Electromagnetic Induction and Faraday's Law
Help Questions
AP Physics 2 › Electromagnetic Induction and Faraday's Law
A single circular loop lies in the page. A uniform magnetic field points out of the page and its magnitude increases steadily from $0$ to $0.40\ \text{T}$ while the loop’s area and orientation stay constant. Which statement correctly describes the induced current in the loop?
A counterclockwise current is induced to create a field into the page, opposing the increase in outward flux.
A clockwise current is induced because the magnetic field points out of the page.
A current is induced only if a magnet moves through the loop, so none is induced here.
No current is induced because the loop’s area does not change.
Explanation
This question tests understanding of electromagnetic induction and Faraday's law. According to Faraday's law, a changing magnetic flux through a loop induces an electromotive force (emf), which drives a current if the loop is conducting. The magnetic flux increases because the field strength grows from 0 to 0.40 T while pointing out of the page, and Lenz's law states that the induced current opposes this change by creating a magnetic field into the page. Choice C incorrectly assumes no current flows because the area doesn't change, missing that flux depends on both field strength and area. To solve such problems, always identify what causes the flux change (here, increasing field strength) and apply Lenz's law to find the opposing field direction.
A loop of wire is in a uniform magnetic field pointing into the page. The loop is stretched so its area increases while its orientation and the field strength remain constant. Which statement correctly describes the induced current in the loop?
A current is induced only if the magnetic field direction reverses, so none is induced here.
A clockwise current is induced because the loop’s area increases.
A counterclockwise current is induced to create a field out of the page, opposing the increase in inward flux.
No current is induced because the magnetic field is uniform.
Explanation
This question tests understanding of electromagnetic induction and Faraday's law. When a loop's area increases in a uniform magnetic field pointing into the page, the magnetic flux through the loop increases because flux equals BA and A is growing. By Lenz's law, the induced current must oppose this flux increase by creating a magnetic field out of the page. A counterclockwise current (viewed from above) produces a field out of the page, making A correct. Choice C incorrectly claims uniform fields cannot induce current, missing that changing the loop's area changes the flux even in uniform fields. Always identify all factors affecting flux: field strength, area, and orientation angle.
A square loop is in a region where a uniform magnetic field points into the page. The loop is pulled to the right at constant speed, leaving the field region so the area of the loop within the field decreases. Which statement correctly describes the induced current while the loop is partly leaving the field?
No current is induced because the magnetic field direction does not change.
A clockwise current is induced because the loop is moving to the right.
A counterclockwise current is induced to create a field into the page, opposing the decrease in inward flux.
A clockwise current is induced to create a field into the page, opposing the decrease in inward flux.
Explanation
This question tests understanding of electromagnetic induction and Faraday's law. When a conducting loop moves out of a magnetic field region, the magnetic flux through it changes because the effective area within the field decreases. Since the field points into the page and the flux is decreasing, Lenz's law requires the induced current to oppose this change by creating a magnetic field that also points into the page. A clockwise current (viewed from above) produces a field into the page, making C correct. Choice D incorrectly attributes the current direction to the loop's motion rather than to Lenz's law opposing the flux change. Always determine the flux change first, then apply Lenz's law to find which current direction opposes that change.
A loop remains in a uniform, steady magnetic field, but its area and orientation stay constant. Which statement correctly describes the induced current?
No induced current is present because induced current requires a permanent magnet, not an electromagnet.
An induced current is present because the loop encloses magnetic flux.
No induced current is present because the magnetic flux through the loop is constant.
An induced current is present because the magnetic field passes through the loop.
Explanation
This question tests the skill of Electromagnetic induction and Faraday’s law. Induced emf arises from changing magnetic flux, but here the uniform field, area, and orientation are all constant, resulting in steady flux. Faraday's law predicts no emf since the rate of flux change is zero. Lenz’s law determines direction only when there is a change to oppose, which is absent in this steady-state scenario. Choice B reflects the misconception that enclosing any flux induces current, confusing constant flux with changing flux. Always identify what changes the magnetic flux; if nothing does, no induction occurs.
A loop rotates in a uniform magnetic field, changing only its orientation so flux changes from positive to zero. Which statement correctly describes the induced current?
An induced current is present because the flux is momentarily zero.
No induced current is present because the magnetic field strength is constant.
An induced current is present because the flux changes as the loop’s orientation changes.
No induced current is present because only changing area can induce current.
Explanation
This question tests the skill of Electromagnetic induction and Faraday’s law. Induced emf arises from changing magnetic flux, in this case due to the rotating loop altering the angle between the field and the loop's area vector. As the flux changes from positive to zero, Faraday's law indicates an emf based on the rate of this flux variation. Lenz’s law determines the direction of the induced current to oppose the specific change in flux during rotation. Choice A illustrates the misconception that constant field strength prevents induction, ignoring flux changes from orientation shifts. Always identify what changes the magnetic flux, including rotational motion affecting the cosine of the angle.
A rectangular loop is in a region with uniform magnetic field pointing into the page. The loop is stretched so its area increases while its orientation and the field strength remain constant. Which statement correctly describes the induced current direction during the stretching?
A counterclockwise induced current occurs because it produces a field out of the page.
A clockwise induced current occurs because it produces a field into the page.
No induced current occurs because the magnetic field is uniform.
A clockwise induced current occurs because it increases the flux into the page.
Explanation
This question tests understanding of electromagnetic induction and Faraday's law. As the loop is stretched, its area increases while in a field into the page, increasing the flux into the page. Faraday's law states that changing flux induces an emf: ε = -dΦ/dt. By Lenz's law, the induced current must oppose this flux increase by creating a magnetic field out of the page. Using the right-hand rule, a counterclockwise current (viewed from above) produces a field out of the page, making B correct. Choice D incorrectly states the induced field increases flux into the page, violating Lenz's law which requires opposition to change. Always verify your answer satisfies Lenz's law: induced effects oppose their cause.
A $50$-turn coil surrounds a long straight wire. The current in the wire increases steadily, increasing the magnetic field through the coil; the coil’s area and orientation are constant. Which statement correctly describes the induced current in the coil during the increase?
An induced current is present because the flux is nonzero even if it is constant.
No induced current occurs because the magnetic field lines are circular.
No induced current occurs because the coil is not moving.
An induced current is present because the magnetic flux through the coil changes.
Explanation
This question tests understanding of electromagnetic induction and Faraday's law. The increasing current in the straight wire creates an increasing magnetic field that passes through the surrounding coil. This causes the magnetic flux through the coil to increase over time. According to Faraday's law, changing flux induces an emf: ε = -N(dΦ/dt). By Lenz's law, the induced current in the coil opposes this flux increase, making B correct. Choice C incorrectly assumes circular field lines prevent induction, but what matters is whether flux through the coil changes, not the field line shape. Always focus on flux change through the conducting loop, regardless of field geometry.
The magnetic flux through a loop decreases linearly from $+3,\text{mWb}$ to $0$ over $2,\text{s}$, while the loop’s area and orientation are constant. Which statement correctly describes the induced current’s magnetic field direction during the decrease?
It points opposite the original flux direction to make the flux decrease faster.
It is zero because the flux remains positive during the interval.
It points perpendicular to the original flux direction because the loop is stationary.
It points in the same direction as the original flux to oppose the decrease.
Explanation
This question tests understanding of electromagnetic induction and Faraday's law. As flux decreases from +3 mWb to 0, the rate of change dΦ/dt is negative, inducing an emf by Faraday's law: ε = -dΦ/dt. Lenz's law states that induced effects oppose the change causing them—here, the induced current must oppose the flux decrease. To oppose a decreasing positive flux, the induced current creates a magnetic field in the same direction as the original flux, trying to maintain it, making B correct. Choice A incorrectly suggests the induced field speeds up the decrease, violating Lenz's law. Always remember: induced currents create fields that oppose flux changes, not flux itself.
A solenoid’s current decreases, reducing the magnetic field through a nearby stationary loop. Which statement correctly describes the induced current in the loop?
An induced current is present because the flux is decreasing, so the loop’s flux must decrease too.
An induced current is present because the magnetic flux through the loop is changing.
No induced current is present because the loop is stationary.
No induced current is present because only moving magnets can induce current.
Explanation
This question tests the skill of Electromagnetic induction and Faraday’s law. Induced emf arises from changing magnetic flux, in this scenario from the decreasing current in the solenoid reducing the field through the stationary loop. Faraday's law links the emf to the rate of flux decrease, even though the loop is not moving. Lenz’s law determines the induced current's direction to oppose the flux reduction. Choice A embodies the misconception that a stationary loop cannot experience induction, ignoring flux changes from external sources. Always identify what changes the magnetic flux, including variations in nearby fields.
A loop is flipped 180° in a constant uniform magnetic field, changing only its orientation so flux reverses sign. Which statement correctly describes the induced current?
No induced current is present because the field strength is constant.
No induced current is present because the loop’s area does not change.
An induced current is present because reversing the loop reverses the magnetic field.
An induced current is present because the flux changes as the loop’s orientation reverses.
Explanation
This question tests the skill of Electromagnetic induction and Faraday’s law. Induced emf arises from changing magnetic flux, occurring here as the 180° flip reverses the flux sign by changing the orientation. Faraday's law calculates the emf based on this flux reversal rate. Lenz’s law determines the induced current direction to oppose the flux sign change during the flip. Choice A illustrates the misconception that constant field strength precludes induction, overlooking orientation-induced flux shifts. Always identify what changes the magnetic flux, such as flipping that alters the effective direction.