polarity of an electromagnet is determined by the right-hand thumb rule, which links the direction of current flow to the magnetic field produced. If the current direction is reversed, the magnetic field lines also reverse, leading to a reversal of the poles.
The reason (R) correctly explains assertion (A) as it directly links the magnetic polarity to the direction of current flow. Since both the assertion and the reason are true and the reason correctly explains the assertion, the correct option is:

Key Concept: Force on Current-Carrying Conductor, Fleming’s Left-Hand Rule

c) Perpendicular to both the current and the magnetic field
[Solution Description]
According to Fleming’s left-hand rule: stretch the thumb, forefinger, and middle finger of the left hand such that they are mutually perpendicular. The forefinger points in the direction of the magnetic field ($B$), the middle finger in the direction of the current ($I$), and the thumb gives the direction of the force ($F$). Here, the force is perpendicular to both $B$ and $I$.

Key Concept: Polarity Reversal

d) Electromagnet
[Solution Description]
An electromagnet's polarity can be reversed by changing the direction of current flow in the solenoid. This is not possible with a permanent magnet.

Key Concept: Uses of electromagnet, Electric bell

c) The hammer strikes the gong repeatedly
[Solution Description]
In an electric bell, when the circuit is closed, current flows through the electromagnet, creating a magnetic field. This attracts the soft iron armature, causing the hammer to strike the gong. The movement of the armature breaks the circuit, demagnetizing the electromagnet, and the spring pulls the armature back, completing the circuit again. This cycle repeats, producing continuous ringing.

Key Concept: Field strength change, Multiple concepts

b) Field strength doubles and filings show extended pattern
[Solution Description]
From the formula $B = \frac{\mu_0 I}{2 \pi r}$, we see that magnetic field is directly proportional to current. Doubling the current doubles the magnetic field strength.
Regarding the iron filings:
- The increased field strength makes the field detectable at greater distances
- The filings arrange themselves in concentric circles
- The circles become more dense because the field is stronger
- The radius of observable patterns increases as the field extends further
So both the strength increases and the observable pattern expands outward.

Key Concept: Right Hand Thumb Rule Application

c) Direction of magnetic field lines
[Solution Description]
The right-hand thumb rule states that if the thumb points in the direction of the current, the curled fingers indicate the direction of the circular magnetic field lines around the wire.

Key Concept: Magnetic Field due to Straight Wire

b) Concentric circles around the wire
[Solution Description]
Iron filings align themselves along the magnetic field lines generated by the current-carrying wire. For a straight wire, these field lines are concentric circles centered on the wire.

Key Concept: Fleming’s left-hand rule, Split ring commutator

c) The force reverses its direction while maintaining the same magnitude
[Solution Description]
According to Fleming’s left-hand rule, the force acting on a current-carrying conductor in a magnetic field is given by $F = BIL\sin\theta$. The direction of the force depends on the current direction and magnetic field orientation. When the split-ring commutator reverses the current direction in the coil at the end of each half rotation, the direction of the force also reverses. This ensures continuous rotation in one direction despite the periodic reversals.

Key Concept: Force calculation, combined concepts

b) 0.60 N
[Solution Description]
First find original magnetic field B using F = IBl:
0.6 = 8 × B × 2.5 → B = 0.6/(8×2.5) = 0.03 T
Now calculate new force with I=5A, l=4m:
F = 5 × 0.03 × 4 = 0.6 N
The force remains same despite changes.

Key Concept: Neutral Point

b) Far away from the wire
[Solution Description]
A neutral point occurs where the magnetic field due to the current-carrying wire and the Earth's magnetic field are equal and opposite, resulting in a net magnetic field of zero. This usually happens at a certain distance from the wire where the two fields balance each other.

Key Concept: Magnetic field due to current-carrying wire, Right-Hand Thumb Rule

d) Assertion is false, but Reason is true.
[Solution Description]
In Oersted's experiment, when the compass needle is placed above the wire with current flowing from south to north, the north pole of the needle deflects towards the east, not west (Assertion is false). The Reason correctly states the nature of magnetic field lines and the application of the Right-Hand Thumb Rule, which is true.

Key Concept: Faraday's law, energy consideration

c) 0.08 W
[Solution Description]
The induced emf is generated due to the motion of the loop in the magnetic field: $e = B l v = 0.4 \times 0.2 \times 5 = 0.4\, \text{V}$.
The induced current is $I = \frac{e}{R} = \frac{0.4}{2} = 0.2\, \text{A}$.
The force opposing the motion is $F = I l B = 0.2 \times 0.2 \times 0.4 = 0.016\, \text{N}$.
The mechanical power required is $P = F v = 0.016 \times 5 = 0.08\, \text{W}$.

Key Concept: Soft iron core, Current

d) It decreases compared to the original field strength.
[Solution Description]
The presence of a soft iron core significantly increases the magnetic field strength due to its high permeability. If the core is removed, the field decreases. Doubling the current without the core will increase the field, but not enough to compensate for the loss of the core's effect. Assuming initial field $B_1 = k \cdot (N \cdot I \cdot \mu_{core})$, after removal, the field becomes $B_2 = k \cdot (N \cdot 2I \cdot \mu_{air})$, where $\mu_{air} \ll \mu_{core}$. Hence, $B_2 < B_1$.

Key Concept: Transformer Principle

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
A transformer operates based on electromagnetic induction. When an alternating current flows through the primary coil, it creates a varying magnetic field. This varying magnetic field links with the secondary coil, inducing an electromotive force (e.m.f.) in it. Thus, both Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Horse-shoe magnet, Armature rotation, Energy conversion

c) The direction of rotation reverses
[Solution Description]
The direction of rotation of the armature coil in a DC motor is determined by the relative directions of the current in the coil and the magnetic field (Fleming’s left-hand rule). Reversing the polarity of the horse-shoe magnet reverses the direction of the magnetic field. Consequently, the direction of the force acting on the coil—and hence the direction of rotation—will reverse. However, the split-ring commutator continues to reverse the current direction in the coil at the appropriate times, ensuring the motor continues to run smoothly but now in the opposite direction.

Key Concept: Fleming's Left Hand Rule

b) Forefinger
[Solution Description]
In Fleming's left hand rule, the forefinger (index finger) points in the direction of the magnetic field ($B$).

Key Concept: Electromagnet Construction

d) The north and south poles interchange their positions.
[Solution Description]
The polarity of an electromagnet depends on the direction of current flow in the solenoid. In a U-shaped electromagnet, the end where the current flows clockwise becomes the south pole, and the end with anticlockwise current becomes the north pole. Reversing the current reverses the direction of these polarities.
Step-by-step explanation:
1. Initially, let’s say arm P has clockwise current (south pole) and arm Q has anticlockwise current (north pole).
2. When current direction is reversed, the current in arm P becomes anticlockwise (north pole) and in arm Q becomes clockwise (south pole).
3. Thus, the polarities at the ends are reversed.

Key Concept: Transformer Principle

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that a transformer works only with alternating current (a.c.), which is true because an a.c. source produces a continuously changing magnetic flux in the primary coil. The reason explains that this changing flux is necessary for inducing an e.m.f. in the secondary coil via electromagnetic induction, which directly justifies the assertion. Hence, both are true, and the reason correctly explains the assertion.

Key Concept: Main parts of an electric motor

c) Split ring commutator
[Solution Description]
The split ring commutator in an electric motor reverses the direction of current in the armature coil every half rotation. This ensures continuous rotation of the coil in the same direction.

Key Concept: Transformer, AC vs DC

d) DC does not produce a changing magnetic field needed for induction.
[Solution Description]
A transformer works on the principle of electromagnetic induction, which requires a changing magnetic field to induce an emf in the secondary coil. In DC, the current is constant (no change in flux), so there is no induced emf in the secondary coil. Thus, transformers cannot be used with DC sources.

Key Concept: Electromagnet Polarity Change

b) The bell rings continuously as the armature remains attracted irrespective of polarity changes.
[Solution Description]
The working of the electric bell depends on the magnetic attraction between the electromagnet and the armature, regardless of polarity. When a.c. is used, the polarity of the electromagnet reverses periodically, but since the armature is made of soft iron (which gets attracted regardless of polarity), the bell continues to ring as long as the circuit is closed.

Key Concept: Magnetic Field Due to Current in a Straight Wire, Right-Hand Thumb Rule

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that magnetic field lines around a straight current-carrying wire are concentric circles centered on the wire, which is true as observed in experiments with iron filings. The Reason refers to the right-hand thumb rule, which correctly describes the relationship between the current direction and the resulting magnetic field direction. The Reason provides a valid explanation for the pattern described in the Assertion.

Key Concept: Magnetic field inside solenoid, Polarity of solenoid

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
To analyze the assertion and reason:
1) For an ideal solenoid, the magnetic field inside is indeed uniform and directed along the axis due to symmetry. This is because the solenoid's length is much greater than its diameter, and the field lines are parallel and closely spaced.
2) The reason states that the transverse components cancel out due to the helical nature of the current flow in adjacent loops. This is correct because the current in neighboring turns flows in opposite transverse directions, leading to cancellation of transverse field components, while the axial components add up.
3) Thus, the reason correctly explains why the assertion is true for an ideal solenoid.

Key Concept: Circuit Make-and-Break Mechanism

c) The armature alternately makes and breaks the circuit, creating intermittent strikes.
[Solution Description]
The armature moves towards the electromagnet when current flows, breaking the contact with the screw. This interrupts the circuit, demagnetizing the electromagnet. The spring strip then pulls the armature back, re-establishing contact and restarting the cycle. This make-and-break mechanism causes the hammer to strike the gong repeatedly.

Key Concept: Electromagnetic Induction, Faraday’s Observations

c) The deflection doubles
[Solution Description]
From Faraday’s observations, the magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux, which depends on the speed of the magnet. If the speed is doubled, the induced e.m.f. increases, causing a larger deflection in the galvanometer.

Key Concept: Electromagnet vs Permanent Magnet

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that an electromagnet can be demagnetized by switching off the current in its coil, which is true because an electromagnet operates only when current flows through it. The reason states that an electromagnet is made of soft iron, which has low retentivity, and this is also true since soft iron loses its magnetism quickly once the current is turned off. Furthermore, the reason correctly explains why the assertion is true because low retentivity of soft iron allows quick demagnetization when the current is switched off.

Key Concept: Faraday’s Laws, Lenz’s Law

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
Faraday’s second law states that the magnitude of the induced e.m.f. is proportional to the rate of change of magnetic flux. Lenz’s Law further explains that the direction of the induced current opposes the change in flux, ensuring energy conservation. Here, the Assertion correctly describes the behavior of induced current, and the Reason accurately provides the underlying principle (Lenz’s Law). Thus, both are true, and the Reason correctly explains the Assertion.

Key Concept: Magnetic Field Direction

c) Into the plane (away from the observer)
[Solution Description]
Using the right-hand thumb rule:
\begin{itemize}

Key Concept: Force direction, Fleming's left hand rule

b) Vertically upwards
[Solution Description]
Using Fleming's left hand rule:
First finger points north (magnetic field)
Middle finger points east (current)
Thumb gives force direction upward (vertically upwards)
So the force acts vertically upwards.

Key Concept: Polarity Reversal

c) Changing the direction of current in the solenoid
[Solution Description]
The polarity of an electromagnet can be reversed simply by changing the direction of the current flowing through its solenoid. This is not possible with a permanent magnet, as its polarity is fixed.

Key Concept: Transformer Principle

b) Electromagnetic induction
[Solution Description]
A transformer operates based on electromagnetic induction, where a changing magnetic field in the primary coil induces an electromotive force (emf) in the secondary coil. Thus, its principle is electromagnetic induction.

Key Concept: Factors affecting induced e.m.f.

c) The rate of change of magnetic flux and the number of turns in the coil
[Solution Description]
The magnitude of the induced e.m.f. depends on:
1. The rate of change of magnetic flux linked with each turn, and
2. The number of turns in the coil.
Thus, both the number of turns and the rate of change of flux are key factors.

Key Concept: Frequency of AC in household supplies

b) 50 Hz
[Solution Description]
The syllabus states that in India, the frequency of alternating current supplied in households and factories is 50 Hz.

Key Concept: Use of Electromagnet in an Electric Bell

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the armature in an electric bell is made of soft iron, which is true because soft iron is used to allow quick magnetization and demagnetization. The reason provided is also correct as soft iron indeed exhibits these properties, making it suitable for use in electric bells. Furthermore, the reason correctly explains why soft iron is chosen for the armature in an electric bell.

Key Concept: Direction of force using Fleming's left-hand rule

d) Upward
[Solution Description]
According to Fleming’s left-hand rule, the thumb represents the force ($F$), forefinger the magnetic field ($B$), and middle finger the current ($I$).
- Point the forefinger eastward (magnetic field).
- Point the middle finger southward (current direction).
- The thumb then points upward, indicating the force acts vertically upwards.
Thus, the force is directed upward.

Key Concept: Factors Affecting Induced E.M.F.

c) Resistance of the coil
[Solution Description]
The magnitude of the induced e.m.f. in a coil is given by $e = -N \frac{d\phi}{dt}$. It depends on:
1. The number of turns ($N$) in the coil.
2. The rate of change of magnetic flux ($\frac{d\phi}{dt}$).
The resistance of the coil affects the induced current if the circuit is closed but does not affect the induced e.m.f. itself.

Key Concept: Construction of A.C. Generator

c) To maintain continuous electrical contact with the stationary brushes while the armature rotates
[Solution Description]
The slip rings in an A.C. generator serve as connectors between the rotating armature coil and the stationary external circuit through brushes. They allow the current generated in the rotating coil to be transferred to the external load without twisting the wires. Since the coil rotates, direct connection would tangle the wires, so slip rings ensure smooth transmission of alternating current.

Key Concept: Faraday's Laws, Rate of Change of Flux

c) $0.4 \, \text{A}$
[Solution Description]
First, calculate the induced e.m.f. using Faraday's law: $e = -N \frac{d\phi}{dt} = -100 \times 0.02 = -2 \, \text{V}$. The magnitude of the current is then found using Ohm's law: $I = \frac{e}{R} = \frac{2}{5} = 0.4 \, \text{A}$. The negative sign indicates direction but is irrelevant for magnitude.

Key Concept: Force dependence on angle, Multiple concepts

c) 0.18 N
[Solution Description]
The force formula for a current-carrying wire at an angle $\theta$ to the magnetic field is $F = I \cdot B \cdot l \cdot \sin\theta$.
Here, $\theta = 30^\circ$, so $\sin 30^\circ = 0.5$.
Substituting: $F = 3 \times 0.2 \times 0.6 \times 0.5 = 0.18 \, \text{N}$.

Key Concept: Effect of Speed on AC Generation

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
According to the syllabus, the frequency of AC is equal to the frequency of rotation of the coil, so increasing the rotation speed ($n$) increases the frequency of AC.
The maximum induced e.m.f. is given by $e_0 = 2\pi n BAN$, which shows that $e_0$ is directly proportional to $n$. Thus, as the speed of rotation increases, $e_0$ also increases.
Therefore, both Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Construction and its main parts

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that brushes in an A.C. generator do not rotate along with the armature coil, which is true as they remain stationary to ensure consistent contact with the slip rings. The reason explains that brushes are stationary to maintain continuous electrical contact with the external circuit, which is also correct and provides a valid explanation for why brushes do not rotate. Thus, both Assertion and Reason are true, and the Reason correctly explains the Assertion.

Key Concept: Comparison Between Electromagnet and Permanent Magnet

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the polarity of an electromagnet can be reversed by reversing the direction of current in its solenoid. This is true because changing the current direction changes the direction of the magnetic field produced by the solenoid. The reason states that an electromagnet is made of soft iron, which allows easy reversal of magnetic polarity. Soft iron has low retentivity, meaning it loses its magnetism quickly when the current is turned off or reversed, making it suitable for applications requiring frequent polarity changes. Therefore, both the assertion and the reason are true, and the reason correctly explains the assertion.

Key Concept: Construction of A.C. Generator

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that slip rings in an A.C. generator are connected to the external circuit through carbon brushes, which is true as per the syllabus. The reason states that carbon brushes are used because they provide good electrical contact and wear resistance, which is also true according to the syllabus. Moreover, the reason correctly explains why carbon brushes are used in the construction of an A.C. generator, as they ensure efficient transfer of current from rotating parts to stationary external circuits while being durable.

Key Concept: Energy Conversion, Generator

c) Alternating Current (AC)
[Solution Description]
A generator operates on Faraday's Law of Electromagnetic Induction, where mechanical rotation of the coil in a magnetic field induces an alternating emf due to continuous change in flux linkage. Hence, it produces Alternating Current (AC).

Key Concept: Magnetic Field Inside Solenoid

c) $B = \mu_0 n I$
[Solution Description]
The magnetic field inside a long solenoid is given by the formula:
$B = \mu_0 n I$
Here, $B$ is the magnetic field strength, $\mu_0$ is the permeability of free space, $n$ is the number of turns per unit length, and $I$ is the current through the solenoid. This formula shows that the magnetic field inside the solenoid is directly proportional to the current and the number of turns per unit length.

Key Concept: Right-hand rule for solenoids

c) Direction of the magnetic field (North pole)
[Solution Description]
For a solenoid, the right-hand rule states that if the fingers are curled in the direction of the current flow through the coil, the thumb points in the direction of the magnetic field inside the solenoid, which corresponds to the North pole.

Key Concept: Step-up Transformer

c) Secondary voltage is greater than primary voltage
[Solution Description]
A step-up transformer increases the voltage by having more turns in the secondary coil than the primary coil ($N_s > N_p$).

Key Concept: Magnetic Flux and Induced EMF

c) When the plane of coil is parallel to the magnetic field
[Solution Description]
The magnitude of induced e.m.f. is given by $e = e_0 \sin(2\pi nt)$. It becomes maximum when $\sin(2\pi nt) = \pm 1$, which corresponds to the magnetic flux linked with the coil being zero. This happens when the plane of the coil lies parallel to the magnetic field.

Key Concept: Permanent Magnet Properties

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that a permanent magnet retains its magnetism for a long time, which is true because permanent magnets are designed to maintain their magnetic properties over extended periods. The Reason states that steel has higher retentivity compared to soft iron, which is also true as retentivity is the ability of a material to retain magnetization after the external magnetic field is removed. Since steel's higher retentivity directly explains why permanent magnets (made of steel) retain their magnetism for a long time, the Reason correctly explains the Assertion.

Key Concept: Magnetic Field Due to Current

c) Magnetic field lines are circular around the wire
[Solution Description]
A current-carrying straight wire produces a magnetic field whose field lines form concentric circles around the wire. The direction of these field lines can be determined using the right-hand thumb rule.

Key Concept: Factors affecting Electromagnet Strength

c) Increasing the number of turns in the coil
[Solution Description]
The strength of an electromagnet depends on both the number of turns in the coil and the current flowing through it. Increasing either of these will increase the magnetic field strength.

Key Concept: Right Hand Thumb Rule

b) Direction of magnetic field lines
[Solution Description]
The right-hand thumb rule states that when you hold a current-carrying wire in your right hand with the thumb pointing in the current direction, the curled fingers show the direction of the magnetic field lines around the wire.

Key Concept: Construction and Working of a D.C. Motor

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The split ring commutator reverses the direction of current in the armature coil after every half rotation to ensure that the torque acting on the coil remains in the same direction, enabling continuous rotation. Both Assertion (A) and Reason (R) are true, and Reason correctly explains why the split ring commutator is used in a d.c. motor.

Key Concept: Electromagnet Basics

b) A temporary magnet made by passing current in a coil wound around a soft iron
[Solution Description]
An electromagnet is a temporary strong magnet made by passing current in a coil wound around a soft iron core. It becomes magnetized only when current flows through the coil and loses its magnetism when the current is switched off. This property makes it an artificial and temporary magnet.

Key Concept: Fleming's Right Hand Rule

c) Induced current
[Solution Description]
Fleming's right hand rule is used to determine the direction of induced current in a conductor moving through a magnetic field. If the thumb represents the direction of motion of the conductor, the forefinger represents the direction of the magnetic field, then the middle finger gives the direction of the induced current.

Key Concept: Fleming's Left-Hand Rule - Force Formula

b) $F = I \cdot B \cdot l$
[Solution Description]
The magnitude of the force $F$ acting on a current-carrying conductor placed in a magnetic field is given by:
$F = I \cdot B \cdot l$, where:
- $I$ = current,
- $B$ = magnetic field strength,
- $l$ = length of the conductor in the magnetic field.
This is the standard formula derived from the interaction of current and magnetic field.

Key Concept: D.C. Motor, Torque Calculation

b) 0.5 Nm
[Solution Description]
The torque ($\tau$) on a current-carrying coil in a magnetic field is given by:
$\tau = nIBA \sin \theta$.
Given:
$n = 50$,
$I = 2$ A,
$B = 0.5$ T,
$A = 0.01$ m$^2$,
$\theta = 90°$ (for maximum torque, $\sin 90° = 1$).
Substituting values:
$\tau = 50 \times 2 \times 0.5 \times 0.01 \times 1 = 0.5$ Nm.

Key Concept: Applications of Electromagnet in lifting heavy objects

b) To lift and transport heavy iron objects
[Solution Description]
Electromagnets are used to lift heavy iron objects like scrap, girders, and plates because they can hold a large amount of weight (up to 20,000 kg). Once the objects need to be released, the current to the electromagnet is turned off, demagnetizing it and releasing the load.

Key Concept: Role of Armature Coil

c) To strengthen the magnetic field and improve induction efficiency
[Solution Description]
The soft iron core is used in the armature coil because it enhances the magnetic flux linkage when the coil rotates within the magnetic field of the horse-shoe magnet. Soft iron has high permeability, which means it strengthens the magnetic field significantly, increasing the induced EMF in the coil. It also reduces energy losses due to hysteresis.

Key Concept: Fleming’s Left-Hand Rule Direction

b) Towards the west
[Solution Description]
According to Fleming’s left-hand rule:
- Forefinger points in the direction of the magnetic field (north).
- Central finger points in the direction of the current (upwards).
- The thumb will point towards the west, indicating the direction of the force.
Therefore, the force acts towards the west.

Key Concept: Armature coil, Magnetic field, Torque

b) 0.5 Nm
[Solution Description]
The torque ($\tau$) on a current-carrying coil in a magnetic field is given by $\tau = nBIA\sin\theta$, where $n$ is the number of turns, $B$ is the magnetic field, $I$ is the current, $A$ is the area of the coil, and $\theta$ is the angle between the normal to the coil and the magnetic field. For maximum torque, $\sin\theta = 1$, which occurs when the plane of the coil is parallel to the magnetic field (i.e., $\theta = 90^\circ$).
Substituting the values:
$\tau = 50 \times 0.5 \times 2 \times 0.01 \times \sin(90^\circ) = 50 \times 0.5 \times 2 \times 0.01 \times 1 = 0.5 \text{ Nm}$

Key Concept: Electromagnet - Construction and Working

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion states that the polarity of an electromagnet can be reversed by changing the direction of current in its solenoid, which is true. The Reason explains that the magnetic field produced by a solenoid depends on the direction of current, which is also correct and directly explains why the polarity can be reversed by changing the current direction. Therefore, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Force direction using Fleming's left-hand rule

b) Along the positive Z-axis
[Solution Description]
According to Fleming’s left-hand rule, stretch the thumb, forefinger, and middle finger of the left hand mutually perpendicular to each other. If the forefinger points along the direction of the magnetic field (Y-axis) and the middle finger along the current (X-axis), then the thumb indicates the direction of the force (Z-axis). Here, the force acts along the positive Z-direction.

Key Concept: Magnitude of force calculation

c) 1.5 N
[Solution Description]
The force on a current-carrying conductor in a magnetic field is given by $F = IBl$. Here, $I = 2\,\text{A}$, $B = 1.5\,\text{T}$, and $l = 0.5\,\text{m}$. Substituting these values into the equation: $F = 2 \times 1.5 \times 0.5 = 1.5\,\text{N}$.

Key Concept: Faraday’s Laws

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The Assertion (A) states that an e.m.f. is induced in a coil when there is a change in the magnetic flux linked with it, which is correct as per Faraday’s first law. The Reason (R) correctly states Faraday’s second law, which explains why and how much e.m.f. is induced. Thus, both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Key Concept: Uses of Electromagnet, Demagnetisation

c) When the iron objects need to be detached easily after lifting
[Solution Description]
An electromagnet is preferred when the ability to easily demagnetize it is required. For lifting heavy iron objects, an electromagnet allows the objects to be detached by simply switching off the current, making it convenient for loading and unloading. A permanent magnet cannot be easily demagnetized, making it unsuitable for such applications.

Key Concept: Neutral Point

c) It rests in any arbitrary direction
[Solution Description]
A neutral point occurs where the magnetic field due to the current-carrying wire cancels the Earth’s magnetic field. Here, the resultant magnetic field is zero, so the compass needle does not experience any torque and can rest in any arbitrary direction.

Key Concept: Permanent Magnet, Electromagnet

b) Only the electromagnet's polarity can be reversed.
[Solution Description]
A permanent magnet is made of steel and retains its magnetism permanently, whereas an electromagnet is made of soft iron and loses its magnetism when the current is switched off. The strength of an electromagnet can be changed by varying the current or number of turns, but this is not possible with a permanent magnet.

Key Concept: Fleming’s Left-Hand Rule

c) Middle finger
[Solution Description]
According to Fleming's Left-Hand Rule:
1. Forefinger: Direction of the magnetic field.
2. Middle finger: Direction of the current.
3. Thumb: Direction of the force.
Thus, the middle finger represents the direction of the current.

Key Concept: Fleming's Left Hand Rule

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that reversing the current direction reverses the force direction while keeping the magnetic field unchanged. This is true because Fleming’s left hand rule shows that force direction depends on both current and magnetic field directions.
The reason correctly explains the assertion by stating that the force direction depends on current and magnetic field directions as per Fleming’s left hand rule. Thus, both assertion and reason are true, and the reason correctly explains the assertion.

Key Concept: Oersted’s Experiment Observations

b) Needle deflects towards the west if placed below the wire and current flows from south to north
[Solution Description]
According to Oersted’s experiment, when a current passes through a wire in the north-south direction, the compass needle deflects from its initial position due to the magnetic field produced by the current. The deflection depends on the direction of the current and the position of the needle relative to the wire.

Key Concept: Magnetic Field due to Current in a Straight Wire

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.
[Solution Description]
The assertion states that the magnetic field lines around a straight current-carrying wire form concentric circles. This is true as observed in experiments where iron filings arrange themselves in concentric circles around the wire when current flows through it. The reason states that the direction of the magnetic field can be determined using the right-hand thumb rule, which is also true. Moreover, the right-hand thumb rule explains why the field lines are circular and their direction, thus the reason correctly explains the assertion.

Key Concept: Right-hand thumb rule, Magnetic field direction

c) Assertion is true, but Reason is false.
[Solution Description]
The assertion (A) correctly describes the application of the right-hand thumb rule. When the thumb points in the direction of conventional current (from positive to negative terminal), the curled fingers show the direction of the magnetic field lines, which are indeed anticlockwise when viewed from above for an upward current. However, the reason (R) incorrectly states that the magnetic field direction is "always tangential" to the field lines. The magnetic field direction is actually tangential to the field lines only at any specific point on the circle; it is not universally true in all contexts. Therefore, Assertion (A) is true, but Reason (R) is false.