AP Physics C: Electricity and Magnetism, AP exams

Unit 13: Electromagnetic Induction

Unit 13 closes the course with changing fields. Magnetic flux, Faraday's law, and Lenz's reasoning connect a changing flux to an induced potential difference and current. Inductance, energy stored in an inductor, and LR and LC circuits extend the treatment to time-dependent circuits.

Position: 6 of 6 units
Topics covered: 6 topics in this guide

What is covered

Topics inside this unit.

These topics describe the scope students most often review for this part of AP Physics C: Electricity and Magnetism. Treat them as a study checklist rather than an exhaustive list of what a single exam form can sample.

Magnetic flux: Flux through a surface and the three ways it can change: field strength, area, or orientation.
Faraday's law and Lenz's law: Induced potential difference from the rate of flux change, and the direction that opposes the change.
Motional emf and induced forces: Emf from a conductor moving through a field, and the retarding force that results.
Inductance: Self-inductance, the energy stored in an inductor, and the field energy density.
LR circuits: Exponential current growth and decay with an inductor, and the circuit time constant.
LC circuits: Oscillation between capacitor and inductor energy, and the angular frequency of the oscillation.

Study tips

How to practice Induction.

Section-specific guidance that follows from how this material is usually tested.

Identify which flux factor is changing before applying Faraday's law; this single habit prevents most errors.
Practice stating the induced current direction in words using opposition to the change, then verify with a rule.
Compare RC and LR circuits side by side; the mathematics is parallel and learning them together halves the work.

Where this fits

Unit 13: Electromagnetic Induction is 6 of 6 units in the AP Physics C: Electricity and Magnetism guide. Use the full guide to balance it against everything else you have to review.

Back to the AP Physics C: Electricity and Magnetism guide Official exam information

Sample Induction questions

Practice questions, not yet expert-reviewed

Original practice questions written to the published framework for this section. No expert has reviewed them, and they are not taken from any official exam. Try each one before you open the answer.

Question 1Foundational
A single square loop of wire 0.20 m on a side lies perpendicular to a uniform magnetic field whose magnitude increases steadily from 0 to 0.60 T over 0.30 s. What is the magnitude of the emf induced in the loop?
1. A0.020 V
2. B0.024 V
3. C0.080 V
4. D0.12 V
Show answer
Answer: C. 0.080 V
The loop area is 0.040 m^2, so the flux change is (0.60 T)(0.040 m^2) = 0.024 Wb and Faraday's law gives emf = 0.024/0.30 = 0.080 V. The 0.024 V choice reports the flux change without dividing by the time interval.
Key insight: Faraday's law involves the rate of change of flux, so the same field change spread over a longer time induces less emf.
Question 2Foundational
A straight conducting rod of length 0.50 m moves at 4.0 m/s through a uniform 0.30 T magnetic field, with the rod, its velocity, and the field all mutually perpendicular. What is the magnitude of the motional emf induced between the ends of the rod?
1. A0.075 V
2. B0.15 V
3. C0.60 V
4. D6.0 V
Show answer
Answer: C. 0.60 V
Motional emf is BLv = (0.30 T)(0.50 m)(4.0 m/s) = 0.60 V, which is also what Faraday's law gives for a circuit whose area sweeps out at Lv. The 0.15 V choice leaves the speed out of the product entirely.
Key insight: Motional emf is Faraday's law in disguise: the moving rod changes the area of the circuit and therefore the flux.
Question 3Intermediate
An inductor of inductance 0.40 H carries a steady current of 3.0 A. How much energy is stored in its magnetic field?
1. A0.60 J
2. B1.2 J
3. C1.8 J
4. D3.6 J
Show answer
Answer: C. 1.8 J
Stored energy is (1/2)LI^2 = (1/2)(0.40)(3.0)^2 = 1.8 J. The 3.6 J choice omits the factor of one half, and 0.60 J uses I in place of I squared.
Key insight: An inductor stores energy in its magnetic field just as a capacitor stores energy in its electric field.
Question 4Intermediate
A 0.20 H inductor is connected in series with a 50 ohm resistor and a battery. What is the time constant of this LR circuit?
1. A4.0 x 10^-3 s
2. B0.25 s
3. C10 s
4. D2.5 x 10^2 s
Show answer
Answer: A. 4.0 x 10^-3 s
The LR time constant is L/R = 0.20/50 = 4.0 x 10^-3 s. The 10 s choice multiplies L by R instead of dividing, which does not produce units of time.
Key insight: In an LR circuit a larger resistance shortens the time constant, the opposite of its effect in an RC circuit.
Question 5Advanced
An ideal LC circuit contains a 2.0 x 10^-3 H inductor and a 5.0 x 10^-6 F capacitor. What is the angular frequency of the resulting oscillation?
1. A1.0 x 10^-4 rad/s
2. B1.6 x 10^3 rad/s
3. C1.0 x 10^4 rad/s
4. D1.0 x 10^8 rad/s
Show answer
Answer: C. 1.0 x 10^4 rad/s
The loop equation has the form of a harmonic oscillator with omega = 1/sqrt(LC) = 1/sqrt(1.0 x 10^-8) = 1.0 x 10^4 rad/s. The 1.6 x 10^3 choice is the frequency in hertz, which is omega divided by 2 pi rather than the angular frequency.
Key insight: An LC circuit trades energy between capacitor and inductor exactly as a mass-spring system trades potential for kinetic energy.

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Unit 13: Electromagnetic Induction