AP Physics C: Electricity and Magnetism, AP exams

Unit 12: Magnetic Fields

Unit 12 covers magnetic force and the fields that produce it. Forces on moving charges and current-carrying wires lead into the Biot-Savart law for arbitrary current elements and Ampere's law for symmetric configurations. As with Gauss's law, recognizing when symmetry makes Ampere's law usable is the central judgment.

Position: 5 of 6 units
Topics covered: 5 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 force on moving charges: The velocity-dependent force, circular and helical paths, and the velocity selector configuration.
Magnetic force on current-carrying wires: Force on a straight or curved wire in a field, and torque on a current loop.
Biot-Savart law: Field from a current element, and integrating it for straight segments, arcs, and loops.
Ampere's law: Using symmetry to find the field of long wires, solenoids, and toroids.
Fields of standard current configurations: Comparing the field patterns of a straight wire, a loop, and a solenoid.

Study tips

How to practice Magnetic Fields.

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

Drill the right-hand rules in short daily sessions; three-dimensional orientation errors are the dominant loss here.
Practice choosing an Amperian loop and justifying the choice from the symmetry present.
Contrast Biot-Savart with Ampere's law explicitly: one always works but is slower, the other is fast only with symmetry.

Where this fits

Unit 12: Magnetic Fields is 5 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 Magnetic Fields 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 long straight wire carries a steady current of 5.0 A. Using the permeability of free space 4(pi) x 10^-7 T m/A, what is the magnitude of the magnetic field at a perpendicular distance of 0.10 m from the wire?
1. A1.0 x 10^-6 T
2. B5.0 x 10^-6 T
3. C1.0 x 10^-5 T
4. D2.0 x 10^-5 T
Show answer
Answer: C. 1.0 x 10^-5 T
Ampere's law applied to a circular loop around the wire gives B = mu0(I)/(2(pi)r) = (2 x 10^-7)(5.0)/(0.10) = 1.0 x 10^-5 T. The 2.0 x 10^-5 T choice omits the factor of 2 in the denominator.
Key insight: The field of a long straight wire falls off as 1/r and circles the wire in the direction given by the right hand.
Question 2Intermediate
A charge of 3.0 x 10^-6 C moves at 4.0 x 10^4 m/s through a uniform 0.20 T magnetic field, with its velocity making an angle of 30 degrees with the field direction. What is the magnitude of the magnetic force on the charge?
1. A6.0 x 10^-3 N
2. B1.2 x 10^-2 N
3. C2.1 x 10^-2 N
4. D2.4 x 10^-2 N
Show answer
Answer: B. 1.2 x 10^-2 N
The magnitude is qvB sin(theta) = (3.0 x 10^-6)(4.0 x 10^4)(0.20)(0.50) = 1.2 x 10^-2 N. The 2.4 x 10^-2 N choice ignores the angle, and 2.1 x 10^-2 N uses the cosine, which would wrongly maximize the force for motion along the field.
Key insight: The magnetic force vanishes for motion parallel to the field and peaks for motion perpendicular to it.
Question 3Intermediate
A long solenoid has 2000 turns per meter and carries a current of 3.0 A. Using the permeability of free space 4(pi) x 10^-7 T m/A, what is the magnitude of the magnetic field deep inside the solenoid?
1. A7.5 x 10^-4 T
2. B1.2 x 10^-3 T
3. C2.5 x 10^-3 T
4. D7.5 x 10^-3 T
Show answer
Answer: D. 7.5 x 10^-3 T
An Amperian rectangle gives B = mu0(n)I = (4(pi) x 10^-7)(2000)(3.0) = 7.5 x 10^-3 T. The 7.5 x 10^-4 T choice loses a power of ten in the turn density, which is per meter and not per centimeter.
Key insight: Inside a long solenoid the field is uniform and depends on turns per unit length, not on the total number of turns.
Question 4Foundational
In a velocity selector, a uniform electric field of 3.0 x 10^4 V/m and a uniform magnetic field of 0.20 T are perpendicular to each other and to the beam. What speed must a charged particle have to pass through undeflected?
1. A6.7 x 10^-6 m/s
2. B1.5 x 10^3 m/s
3. C6.0 x 10^3 m/s
4. D1.5 x 10^5 m/s
Show answer
Answer: D. 1.5 x 10^5 m/s
Undeflected motion requires qE = qvB, so v = E/B = (3.0 x 10^4)/(0.20) = 1.5 x 10^5 m/s, independent of the charge and mass. The 6.0 x 10^3 m/s choice multiplies the fields instead of dividing.
Key insight: A velocity selector picks a speed, not a particle type, because the charge cancels from both sides.
Question 5Advanced
A long straight cylindrical wire of radius R carries a total current I distributed uniformly over its cross-section. In terms of mu0, I, and R, what is the magnitude of the magnetic field at a point a distance R/2 from the axis of the wire?
1. AZero
2. Bmu0 I / (4 pi R)
3. Cmu0 I / (2 pi R)
4. Dmu0 I / (pi R)
Show answer
Answer: B. mu0 I / (4 pi R)
An Amperian circle of radius R/2 encloses one quarter of the current, so B(2(pi))(R/2) = mu0(I/4) gives B = mu0(I)/(4(pi)R). The mu0 I/(2 pi R) choice is the external formula evaluated at the surface r = R, and mu0 I/(pi R) is that same external formula pushed in to r = R/2; both ignore that only part of the current is enclosed.
Key insight: Inside a uniform current distribution the field grows linearly with distance from the axis, then falls off as 1/r outside.

Continue through AP Physics C: Electricity and Magnetism

Practice Magnetic Fields deliberately.

Create your Arcade Academy workspace to turn this topic list into spaced-repetition reviews, linked notes, and progress you can act on.

Create your account

Unit 12: Magnetic Fields