Physics Quiz: Explain Electromagnetic Induction

What this quiz covers

This quiz focuses on Explain Electromagnetic Induction, giving you a quick way to practice the rules, question types, and explanations that matter most for Physics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. The magnetic flux $\Phi = BA\cos(\theta)$ through the loop is changing with time, so an EMF is induced (correct answer)
2. Any magnetic field automatically causes current to flow in a closed loop
3. The induced current appears because the loop’s resistance decreases when a magnetic field is present
4. The induced current appears because the loop’s area must be changing when the field changes

Explanation: This question tests understanding of electromagnetic induction, specifically how changing magnetic field strength induces EMF even when the conductor remains stationary. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where the magnetic flux Φ = BA cos(θ) depends on field strength B, loop area A, and angle θ—any change in these parameters that changes Φ will induce EMF. In this scenario, the loop is stationary with fixed area A, and the field remains perpendicular (θ = 0°, so cos(θ) = 1), but the field strength B is increasing steadily over time—this means the flux Φ = BA through the loop is increasing, giving ΔΦ/Δt > 0, which induces an EMF in the loop according to Faraday's law. By Lenz's law, the induced current flows in a direction that creates a magnetic field opposing the flux increase—since the external field is increasing upward through the loop, the induced current creates a downward field to oppose this change. Choice A is correct because it accurately identifies that the changing flux (due to changing B in Φ = BA cos(θ)) is what induces the current, properly citing the flux formula and recognizing that time-varying flux is the key requirement. Choice B confuses the presence of a magnetic field with changing magnetic flux—just having a field present (even a strong field) doesn't induce current; what matters is whether the flux through the coil is changing over time, which in this case it is because B is increasing even though the loop is stationary. To analyze electromagnetic induction scenarios: (1) identify all factors in flux Φ = BA cos(θ), (2) determine which are changing with time (here, B is increasing), (3) if any factor changes such that Φ changes, then ΔΦ/Δt ≠ 0 and EMF is induced, (4) the induced current direction follows Lenz's law to oppose the flux change. This principle is used in many applications: variable inductors change B to control inductance, magnetic field sensors detect changing fields by measuring induced currents, and eddy current brakes use changing fields to induce opposing currents that create braking forces.

Question 2

1. The induced magnetic field points to the right to help the flux increase faster.
2. The induced magnetic field points to the left to oppose the increasing rightward flux. (correct answer)
3. The induced magnetic field is zero because only electric fields can induce current.
4. The induced magnetic field points to the right only if the magnet is stationary.

Explanation: This question tests understanding of electromagnetic induction, specifically Lenz's law that the induced current opposes the change in magnetic flux, in the context of a magnet approaching a coil. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. Lenz's law (the negative sign in Faraday's equation) states that the induced current flows in a direction that creates a magnetic field opposing the change in flux, which is a consequence of energy conservation: work must be done against the induced magnetic force to change the flux. When the magnet moves into the coil, the magnetic field strength B at the location of the coil increases, causing the magnetic flux Φ = BA through the coil to change—this changing flux (ΔΦ/Δt ≠ 0) induces an EMF in the coil according to Faraday's law, which drives a current through the circuit if the circuit is complete (galvanometer provides complete circuit); by Lenz's law, the induced current flows in a direction that creates a magnetic field opposing the incoming magnet to oppose the flux change—this is why you feel resistance when pushing the magnet in, as the induced field tries to push the magnet back out. Choice B is correct because it properly applies Lenz's law to predict that induced current opposes the flux change, stating the induced field points left to oppose the increasing rightward flux from the approaching north pole. Choice A incorrectly reverses Lenz's law, predicting the induced current creates a field that aids the flux change instead of opposing it—this would violate energy conservation because it would mean the induced effect amplifies the change, creating a runaway situation, when actually Lenz's law ensures the induced effect opposes the change (you must do work to overcome this opposition). To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction).

Question 3

1. It reverses direction because the magnetic flux change reverses sign when the magnet is pulled out instead of pushed in. (correct answer)
2. It stays the same direction because the magnet’s field polarity does not change.
3. It becomes zero because induction only occurs when a magnet enters a coil, not when it leaves.
4. It reverses only if the coil has more than one turn.

Explanation: This question tests understanding of electromagnetic induction, specifically Lenz's law and how the direction of induced current reverses when the flux change reverses in a magnet-coil setup. Lenz's law (the negative sign in Faraday's equation) states that the induced current flows in a direction that creates a magnetic field opposing the change in flux, which is a consequence of energy conservation: work must be done against the induced magnetic force to change the flux. When the magnet moves into the coil, the magnetic field strength B at the location of the coil increases, causing the magnetic flux Φ = BA through the coil to change—this changing flux (ΔΦ/Δt ≠ 0) induces an EMF in the coil according to Faraday's law, which drives a current through the circuit if the circuit is complete (galvanometer provides complete circuit); by Lenz's law, the induced current flows in a direction that creates a magnetic field opposing the incoming magnet to oppose the flux change—this is why you feel resistance when pushing the magnet in, as the induced field tries to push the magnet back out; when pulling out, the flux decreases, so the induced field tries to maintain the flux by attracting the magnet. Choice A is correct because it properly applies Lenz's law to predict that induced current opposes the flux change, with the direction reversing because the flux change sign reverses (increase vs. decrease), leading to opposite galvanometer deflection. Choice B incorrectly predicts the current direction stays the same, getting the opposition backwards: when flux is decreasing during pull-out, Lenz's law requires the induced field to oppose the decrease by pointing in the same direction as the departing magnet's field, which means the induced current must flow in the opposite direction compared to when flux was increasing. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Key insight: it's not the mere presence of a magnetic field that induces current, but rather the change in flux—this is why moving a magnet toward a coil induces current (flux increasing), holding it stationary produces no current (flux constant), and moving it away again induces current in the opposite direction (flux decreasing), and why generators work through continuous rotation (flux continuously changing) while a coil sitting in a steady field produces no power.

Question 4

1. The galvanometer deflects only while the magnet is moving into or out of the coil, and it returns to zero when the magnet is held stationary. (correct answer)
2. The galvanometer deflects most when the magnet is held stationary inside the coil because the magnetic field is strongest there.
3. The galvanometer deflects whenever the magnet is near the coil, even if the magnet is not moving, because any magnetic field induces current.
4. The galvanometer deflects only when the magnet is completely outside the coil because flux is zero inside the coil.

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law that a changing magnetic flux induces an EMF, and how it applies to a magnet moving relative to a coil. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. When the magnet moves into or out of the coil, the magnetic field strength B at the location of the coil increases or decreases, causing the magnetic flux Φ = BA through the coil to change—this changing flux (ΔΦ/Δt ≠ 0) induces an EMF in the coil according to Faraday's law, which drives a current through the circuit if the circuit is complete (galvanometer provides complete circuit); when the magnet is held stationary inside the coil, the flux is constant (ΔΦ/Δt = 0), so no EMF is induced and the galvanometer shows zero current. Choice A is correct because it accurately identifies that induction occurs when magnetic flux is changing, not when it's constant, directly supporting Faraday's law by showing deflection only during motion (flux change) and zero when stationary (no flux change). Choice B incorrectly claims current is induced when the magnet is stationary inside the coil, but Faraday's law requires changing flux (ΔΦ/Δt ≠ 0)—when the magnet isn't moving, the flux through the coil is constant, so ΔΦ/Δt = 0 and no EMF is induced, which is why the galvanometer shows zero. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Key insight: it's not the mere presence of a magnetic field that induces current, but rather the change in flux—this is why moving a magnet toward a coil induces current (flux increasing), holding it stationary produces no current (flux constant), and moving it away again induces current in the opposite direction (flux decreasing), and why generators work through continuous rotation (flux continuously changing) while a coil sitting in a steady field produces no power.

Question 5

1. When $\theta = 0^\circ$ because the flux $\Phi$ is maximum.
2. When $\theta = 90^\circ$ because the flux is changing most rapidly with rotation at that instant. (correct answer)
3. When $\theta = 180^\circ$ because the flux is minimum.
4. At all angles equally, because rotation always induces the same EMF.

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law in a rotating coil generator, where the induced EMF varies with the rate of flux change. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. For rotating coil: As the coil rotates in the magnetic field, the angle θ between the field and the normal to the coil changes continuously, causing flux Φ = BA cos(θ) to change from maximum (Φ = BA when θ = 0°, coil face perpendicular to field) to zero (Φ = 0 when θ = 90°, coil face parallel to field) and back—this continuous flux change induces a continuously varying EMF that alternates in direction, producing alternating current (AC); the induced EMF is maximum when the coil passes through the position where flux is changing fastest (θ = 90°, coil face parallel to field) and zero when flux is momentarily constant at maximum or minimum (θ = 0° or 180°). Choice B is correct because it correctly identifies that the maximum EMF occurs when the rate of flux change |dΦ/dt| is greatest, which for constant rotation speed happens at θ = 90° where d(cosθ)/dθ is maximum. Choice A incorrectly claims the EMF is maximum when flux is maximum, but Faraday's law depends on the rate of change ΔΦ/Δt, not the absolute flux value—at θ = 0°, flux is max but momentarily not changing (dΦ/dt = 0), so EMF is zero there. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Practical applications of electromagnetic induction: generators convert mechanical rotation into electrical power (power plants, wind turbines, bike dynamos), transformers use changing flux in primary coil to induce current in secondary (step up or step down voltage), electric guitar pickups sense vibrating metal strings (changing flux from string motion induces current in coil), induction cooktops create changing field that induces currents in metal pots (heats the pot directly), and metal detectors sense conductive objects by detecting the induced currents (eddy currents) created when the detector's changing field passes through metal.

Question 6

1. A steady deflection, because any motion of a magnet produces a steady induced current.
2. No significant deflection, because the magnetic flux through the loop is approximately constant ($\Delta\Phi/\Delta t \approx 0$). (correct answer)
3. A deflection only if the magnet is strong enough to create flux, regardless of whether flux changes.
4. A deflection whose direction depends only on the magnet’s speed, not on flux change.

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law and whether parallel motion causes a change in flux through a loop. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. In this scenario, moving the magnet parallel to the plane of the loop (sideways, same distance) means the magnetic field through the loop remains approximately unchanged, as the magnet's position relative to the loop's area doesn't alter the effective B or θ significantly, so flux Φ is roughly constant (ΔΦ/Δt ≈ 0), resulting in no induced EMF or galvanometer deflection. Choice B is correct because it accurately identifies that induction occurs only when magnetic flux is changing, not when it's constant, explaining no deflection due to negligible flux change. Choice C confuses the presence of a magnetic field with changing magnetic flux—just having a field present (even a strong field) doesn't induce current; what matters is whether the flux through the coil is changing over time, which requires motion, rotation, or varying field strength. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Key insight: it's not the mere presence of a magnetic field that induces current, but rather the change in flux—this is why moving a magnet toward a coil induces current (flux increasing), holding it stationary produces no current (flux constant), and moving it away again induces current in the opposite direction (flux decreasing), and why generators work through continuous rotation (flux continuously changing) while a coil sitting in a steady field produces no power.

Question 7

1. The resistive force occurs because the induced current creates a magnetic field that opposes the increase in flux (Lenz’s law). (correct answer)
2. The resistive force occurs because the coil’s metal attracts magnets whenever the magnet is moving.
3. The resistive force occurs because the magnet’s field is strongest inside the coil, so the magnet is pulled in faster.
4. The resistive force occurs because a constant magnetic flux always produces a constant opposing force.

Explanation: This question tests understanding of electromagnetic induction, specifically Lenz's law explaining the resistive force felt when pushing a magnet into a conducting coil. Lenz's law (the negative sign in Faraday's equation) states that the induced current flows in a direction that creates a magnetic field opposing the change in flux, which is a consequence of energy conservation: work must be done against the induced magnetic force to change the flux. When the magnet moves into the coil, the magnetic field strength B at the location of the coil increases, causing the magnetic flux Φ = BA through the coil to change—this changing flux (ΔΦ/Δt ≠ 0) induces an EMF in the coil according to Faraday's law, which drives a current through the circuit if the circuit is complete (galvanometer provides complete circuit); by Lenz's law, the induced current flows in a direction that creates a magnetic field opposing the incoming magnet to oppose the flux change—this is why you feel resistance when pushing the magnet in, as the induced field tries to push the magnet back out. Choice A is correct because it properly applies Lenz's law to predict that induced current opposes the flux change, connecting the resistive force to the opposing induced magnetic field during flux increase. Choice D incorrectly claims that a constant magnetic flux always produces a constant opposing force, but Faraday's law requires changing flux (ΔΦ/Δt ≠ 0) for any induction—when flux is constant (e.g., magnet stationary), no EMF, no induced current, and no force, which is why there's no resistance when holding the magnet still inside the coil. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Key insight: it's not the mere presence of a magnetic field that induces current, but rather the change in flux—this is why moving a magnet toward a coil induces current (flux increasing), holding it stationary produces no current (flux constant), and moving it away again induces current in the opposite direction (flux decreasing), and why generators work through continuous rotation (flux continuously changing) while a coil sitting in a steady field produces no power.

Question 8

1. The magnetic flux changes because $\Phi = BA\cos\theta$ changes as $\theta$ changes (correct answer)
2. The magnetic flux stays the same because $B$ and $A$ are constant
3. An EMF is induced only if the loop’s area $A$ changes, not if it rotates
4. An EMF is induced because the loop’s current creates the external magnetic field

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law (changing magnetic flux induces EMF) due to changing orientation. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. For rotating coil: As the coil rotates in the magnetic field, the angle θ between the field and the normal to the coil changes continuously, causing flux Φ = BA cos(θ) to change from maximum (Φ = BA when θ = 0°, coil face perpendicular to field) to zero (Φ = 0 when θ = 90°, coil face parallel to field) and back—this continuous flux change induces a continuously varying EMF that alternates in direction, producing alternating current (AC); the induced EMF is maximum when the coil passes through the position where flux is changing fastest (θ = 90°, coil face parallel to field) and zero when flux is momentarily constant at maximum or minimum (θ = 0° or 180°). Choice A is correct because it accurately identifies that induction occurs when magnetic flux is changing, not when it's constant, properly explaining the role of changing θ in Φ = BA cos(θ). Choice B confuses the presence of a magnetic field with changing magnetic flux—just having a field present (even a strong field) doesn't induce current; what matters is whether the flux through the coil is changing over time, which requires motion, rotation, or varying field strength. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Practical applications of electromagnetic induction: generators convert mechanical rotation into electrical power (power plants, wind turbines, bike dynamos), transformers use changing flux in primary coil to induce current in secondary (step up or step down voltage), electric guitar pickups sense vibrating metal strings (changing flux from string motion induces current in coil), induction cooktops create changing field that induces currents in metal pots (heats the pot directly), and metal detectors sense conductive objects by detecting the induced currents (eddy currents) created when the detector's changing field passes through metal.

Question 9

1. Trial 1 has larger $|\varepsilon|$ because the magnet spends more time inside the coil
2. Trial 2 has larger $|\varepsilon|$ because $|\Delta\Phi/\Delta t|$ is larger (correct answer)
3. They are equal because $|\varepsilon|$ depends only on the magnet’s field strength, not motion
4. Trial 2 has smaller $|\varepsilon|$ because faster motion gives the charges less time to move

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law (changing magnetic flux induces EMF) and how the rate of change affects magnitude. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. When the magnet moves into the coil, the magnetic field strength B at the location of the coil increases, causing the magnetic flux Φ = BA through the coil to change—this changing flux (ΔΦ/Δt ≠ 0) induces an EMF in the coil according to Faraday's law, which drives a current through the circuit if the circuit is complete (galvanometer provides complete circuit); by Lenz's law, the induced current flows in a direction that creates a magnetic field opposing the incoming magnet to oppose the flux change—this is why you feel resistance when pushing the magnet in, as the induced field tries to push the magnet back out. Choice B is correct because it correctly predicts faster motion creates larger ΔΦ/Δt and thus larger induced EMF, accurately explaining that the changing flux is what induces the current, citing Faraday's law. Choice D suggests that faster motion of the magnet produces smaller induced current, when actually faster motion means larger ΔΦ/Δt (flux changing more rapidly), which by Faraday's law |ε| = N|ΔΦ/Δt| produces larger induced EMF and thus larger induced current I = ε/R. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Key insight: it's not the mere presence of a magnetic field that induces current, but rather the change in flux—this is why moving a magnet toward a coil induces current (flux increasing), holding it stationary produces no current (flux constant), and moving it away again induces current in the opposite direction (flux decreasing), and why generators work through continuous rotation (flux continuously changing) while a coil sitting in a steady field produces no power.

Question 10

1. Decrease the number of turns $N$ in the coil
2. Rotate the coil more slowly so charges have more time to move
3. Increase the rotation speed so the flux changes faster (correct answer)
4. Keep the coil’s normal always aligned with the magnetic field so $\theta$ stays constant

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law (changing magnetic flux induces EMF) in rotating coils like generators. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. For rotating coil: As the coil rotates in the magnetic field, the angle θ between the field and the normal to the coil changes continuously, causing flux Φ = BA cos(θ) to change from maximum (Φ = BA when θ = 0°, coil face perpendicular to field) to zero (Φ = 0 when θ = 90°, coil face parallel to field) and back—this continuous flux change induces a continuously varying EMF that alternates in direction, producing alternating current (AC); the induced EMF is maximum when the coil passes through the position where flux is changing fastest (θ = 90°, coil face parallel to field) and zero when flux is momentarily constant at maximum or minimum (θ = 0° or 180°). Choice C is correct because it correctly predicts faster motion creates larger ΔΦ/Δt and thus larger induced EMF. Choice B suggests that faster motion of the magnet produces smaller induced current, when actually faster motion means larger ΔΦ/Δt (flux changing more rapidly), which by Faraday's law |ε| = N|ΔΦ/Δt| produces larger induced EMF and thus larger induced current I = ε/R. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Key insight: it's not the mere presence of a magnetic field that induces current, but rather the change in flux—this is why moving a magnet toward a coil induces current (flux increasing), holding it stationary produces no current (flux constant), and moving it away again induces current in the opposite direction (flux decreasing), and why generators work through continuous rotation (flux continuously changing) while a coil sitting in a steady field produces no power.

Question 11

1. Only while the primary current is steady, because a steady current produces the strongest magnetic field.
2. Only when the secondary coil is connected to its own battery.
3. At the moments when the switch is closed or opened, because the magnetic flux through the secondary is changing then. (correct answer)
4. Continuously, because the presence of any magnetic field in the primary always induces current in the secondary.

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law in the context of mutual induction between two coils, like a simple transformer setup. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. For two coils/transformer: When the current in the primary coil changes (AC current, or switching DC on/off), it creates a changing magnetic field that passes through the secondary coil—this changing field means changing flux through the secondary (ΔΦ/Δt ≠ 0), which induces an EMF in the secondary coil by Faraday's law, driving current through the secondary even though there's no battery connected to it; if the primary current is steady DC (not changing), the magnetic field is constant, flux through secondary is constant (ΔΦ/Δt = 0), and no EMF is induced—this is why transformers only work with AC, not DC. Choice C is correct because it accurately explains that the changing flux is what induces the current, citing Faraday's law, with deflection occurring at the moments of switch closing/opening when primary current (and thus flux) is changing. Choice A incorrectly claims current is induced when the primary current is steady, but Faraday's law requires changing flux (ΔΦ/Δt ≠ 0)—when the current is steady, the flux through the secondary is constant, so ΔΦ/Δt = 0 and no EMF is induced, which is why the galvanometer shows zero during steady state. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Practical applications of electromagnetic induction: generators convert mechanical rotation into electrical power (power plants, wind turbines, bike dynamos), transformers use changing flux in primary coil to induce current in secondary (step up or step down voltage), electric guitar pickups sense vibrating metal strings (changing flux from string motion induces current in coil), induction cooktops create changing field that induces currents in metal pots (heats the pot directly), and metal detectors sense conductive objects by detecting the induced currents (eddy currents) created when the detector's changing field passes through metal.

Question 12

1. The loop’s resistance is changing, which creates an EMF.
2. The magnetic flux $\Phi = BA\cos(\theta)$ is changing because $B$ is increasing. (correct answer)
3. The loop’s area $A$ is increasing even though the loop does not move.
4. The magnetic field is present, so an EMF exists even if $\Phi$ is constant.

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law and what causes changing magnetic flux in a stationary loop with a varying field strength. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. In this scenario, even though the loop is not moving and its area A and orientation θ are constant, the magnetic field strength B is increasing with time, which causes the flux Φ = BA cos(θ) to increase accordingly—this changing flux (ΔΦ/Δt ≠ 0 due to dB/dt > 0) induces an EMF in the loop according to Faraday's law. Choice B is correct because it accurately identifies that induction occurs when magnetic flux is changing, not when it's constant, here due to the increasing B causing ΔΦ/Δt ≠ 0. Choice D confuses the presence of a magnetic field with changing magnetic flux—just having a field present (even a strong field) doesn't induce current; what matters is whether the flux through the coil is changing over time, which requires motion, rotation, or varying field strength. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Key insight: it's not the mere presence of a magnetic field that induces current, but rather the change in flux—this is why moving a magnet toward a coil induces current (flux increasing), holding it stationary produces no current (flux constant), and moving it away again induces current in the opposite direction (flux decreasing), and why generators work through continuous rotation (flux continuously changing) while a coil sitting in a steady field produces no power.

Question 13

1. The needle deflects when the magnet is moving, returns to zero when the magnet is held still, and deflects the opposite way when the magnet is pulled out because the magnetic flux through the coil changes only during motion. (correct answer)
2. The needle deflects most when the magnet is held stationary inside the coil because the magnetic flux is largest then.
3. The needle deflects in the same direction while pushing in and pulling out because the magnet’s field direction through the coil is the same in both cases.
4. The needle deflects whenever the magnet is near the coil, even if it is not moving, because any magnetic field produces an induced EMF.

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law (changing magnetic flux induces EMF) and Lenz's law (induced current opposes the change). Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. When the magnet moves into the coil, the magnetic field strength B at the location of the coil increases, causing the magnetic flux Φ = BA through the coil to change—this changing flux (ΔΦ/Δt ≠ 0) induces an EMF in the coil according to Faraday's law, which drives a current through the circuit if the circuit is complete (galvanometer provides complete circuit); by Lenz's law, the induced current flows in a direction that creates a magnetic field opposing the incoming magnet to oppose the flux change—this is why you feel resistance when pushing the magnet in, as the induced field tries to push the magnet back out; when the magnet is held stationary inside the coil, the flux is constant (ΔΦ/Δt = 0), so no EMF is induced and the galvanometer shows zero current; when pulling out, the flux decreases, inducing current in the opposite direction to oppose the decrease. Choice A is correct because it accurately identifies that induction occurs when magnetic flux is changing, not when it's constant, and properly applies Lenz's law to predict that induced current opposes the flux change by deflecting oppositely when pulling out. Choice B incorrectly claims current is induced when the magnet is stationary inside the coil, but Faraday's law requires changing flux (ΔΦ/Δt ≠ 0)—when the magnet isn't moving, the flux through the coil is constant, so ΔΦ/Δt = 0 and no EMF is induced, which is why the galvanometer shows zero. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Key insight: it's not the mere presence of a magnetic field that induces current, but rather the change in flux—this is why moving a magnet toward a coil induces current (flux increasing), holding it stationary produces no current (flux constant), and moving it away again induces current in the opposite direction (flux decreasing), and why generators work through continuous rotation (flux continuously changing) while a coil sitting in a steady field produces no power.

Question 14

1. Coil X deflects more because fewer turns means less resistance.
2. Both coils deflect the same because the magnet’s field is the same.
3. Coil Y deflects more because $|\varepsilon| = N\left|\frac{\Delta\Phi}{\Delta t}\right|$ increases with the number of turns. (correct answer)
4. Coil Y deflects less because more turns reduces the rate of flux change.

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law (changing magnetic flux induces EMF) and Lenz's law (induced current opposes the change). Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): $\varepsilon = -N \left( \frac{\Delta \Phi}{\Delta t} \right)$, where N is the number of turns in the coil, $\Phi$ is the magnetic flux ($\Phi = BA \cos(\theta)$), and the rate of change $\Delta \Phi / \Delta t$ determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then $\Delta \Phi / \Delta t = 0$ and no EMF is induced. When the magnet moves into the coil, the magnetic field strength B at the location of the coil increases, causing the magnetic flux $\Phi = BA$ through the coil to change—this changing flux ($\Delta \Phi / \Delta t \neq 0$) induces an EMF in the coil according to Faraday's law, which drives a current through the circuit if the circuit is complete (galvanometer provides complete circuit). Choice C is correct because it correctly predicts that more turns create larger $|\varepsilon| = N |\Delta \Phi / \Delta t|$ and thus larger deflection. Choice A suggests that fewer turns produce larger deflection, when actually more turns mean larger N in Faraday's law, increasing the induced EMF and thus the current $I = \varepsilon / R$ causing greater galvanometer deflection. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux $\Phi$ through the conductor ($\Phi = BA \cos(\theta)$), (3) if $\Phi$ is changing, then $\Delta \Phi / \Delta t \neq 0$ and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current $I = \varepsilon / R$, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Practical applications of electromagnetic induction: generators convert mechanical rotation into electrical power (power plants, wind turbines, bike dynamos), transformers use changing flux in primary coil to induce current in secondary (step up or step down voltage), electric guitar pickups sense vibrating metal strings (changing flux from string motion induces current in coil), induction cooktops create changing field that induces currents in metal pots (heats the pot directly), and metal detectors sense conductive objects by detecting the induced currents (eddy currents) created when the detector's changing field passes through metal.

Question 15

1. The coil heats up and expands, increasing friction on the magnet.
2. The induced current creates a magnetic field that opposes the increase in flux, producing a force that resists the magnet’s motion. (correct answer)
3. The magnet loses strength as it approaches the coil, so extra force is needed to keep it moving.
4. The induced current always pulls the magnet inward, so the student must push harder to prevent it from accelerating.

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law (changing magnetic flux induces EMF) and Lenz's law (induced current opposes the change). Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. Lenz's law (the negative sign in Faraday's equation) states that the induced current flows in a direction that creates a magnetic field opposing the change in flux, which is a consequence of energy conservation: work must be done against the induced magnetic force to change the flux. Choice B is correct because it properly applies Lenz's law to predict that induced current opposes the flux change. Choice D reverses Lenz's law, predicting the induced current creates a field that aids the flux change instead of opposing it—this would violate energy conservation because it would mean the induced effect amplifies the change, creating a runaway situation, when actually Lenz's law ensures the induced effect opposes the change (you must do work to overcome this opposition). To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Key insight: it's not the mere presence of a magnetic field that induces current, but rather the change in flux—this is why moving a magnet toward a coil induces current (flux increasing), holding it stationary produces no current (flux constant), and moving it away again induces current in the opposite direction (flux decreasing), and why generators work through continuous rotation (flux continuously changing) while a coil sitting in a steady field produces no power.

Question 16

1. Counterclockwise, to create a magnetic field out of the page that reinforces the increase.
2. Clockwise, to create a magnetic field into the page that opposes the increasing out-of-page flux. (correct answer)
3. No current, because the loop is not moving.
4. Clockwise, because induced current always flows clockwise when the field points out of the page.

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law (changing magnetic flux induces EMF) and Lenz's law (induced current opposes the change). Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. Lenz's law (the negative sign in Faraday's equation) states that the induced current flows in a direction that creates a magnetic field opposing the change in flux, which is a consequence of energy conservation: work must be done against the induced magnetic force to change the flux. Choice B is correct because it properly applies Lenz's law to predict that induced current opposes the flux change by flowing clockwise to create a field into the page that counters the increasing out-of-page flux. Choice A reverses Lenz's law, predicting the induced current creates a field that aids the flux change instead of opposing it—this would violate energy conservation because it would mean the induced effect amplifies the change, creating a runaway situation, when actually Lenz's law ensures the induced effect opposes the change (you must do work to overcome this opposition). To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Key insight: it's not the mere presence of a magnetic field that induces current, but rather the change in flux—this is why moving a magnet toward a coil induces current (flux increasing), holding it stationary produces no current (flux constant), and moving it away again induces current in the opposite direction (flux decreasing), and why generators work through continuous rotation (flux continuously changing) while a coil sitting in a steady field produces no power.

Question 17

1. Trial 1 produces a larger induced EMF because the magnet spends more time inside the coil.
2. Trial 2 produces a larger induced EMF because the rate of flux change $|\Delta \Phi/\Delta t|$ is greater. (correct answer)
3. Both trials produce the same induced EMF because the maximum flux is the same.
4. Trial 2 produces a smaller induced EMF because faster motion reduces the time for current to form.

Explanation: This question tests understanding of electromagnetic induction, specifically Faraday's law and how the rate of flux change affects the induced EMF magnitude in a magnet-through-coil experiment. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. When the magnet moves into the coil, the magnetic field strength B at the location of the coil increases, causing the magnetic flux Φ = BA through the coil to change—this changing flux (ΔΦ/Δt ≠ 0) induces an EMF in the coil according to Faraday's law, which drives a current through the circuit if the circuit is complete (galvanometer provides complete circuit). Choice B is correct because it correctly predicts faster motion creates larger ΔΦ/Δt and thus larger induced EMF, as |ε| = N|ΔΦ/Δt| directly depends on the rate of flux change, which is greater when the magnet is pushed quickly. Choice D incorrectly suggests that faster motion of the magnet produces smaller induced current, when actually faster motion means larger ΔΦ/Δt (flux changing more rapidly), which by Faraday's law |ε| = N|ΔΦ/Δt| produces larger induced EMF and thus larger induced current I = ε/R. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Key insight: it's not the mere presence of a magnetic field that induces current, but rather the change in flux—this is why moving a magnet toward a coil induces current (flux increasing), holding it stationary produces no current (flux constant), and moving it away again induces current in the opposite direction (flux decreasing), and why generators work through continuous rotation (flux continuously changing) while a coil sitting in a steady field produces no power.

Question 18

1. Coil X has the larger induced EMF because fewer turns reduce opposition to current.
2. Coil Y has the larger induced EMF because $|\varepsilon| = N|\Delta\Phi/\Delta t|$ is proportional to $N$. (correct answer)
3. They have the same induced EMF because the magnetic field is the same for both.
4. Coil X has the larger induced EMF because induced EMF depends only on coil area, not turns.

Explanation: This question tests understanding of electromagnetic induction, specifically how the number of turns N affects the induced EMF in Faraday's law for coils in the same changing field. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where N is the number of turns in the coil, Φ is the magnetic flux (Φ = BA cos(θ)), and the rate of change ΔΦ/Δt determines the magnitude of induced EMF—the key requirement is that flux must be changing with time; if the flux is constant (magnet stationary, steady field, constant orientation), then ΔΦ/Δt = 0 and no EMF is induced. Since both coils experience the same changing magnetic field and have the same size (same A and ΔΦ/Δt per turn), the induced EMF is directly proportional to N, so Coil Y with 200 turns will have four times the EMF of Coil X with 50 turns, leading to larger galvanometer deflection for Y (assuming same resistance, I = ε/R). Choice B is correct because it accurately explains that the changing flux is what induces the current, citing Faraday's law with |ε| proportional to N, so more turns mean larger EMF. Choice C incorrectly states they have the same EMF because the field is the same, but this ignores the role of N in Faraday's law—each turn experiences the same ΔΦ/Δt, but more turns add up to a larger total EMF, like linking multiple loops in series. To analyze electromagnetic induction scenarios, follow these steps: (1) identify what is changing (magnet position, coil orientation, field strength, loop area), (2) determine if this change affects the magnetic flux Φ through the conductor (Φ = BA cos(θ)), (3) if Φ is changing, then ΔΦ/Δt ≠ 0 and EMF is induced by Faraday's law, (4) the magnitude of induced EMF increases with faster change, more coil turns, and complete circuit allows current I = ε/R, (5) use Lenz's law to predict current direction: induced field opposes the flux change (if flux increasing, induced field points opposite; if flux decreasing, induced field points same direction). Practical applications of electromagnetic induction: generators convert mechanical rotation into electrical power (power plants, wind turbines, bike dynamos), transformers use changing flux in primary coil to induce current in secondary (step up or step down voltage), electric guitar pickups sense vibrating metal strings (changing flux from string motion induces current in coil), induction cooktops create changing field that induces currents in metal pots (heats the pot directly), and metal detectors sense conductive objects by detecting the induced currents (eddy currents) created when the detector's changing field passes through metal.

Question 19

1. Closing the switch changes the current in the primary, changing the magnetic flux through the secondary and inducing an EMF. (correct answer)
2. The secondary coil must have a battery, so the deflection is caused by a hidden power source.
3. A steady current in the primary always produces a steady current in the secondary.
4. The galvanometer deflects because the magnetic field itself (not flux) automatically creates current in any nearby wire.

Explanation: This question tests understanding of electromagnetic induction in transformer-like setups, specifically how changing current in one coil induces EMF in a nearby coil. Faraday's law states that a changing magnetic flux through a conductor induces EMF, and in coupled coils, the magnetic field from the primary coil provides the flux through the secondary coil—when primary current changes, so does its magnetic field and thus the flux through the secondary. When the switch closes, current in the primary coil rises from zero to its steady value, creating an increasing magnetic field that extends through the secondary coil—this changing field means changing flux through the secondary (ΔΦ/Δt ≠ 0), which induces an EMF in the secondary coil by Faraday's law, driving current through the galvanometer even though there's no battery connected to the secondary circuit. Choice A is correct because it accurately explains that the changing current in the primary (when switch closes) creates a changing magnetic flux through the secondary, inducing EMF as required by Faraday's law. Choice C incorrectly claims that steady current in the primary always produces steady current in the secondary, but Faraday's law requires changing flux (ΔΦ/Δt ≠ 0)—once the primary current becomes steady, its magnetic field is constant, flux through secondary is constant (ΔΦ/Δt = 0), and no EMF is induced. To analyze mutual induction: (1) current in primary coil creates magnetic field, (2) some field lines pass through secondary (mutual flux), (3) changing primary current means changing field and changing flux through secondary, (4) by Faraday's law, this changing flux induces EMF in secondary, (5) steady primary current means steady field and no induction. This principle is the basis for transformers, which require AC (continuously changing current) to function—DC transformers don't exist because steady DC produces no flux change and thus no secondary voltage.

Question 20

1. It deflects in the same direction for both pushing in and pulling out because the magnet is the same.
2. It deflects only when the magnet is fully inside the coil, not during motion.
3. It deflects during both motions, and the deflection reverses direction when the motion reverses. (correct answer)
4. It never deflects because magnetic flux depends only on coil area, not on magnet motion.

Explanation: This question tests understanding of electromagnetic induction, specifically how the direction of induced current depends on whether flux is increasing or decreasing. Faraday's law states that a changing magnetic flux through a conductor induces an electromotive force (EMF): ε = -N(ΔΦ/Δt), where the magnitude depends on the rate of flux change and the sign (from Lenz's law) ensures the induced effect opposes the change. When the magnet is pushed into the coil, the magnetic flux through the coil increases (flux becoming more positive or more negative depending on pole orientation), inducing a current in one direction; when the magnet is pulled out, the flux decreases (returning toward zero), inducing current in the opposite direction—the galvanometer needle deflects one way for increasing flux and the opposite way for decreasing flux. Choice C is correct because it accurately identifies that induction occurs during both motions (flux changing in both cases) and that the deflection reverses when the motion reverses (increasing flux vs. decreasing flux produces opposite current directions). Choice A incorrectly claims the deflection is the same for both directions, ignoring that pushing in increases flux while pulling out decreases flux—by Lenz's law, these opposite flux changes must produce opposite current directions to properly oppose each change. To analyze electromagnetic induction scenarios: (1) identify the flux change direction (increasing when magnet approaches, decreasing when it recedes), (2) apply Lenz's law (induced current opposes the change), (3) recognize that opposite flux changes produce opposite induced currents. This principle is used in AC generators where continuous rotation causes flux to alternate between increasing and decreasing, producing alternating current that reverses direction with each half rotation.