---
title: "AP Physics C: E&M Unit 13 Practice Test"
description: "A timed AP Physics C: E&M Unit 13 (Electromagnetic Induction) practice test in the AP format, drawn from 940 multiple-choice questions and 37 FRQs written for the unit. The standard version takes about 88 minutes."
canonical: "https://fiveable.me/ap-physics-c-e-m/unit-test/13"
type: "unit-test"
subject: "AP Physics C: E&M"
unit: "Unit 13"
---

# AP Physics C: E&M Unit 13 Practice Test

## Overview

A timed AP Physics C: E&M Unit 13 (Electromagnetic Induction) practice test in the AP format, drawn from 940 multiple-choice questions and 37 FRQs written for the unit. The standard version takes about 88 minutes.

## Test Format

- 20 Multiple Choice Questions (40 minutes)
- 1 FRQ – FRQ 1 – Mathematical Routines (24 minutes)
- 1 FRQ – FRQ 2 – Translation Between Representations (24 minutes)

## Unit FRQs by Type

- [FRQ 1 – Mathematical Routines](/ap-physics-c-e-m/frqs/mathematical-routines?unit=13): 11 questions
- [FRQ 2 – Translation Between Representations](/ap-physics-c-e-m/frqs/translation-between-representations?unit=13): 5 questions
- [FRQ 3 – Experimental Design](/ap-physics-c-e-m/frqs/experimental-design?unit=13): 4 questions
- [FRQ 4 – Qualitative/Quantitative Translation](/ap-physics-c-e-m/frqs/qualitative-quantitative-translation?unit=13): 17 questions

## Practice Questions

### Question 1

A circular wire loop of radius $$r$$ is placed in a uniform magnetic field that is perpendicular to the plane of the loop. The magnetic field magnitude changes at a constant rate $$\beta$$, inducing an electromotive force (emf) of magnitude $$\mathcal{E}_0$$. If the loop is replaced by one with radius $$2r$$ and the rate of change of the magnetic field is increased to $$3\beta$$, what is the new induced emf magnitude?

- (A) $$12\mathcal{E}_0$$
- (B) $$6\mathcal{E}_0$$
- (C) $$36\mathcal{E}_0$$
- (D) $$4\mathcal{E}_0$$

**Answer: (A)** Applying Faraday's law requires identifying that induced emf depends on the rate of change of magnetic flux $$\Phi_B = BA$$. Since the area $$A = \pi r^2$$, the emf is proportional to $$r^2$$ and the rate $$\frac{dB}{dt}$$. Doubling the radius increases the area by a factor of 4, and tripling the rate contributes a factor of 3, resulting in a total factor of $$4 \times 3 = 12$$.

### Question 2

A conducting bar of length $$L$$ moves with speed $$v$$ perpendicular to a uniform magnetic field of magnitude $$B$$, generating a motional emf of $$\mathcal{E}$$. If the magnetic field strength is doubled, the bar length is halved, and the speed is quadrupled, what is the new motional emf?

- (A) $$4\mathcal{E}$$
- (B) $$2\mathcal{E}$$
- (C) $$\mathcal{E}$$
- (D) $$8\mathcal{E}$$

**Answer: (A)** Analyzing the functional dependence of motional emf $$\mathcal{E} = BLv$$ reveals how the variable changes combine. Substituting the new values gives $$\mathcal{E}_{new} = (2B)(L/2)(4v) = 4BLv$$, which is four times the original emf.

### Question 3

An ideal solenoid with $$N$$ turns and length $$\ell$$ has a self-inductance that produces an induced emf of magnitude $$\mathcal{E}$$ when the current changes at a rate $$\alpha$$. If a second solenoid has $$2N$$ turns and length $$2\ell$$ but the same cross-sectional area, what is the magnitude of the induced emf for the same rate of current change?

- (A) $$2\mathcal{E}$$
- (B) $$\mathcal{E}$$
- (C) $$4\mathcal{E}$$
- (D) $$\mathcal{E}/2$$

**Answer: (A)** Determining the new emf requires analyzing the functional dependence of inductance $$L = \frac{\mu_0 N^2 A}{\ell}$$. Doubling $$N$$ increases $$L$$ by a factor of 4, while doubling $$\ell$$ decreases $$L$$ by a factor of 2. The net change is a factor of 2, so the induced emf $$\mathcal{E} = L \frac{dI}{dt}$$ doubles.

### Question 4

A rectangular coil with area $$A$$ rotates with angular speed $$\omega$$ in a uniform magnetic field, generating a maximum induced emf $$\mathcal{E}_{max}$$. If the angular speed is doubled to $$2\omega$$ and the area of the coil is reduced to $$A/2$$, what is the new maximum induced emf?

- (A) $$\mathcal{E}_{max}$$
- (B) $$2\mathcal{E}_{max}$$
- (C) $$\mathcal{E}_{max}/2$$
- (D) $$\mathcal{E}_{max}/4$$

**Answer: (A)** Evaluating the generator equation $$\mathcal{E}_{max} = NBA\omega$$ shows the direct proportionality to both area and angular speed. Doubling $$\omega$$ introduces a factor of 2, while halving $$A$$ introduces a factor of 0.5. The product is $$2 \times 0.5 = 1$$, so the emf remains unchanged.

### Question 5

Inside a long solenoid of radius $$R$$ with a changing current, the induced electric field at a distance $$r = R/2$$ from the axis has magnitude $$E_0$$. What is the magnitude of the induced electric field at a distance $$r = R/4$$ from the axis?

- (A) $$E_0/2$$
- (B) $$E_0/4$$
- (C) $$2E_0$$
- (D) $$E_0$$

**Answer: (A)** Using Faraday's law in integral form $$\oint \vec{E} \cdot d\vec{l} = -\frac{d\Phi_B}{dt}$$ for a path of radius $$r < R$$ reveals that $$E(2\pi r) = (\pi r^2) \frac{dB}{dt}$$, simplifying to $$E \propto r$$. Halving the distance from $$R/2$$ to $$R/4$$ therefore halves the electric field magnitude.

### Question 6

A square wire loop of side length $$s$$ moves with constant speed $$v$$ into a uniform magnetic field, generating an induced emf $$\mathcal{E}_0$$. If this loop is replaced by a square loop of side length $$2s$$ moving with speed $$v/2$$, what is the new induced emf?

- (A) $$\mathcal{E}_0$$
- (B) $$2\mathcal{E}_0$$
- (C) $$\mathcal{E}_0/2$$
- (D) $$4\mathcal{E}_0$$

**Answer: (A)** Calculating the motional emf $$\mathcal{E} = B\ell v$$ requires identifying the effective length $$\ell$$ perpendicular to motion. Here $$\ell = s$$. The new emf is $$B(2s)(v/2) = Bsv$$, which is equal to the original emf $$\mathcal{E}_0$$.

### Question 7

The magnetic flux through a loop is given as a function of time by $$\Phi_B(t) = Ct^3$$, where $$C$$ is a constant. At time $$t = T$$, the induced emf has magnitude $$\mathcal{E}_1$$. What is the magnitude of the induced emf at time $$t = 2T$$?

- (A) $$4\mathcal{E}_1$$
- (B) $$2\mathcal{E}_1$$
- (C) $$8\mathcal{E}_1$$
- (D) $$6\mathcal{E}_1$$

**Answer: (A)** Applying calculus to Faraday's law $$\mathcal{E} = |\frac{d\Phi}{dt}|$$ yields $$\mathcal{E}(t) = 3Ct^2$$. This shows the emf depends on the square of time ($$\mathcal{E} \propto t^2$$). Doubling the time $$T$$ results in a factor of $$2^2 = 4$$.

### Question 8

A metal rod of length $$L$$ rotates about one end in a uniform magnetic field with angular speed $$\omega$$, generating an induced emf $$\mathcal{E}$$. If the rod is replaced by one of length $$3L$$ rotating with angular speed $$\omega/3$$, what is the new induced emf?

- (A) $$3\mathcal{E}$$
- (B) $$\mathcal{E}$$
- (C) $$9\mathcal{E}$$
- (D) $$27\mathcal{E}$$

**Answer: (A)** Analyzing the expression for a rotating rod $$\mathcal{E} = \frac{1}{2}B\omega L^2$$ reveals that emf is proportional to $$\omega$$ and $$L^2$$. Tripling $$L$$ introduces a factor of 9, and dividing $$\omega$$ by 3 introduces a factor of 1/3. The product is $$9/3 = 3$$.

### Question 9

A circular loop of wire with radius $$r$$ and resistance $$R$$ is in a changing magnetic field, resulting in an induced current $$I_0$$. If the loop is replaced by one made of the same wire but with radius $$2r$$, what is the new induced current?

- (A) $$2I_0$$
- (B) $$4I_0$$
- (C) $$I_0$$
- (D) $$I_0/2$$

**Answer: (A)** Connecting emf and resistance determines the current. The emf scales with area ($$\propto r^2$$), while resistance scales with circumference ($$\propto r$$) for the same wire type. By Ohm's law, $$I = \mathcal{E}/R \propto r^2/r = r$$. Thus, doubling the radius doubles the current.

### Question 10

The current in a long solenoid varies with time as $$I(t) = kt$$, where $$k$$ is a constant, inducing a constant emf in a nearby loop. If the current function is changed to $$I(t) = kt^2$$, which of the following best describes the time dependence of the new induced emf?

- (A) It increases linearly with time.
- (B) It remains constant.
- (C) It increases quadratically with time.
- (D) It decreases linearly with time.

**Answer: (A)** Applying Faraday's law shows that induced emf is proportional to the rate of change of current $$\frac{dI}{dt}$$. For $$I(t) = kt^2$$, the derivative is $$2kt$$, which depends linearly on time.

## Review the Unit

- [13.1 Magnetic Flux](/ap-physics-c-e-m/unit-13/1-magnetic-flux/study-guide/xWd39wCzttfR8eZG)
- [13.2 Electromagnetic Induction](/ap-physics-c-e-m/unit-13/2-electromagnetic-induction/study-guide/b2D8zUgtWmPcdNoW)
- [13.3 Induced Currents and Magnetic Forces](/ap-physics-c-e-m/unit-13/3-induced-currents-and-magnetic-forces/study-guide/NZE7weqdIZWMqYTM)
- [13.4 Inductance](/ap-physics-c-e-m/unit-13/4-inductance/study-guide/v6xlvrEIaESQJi2U)
- [13.5 Circuits with Resistors and Inductors (LR Circuits)](/ap-physics-c-e-m/unit-13/5-circuits-with-resistors-and-inductors-lr-circuits/study-guide/pX2sUTu1DFkqKZNu)
- [13.6 Circuits with Capacitors and Inductors (LC Circuits)](/ap-physics-c-e-m/unit-13/6-circuits-with-capacitors-and-inductors-lc-circuits/study-guide/nTgyGcr23xjTIU5I)

## Other Unit Tests

- [Unit 8: Electric Charges & Fields: Gauss's Law](/ap-physics-c-e-m/unit-test/8)
- [Unit 9: Electric Potential](/ap-physics-c-e-m/unit-test/9)
- [Unit 10: Conductors and Capacitors](/ap-physics-c-e-m/unit-test/10)
- [Unit 11: Electric Circuits](/ap-physics-c-e-m/unit-test/11)
- [Unit 12: Magnetic Fields & Electromagnetism](/ap-physics-c-e-m/unit-test/12)

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