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Magnetic fields and electromagnetism practice problems AP Physics C: E&M, Unit 12

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

Magnetic forces on moving charges and currents, fields of wires and solenoids, the Biot-Savart law and Ampère's law. 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 magnetic fields and electromagnetism

F = qvB sinθforce on a moving charge
F = ILB sinθforce on a current
B = μ0I/(2πr)long straight wire
B = μ0nIinside a long solenoid
∮ B·dl = μ0IencAmpère's law

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 proton moves at 2.0 × 106 m/s at right angles to a 0.50 T field. What is the magnetic force on it?
N

Hint

F = qvB when the velocity is perpendicular to the field.

Worked solution
  1. F = 1.6 × 10−19 × 2.0 × 106 × 0.50.
  2. F = 1.6 × 10−13 N.
Q2Warm-up
What is the magnetic field 0.050 m from a long straight wire carrying 10 A?
T

Hint

B = μ0I/(2πr).

Worked solution
  1. B = 4π × 10−7 × 10/(2π × 0.050).
  2. B = 4.0 × 10−5 T.
Q3Warm-up
How much work does a magnetic field do on a moving charged particle?

Hint

Look at the direction of the force compared with the motion.

Worked solution
  1. The magnetic force is always perpendicular to the velocity.
  2. So it does no work and cannot change the speed: C.

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
An electron moves at 1.0 × 106 m/s perpendicular to a 0.010 T field. What is the radius of its circular path?
m

Hint

The magnetic force provides the centripetal force: qvB = mv2/r.

Worked solution
  1. r = mv/(qB).
  2. r = 9.11 × 10−31 × 1.0 × 106/(1.6 × 10−19 × 0.010).
  3. r = 5.69 × 10−4 m.
Q5Exam-style
Two long parallel wires 0.10 m apart each carry 5.0 A. What is the force per metre between them?
N/m

Hint

One wire sits in the other's field: F/L = I2B1.

Worked solution
  1. F/L = μ0I1I2/(2πd).
  2. = 4π × 10−7 × 25/(2π × 0.10).
  3. F/L = 5.0 × 10−5 N/m, attractive if the currents are in the same direction.
Q6Exam-style
A long solenoid has 1000 turns per metre and carries 2.0 A. What is the field inside it?
T

Hint

B = μ0nI.

Worked solution
  1. B = 4π × 10−7 × 1000 × 2.0.
  2. B = 2.51 × 10−3 T.
Q7Exam-style
A 0.20 m wire carrying 3.0 A sits at right angles to a 0.40 T field. What is the force on it?
N

Hint

F = ILB.

Worked solution
  1. F = 3.0 × 0.20 × 0.40 = 0.24 N.
Q8Challenge
A long, thick wire of radius R carries current spread uniformly across its cross-section. Inside the wire (r < R), the field:

Hint

Apply Ampère's law to a circle of radius r inside the wire.

Worked solution
  1. The enclosed current is I(r/R)2.
  2. B(2πr) = μ0I r2/R2, so B = μ0Ir/(2πR2).
  3. B grows in proportion to r: C.

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.

Translation between representations style · 6 points · about 20 minutes

A long straight cylindrical wire of radius R carries a current I spread uniformly over its cross-section.

  1. (a) Use Ampère's law to find B at a distance r > R from the axis.
  2. (b) Find B at a distance r < R.
  3. (c) Sketch or describe B against r from 0 to 3R.

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)

Circle of radius r encloses I: B(2πr) = μ0I, so B = μ0I/(2πr).

Part (b)

Enclosed current I r2/R2, so B = μ0Ir/(2πR2).

Part (c)

B rises linearly from zero at the axis to μ0I/(2πR) at the surface, then falls as 1/r.

Your mark: 0 of 6

Common mistakes in magnetic fields and electromagnetism

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