AP Physics C: Electricity & Magnetism practice questions and exam guide

An infinite line of charge λ along the z-axis. The appropriate Gaussian surface for finding E at distance r is:

1. Concentric cylinder of radius r and length L
2. Sphere of radius r
3. Cube centered on a point on the line
4. Plane perpendicular to the line

Answer: A — Concentric cylinder of radius r and length L

A) Cylindrical symmetry matches; E·2πrL = λL/ε₀. B) Wrong symmetry. C) Cube doesn't simplify integral. D) Plane has no closed flux.

A solenoid has n turns per unit length and current I. The magnetic field INSIDE (along axis) is approximately:

1. B = μ₀nI
2. B = μ₀n²I
3. B = μ₀I/n
4. B = μ₀nI/(2π)
5. B = nI/μ₀

Answer: A — B = μ₀nI

Ampère's law applied to ideal infinite solenoid: B = μ₀nI inside (uniform, parallel to axis); B ≈ 0 outside. Direction by right-hand rule (curl fingers in current direction; thumb shows B inside).

Three identical +q charges form an equilateral triangle of side a. The net force on one charge is:

1. Zero by symmetry
2. √3·kq²/a² directed away from the centroid
3. kq²/a²
4. 2kq²/a²

Answer: B — √3·kq²/a² directed away from the centroid

B) Two forces of kq²/a² at 60° add to √3·kq²/a² radially outward. A) Wrong — symmetry gives radial net, not zero. C/D) Missing the vector sum.

Energy delivered by the battery during full charging is U_battery = QV₀. Energy stored on the cap is ½QV₀. The remainder ½QV₀ is:

1. Stored as magnetic energy
2. Recovered after the switch opens
3. Dissipated as heat in the resistor
4. Lost to electromagnetic radiation

Answer: C — Dissipated as heat in the resistor

C) Independent of R(!) — exactly half the battery's energy is always dissipated in R during full charging. A) No inductor present. B/D) Negligible.

A long solenoid has n = 5000 turns/m and current I = 0.4 A. B inside:

1. 2.51 × 10⁻³ T
2. 5 × 10⁻³ T
3. 2.51 × 10⁻⁵ T
4. 0.4 T

Answer: A — 2.51 × 10⁻³ T

A) B = μ₀nI = (4πe−7)(5000)(0.4) = 2.51e−3 T. B/C/D) Arithmetic errors.

Electric field E⃗ relates to force on test charge q:

1. E = qF
2. F⃗ = qE⃗ — field is force per unit charge; E units N/C = V/m
3. E = F²/q
4. E = q/F
5. E = mg

Answer: B — F⃗ = qE⃗ — field is force per unit charge; E units N/C = V/m

Field as a region of influence. Point charge field: E = kq/r². Direction: outward from + charge, inward to −. Field LINES start on + end on −, density proportional to magnitude. Critical mental model.

The capacitance C of a parallel-plate capacitor (plate area A, separation d, vacuum) is:

1. C = ε₀·A/d
2. C = A/d² alone
3. C = ε₀·d/A
4. C = A · d

Answer: A — C = ε₀·A/d

A) Standard formula. B/C/D) Each is incorrect.

In a region V(x,y,z) = 3x² − 2y + 4xz, the y-component of E at (1,2,3) is:

1. +2 V/m
2. −6 V/m
3. 0
4. +12 V/m

Answer: A — +2 V/m

A) E_y = −∂V/∂y = −(−2) = +2 V/m. B) Sign error. C) Forgot the y term. D) Wrong derivative.

Same uniform-ρ sphere — the field at r < R is:

1. Zero (shell theorem)
2. ρ·r/(3ε₀) (linear in r)
3. Q/(4πε₀r²)
4. ρR/(3ε₀)

Answer: B — ρ·r/(3ε₀) (linear in r)

B) Q_enc = ρ·(4/3)πr³; Gauss → E(4πr²) = ρ(4/3)πr³/ε₀ → E = ρr/(3ε₀). A) That's the hollow-shell case. C) Outside formula. D) At r = R, but not interior in general.

A charge q in a uniform electric field E experiences force:

1. F = qE (parallel to E if q > 0; antiparallel if q < 0)
2. F = qE²
3. F = E/q
4. F = q/E
5. F = qE·t

Answer: A — F = qE (parallel to E if q > 0; antiparallel if q < 0)

F = qE. Positive charge accelerates along E; negative charge against E. This defines electric field — force per unit charge.

An inductor has L = 2 H and current changing at 3 A/s. The induced EMF is:

1. 1.5 V
2. 2 V
3. 3 V
4. 6 V
5. 9 V

Answer: D — 6 V

EMF_L = -L·(dI/dt). |EMF| = 2 · 3 = 6 V. The minus sign indicates the EMF opposes current change (Lenz's law). Inductors resist current changes — useful for filtering and energy storage.

A spherical Gaussian surface of radius r encloses a point charge +Q at its center. The flux through the surface is:

1. kQ/r²
2. 4πr²·Q
3. Q·r²
4. Q/ε₀

Answer: D — Q/ε₀

D) Gauss: Φ = Q_enc/ε₀, independent of r. A) That's the field, not the flux. B/C) Confuses area and flux.

Spherical capacitor (concentric shells)?

C = 4πε₀ ab/(b-a). Inner radius a, outer b.

Inductance 0.5 H. dI/dt = 4 A/s. EMF?

EMF = -L·dI/dt = -2 V.

Worked example: Apply Ampère's law to a long solenoid — derive B = μ₀nI.

B = μ₀nI inside an infinite solenoid (uniform, along axis); B ≈ 0 outside.

Magnetic flux Φ_B?

Φ_B = ∫B·dA. 'Amount of B through area.' Units: weber (Wb).

Why does grounding remove charge?

Connects conductor to large reservoir (Earth). Charges flow until potentials equalize (≈ 0).

Energy stored in inductor?

U = ½LI².