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Electromagnetic induction practice problems AP Physics C: E&M, Unit 13

Written by STEM-Tutor's tutors · Updated October 2026 · 8 questions and 1 free-response question

Magnetic flux, Faraday's and Lenz's laws, motional emf, inductance, energy in inductors, and RL circuits. Try each question before you look: use the hint if you are stuck, then reveal the worked solution one step at a time.

On this page
  1. Key equations
  2. Warm-up questions
  3. Exam-style questions
  4. Free-response practice
  5. Common mistakes
  6. Keep going

Key equations for electromagnetic induction

ΦB = BA cosθmagnetic flux
ε = −N dΦB/dtFaraday's law
ε = BLvmotional emf
ε = −L dI/dtself-induced emf
U = ½LI2, τ = L/Rinductor energy, RL time constant

Constants as on the AP reference sheet: k = 9.0 × 109 N·m²/C², ε0 = 8.85 × 10−12 C²/(N·m²), μ0 = 4π × 10−7 T·m/A, e = 1.6 × 10−19 C. You can type answers like 3.6e5 or 3.6x10^5. The full sheet is in our AP Physics C equation sheet.

Warm-up questions

Quick checks on the core ideas. If these feel easy, go straight to the exam-style questions.

Q1Warm-up
A 0.20 T field passes at right angles through a loop of area 0.050 m². What is the flux?
Wb

Hint

Φ = BA when the field is perpendicular to the loop.

Worked solution
  1. Φ = 0.20 × 0.050 = 0.010 Wb.
Q2Warm-up
A 0.40 m rod moves at 3.0 m/s at right angles to a 0.50 T field. What emf is induced across it?
V

Hint

Motional emf.

Worked solution
  1. ε = BLv = 0.50 × 0.40 × 3.0 = 0.60 V.
Q3Warm-up
Lenz's law says the induced current flows in the direction that:

Hint

Think about conservation of energy.

Worked solution
  1. If the induced current increased the change, energy would come from nowhere.
  2. So it opposes the change in flux: B.

Exam-style questions

Questions at the level of the AP Physics C: E&M exam. The ones marked Challenge combine more than one idea.

Q4Exam-style
A 100-turn coil has its flux change by 0.020 Wb in 0.10 s. What is the average induced emf?
V

Hint

Faraday's law, with N turns.

Worked solution
  1. |ε| = NΔΦ/Δt = 100 × 0.020/0.10.
  2. = 20 V.
Q5Exam-style
The current in a 0.50 H inductor changes at 4.0 A/s. What emf is induced?
V

Hint

ε = L dI/dt (magnitude).

Worked solution
  1. |ε| = 0.50 × 4.0 = 2.0 V.
Q6Exam-style
How much energy is stored in a 0.20 H inductor carrying 3.0 A?
J

Hint

U = ½LI2.

Worked solution
  1. U = ½ × 0.20 × 3.02 = 0.90 J.
Q7Exam-style
What is the time constant of an RL circuit with L = 0.30 H and R = 6.0 Ω?
s

Hint

τ = L/R.

Worked solution
  1. τ = 0.30/6.0 = 0.050 s.
Q8Challenge
A 12 V battery, a 4.0 Ω resistor and an inductor are connected in series, and the switch is closed at t = 0. What is the current after one time constant?
A

Hint

The current rises towards ε/R as 1 − e−t/τ.

Worked solution
  1. Final current: 12/4.0 = 3.0 A.
  2. I(τ) = 3.0(1 − e−1) = 3.0 × 0.632.
  3. I = 1.90 A.

Free-response practice

One original question in the style of the exam's free-response section. Answer it in full, with working, before you open the scoring guide.

Qualitative/quantitative translation style · 7 points · about 20 minutes

A conducting rod of length L slides at constant speed v along two parallel rails joined by a resistor R. A uniform field B points into the page, at right angles to the rails.

  1. (a) Derive the emf induced in the circuit.
  2. (b) Find the current, and state its direction using Lenz's law.
  3. (c) Find the external force needed to keep the rod moving at constant speed.
  4. (d) Show that the mechanical power supplied equals the electrical power dissipated in R.

Write your full answer on paper first, then open the scoring guide and tick each point you earned.

Scoring guide and model answer

Part (a)

The area grows at Lv per second, so dΦ/dt = BLv and ε = BLv.

Part (b)

I = BLv/R. The flux into the page is increasing, so the induced current is anticlockwise, making a field out of the page.

Part (c)

The magnetic force on the rod is ILB = B2L2v/R, opposing the motion, so the pulling force must equal it.

Part (d)

Fv = B2L2v2/R, and I2R = (BLv/R)2R = B2L2v2/R. They are equal: energy is conserved.

Your mark: 0 of 7

Common mistakes in electromagnetic induction

Keep going

Revise the ideas behind these questions:

Then try real exam questions: AP Physics C: E&M past papers, with official scoring guidelines. · All AP Physics C: E&M units