Electromagnetic Induction and Faraday's Law
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AP Physics 2 › Electromagnetic Induction and Faraday's Law
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?
No induced current is present because the magnetic field strength is constant.
An induced current is present because the flux is momentarily zero.
No induced current is present because only changing area can induce current.
An induced current is present because the flux changes as the loop’s orientation changes.
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 clockwise induced current occurs because it produces a field into the page.
A clockwise induced current occurs because it increases the flux into the page.
No induced current occurs because the magnetic field is uniform.
A counterclockwise induced current occurs because it produces a field out of 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.
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 in the same direction as the original flux to oppose the decrease.
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 opposite the original flux direction to make the flux decrease faster.
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 $50$-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?
No induced current occurs because the coil is not moving.
An induced current is present because the magnetic flux through the coil changes.
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.
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.
A solenoid’s current decreases, reducing the magnetic field through a nearby stationary loop. Which statement correctly describes the induced current in the loop?
No induced current is present because the loop is stationary.
An induced current is present because the magnetic flux through the loop is changing.
An induced current is present because the flux is decreasing, so the loop’s flux must decrease too.
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 loop’s area does not change.
An induced current is present because reversing the loop reverses the magnetic field.
No induced current is present because the field strength is constant.
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.
The magnetic flux through a loop decreases linearly from a positive value to zero, as shown. Which statement correctly describes the induced current direction?
A counterclockwise induced current is present because the flux is decreasing, so current matches the change.
A counterclockwise induced current is present to oppose the decrease in positive flux.
No induced current is present because the flux becomes zero.
A clockwise induced current is present because the flux is positive.
Explanation
This question tests the skill of Electromagnetic induction and Faraday’s law. Induced emf arises from changing magnetic flux, here as the flux decreases linearly from positive to zero. Faraday's law states the emf is the negative rate of this decreasing flux. Lenz’s law determines the direction of the induced current to oppose the decrease, producing a field to maintain the positive flux, which is counterclockwise. Choice D represents the misconception that induced current matches the flux change direction, contradicting Lenz's opposition principle. Always identify what changes the magnetic flux and determine how to oppose that specific change.
The magnetic flux through a coil varies with time as shown. Which statement correctly describes whether an induced current is present at $t=3,\text{s}$?
An induced current is present because the flux is nonzero at $t=3,\text{s}$.
No induced current is present because the flux is constant at $t=3,\text{s}$.
An induced current is present because the flux is constant at $t=3,\text{s}$.
No induced current is present because magnets create current only when touching the coil.
Explanation
This question tests the skill of Electromagnetic induction and Faraday’s law. Induced emf arises from changing magnetic flux and is zero when the flux is constant, as per Faraday's law stating emf equals the negative rate of flux change. At t=3 s, the flux is constant, so there is no change in flux and thus no induced emf or current. Lenz’s law determines direction only when there is an induced emf, but here it does not apply since there is no change to oppose. Choice A reflects the misconception that nonzero flux alone induces current, confusing static flux with changing flux. Always identify what changes the magnetic flux by examining the rate of change, not just its value.
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 the magnetic flux through the loop is constant.
An induced current is present because the magnetic field passes through the loop.
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.
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 single loop is in a uniform magnetic field pointing into the page. The field magnitude decreases to zero at a steady rate while the loop’s area and orientation remain constant. Which statement correctly describes the induced current direction?
No current is induced because the loop is not moving.
A counterclockwise current is induced to create a field into the page, opposing the decrease in inward flux.
No current is induced because the flux is decreasing rather than increasing.
A clockwise current is induced because the field points into the page.
Explanation
This question tests understanding of electromagnetic induction and Faraday's law. When a magnetic field pointing into the page decreases to zero, the inward flux through the loop decreases steadily. By Lenz's law, the induced current must oppose this change by creating a magnetic field into the page to try to maintain the original flux. A counterclockwise current (viewed from above) produces a field into the page, making A correct. Choice C incorrectly assumes decreasing flux cannot induce current, misunderstanding that any flux change—increase or decrease—induces current according to Faraday's law. Always apply Lenz's law consistently: induced effects oppose the change causing them.