---
title: "AP Physics C: E&M Unit 9 Practice Test"
description: "A timed AP Physics C: E&M Unit 9 (Electric Potential) practice test in the AP format, drawn from 530 multiple-choice questions and 39 FRQs written for the unit. The standard version takes about 88 minutes."
canonical: "https://fiveable.me/ap-physics-c-e-m/unit-test/9"
type: "unit-test"
subject: "AP Physics C: E&M"
unit: "Unit 9"
---

# AP Physics C: E&M Unit 9 Practice Test

## Overview

A timed AP Physics C: E&M Unit 9 (Electric Potential) practice test in the AP format, drawn from 530 multiple-choice questions and 39 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=9): 11 questions
- [FRQ 2 – Translation Between Representations](/ap-physics-c-e-m/frqs/translation-between-representations?unit=9): 3 questions
- [FRQ 3 – Experimental Design](/ap-physics-c-e-m/frqs/experimental-design?unit=9): 5 questions
- [FRQ 4 – Qualitative/Quantitative Translation](/ap-physics-c-e-m/frqs/qualitative-quantitative-translation?unit=9): 20 questions

## Practice Questions

### Question 1

A point charge $$+Q$$ creates an electric potential $$V_0$$ at a distance $$R$$. If the charge is changed to $$-2Q$$ and the distance is reduced to $$R/2$$, what is the new electric potential at that point?

- (A) $$-4V_0$$
- (B) $$-2V_0$$
- (C) $$+2V_0$$
- (D) $$+4V_0$$

**Answer: (A)** Applying the functional dependence $$V = kQ/r$$ requires substituting the new values. Substituting $$-2Q$$ for charge and $$R/2$$ for distance yields $$V_{new} = k(-2Q)/(R/2) = -4(kQ/R) = -4V_0$$.

### Question 2

A uniformly charged ring of radius $$R$$ and total charge $$Q$$ produces an electric potential $$V_0$$ at a point on its axis at distance $$x = R$$ from the center. If the ring's radius and the distance to the point are both doubled to $$2R$$, what is the new potential?

- (A) $$V_0/4$$
- (B) $$V_0/2$$
- (C) $$V_0$$
- (D) $$2V_0$$

**Answer: (B)** Using the potential formula for a ring $$V = kQ/\sqrt{R^2 + x^2}$$, doubling both $$R$$ and $$x$$ results in a denominator of $$\sqrt{(2R)^2 + (2x)^2} = 2\sqrt{R^2 + x^2}$$, reducing the potential by a factor of 2.

### Question 3

A thin semicircular rod with total charge $$Q$$ and radius $$R$$ produces an electric potential $$V_c$$ at its center of curvature. If the radius is doubled to $$2R$$ while keeping the total charge $$Q$$ constant, what is the new potential at the center?

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

**Answer: (B)** Since every element of charge $$dq$$ is at the same distance $$R$$, the potential is $$V = \int k dq/R = kQ/R$$. Doubling $$R$$ while keeping $$Q$$ constant halves the potential.

### Question 4

An infinitely long wire with linear charge density $$\lambda$$ creates a potential difference $$\Delta V$$ between points at distances $$r$$ and $$2r$$ from the wire. If the linear charge density is doubled to $$2\lambda$$, what is the new potential difference between the same points?

- (A) $$\Delta V/2$$
- (B) $$\Delta V$$
- (C) $$2\Delta V$$
- (D) $$4\Delta V$$

**Answer: (C)** The potential difference near an infinite wire is $$\Delta V = (\lambda/2\pi\epsilon_0)\ln(r_2/r_1)$$. Since $$\Delta V$$ is directly proportional to $$\lambda$$, doubling $$\lambda$$ doubles the potential difference.

### Question 5

Three point charges, each with charge $$+q$$, are fixed at the vertices of an equilateral triangle of side length $$d$$. The total electric potential energy of the system is $$U_0$$. If the side length of the triangle is increased to $$3d$$, what is the new potential energy?

- (A) $$U_0/9$$
- (B) $$U_0/3$$
- (C) $$3U_0$$
- (D) $$9U_0$$

**Answer: (B)** The potential energy of the system is the sum of pairwise interactions $$U = \sum k q_i q_j / r_{ij}$$. Since every distance $$r_{ij}$$ scales by 3, the total energy scales by $$1/3$$.

### Question 6

A finite rod of length $$L$$ has a uniform linear charge density $$\lambda$$. The electric potential at a point on the axis at distance $$d$$ from one end is $$V_0$$. If the linear charge density is doubled while $$L$$ and $$d$$ remain constant, what is the new potential?

- (A) $$V_0/4$$
- (B) $$V_0/2$$
- (C) $$2V_0$$
- (D) $$4V_0$$

**Answer: (C)** Electric potential is directly proportional to the charge density $$\lambda$$ (since $$V = \int k \lambda dx / r$$). Doubling $$\lambda$$ directly doubles the potential.

### Question 7

A conducting sphere of radius $$R$$ carries a net charge $$Q$$, resulting in an electric potential $$V_s$$ at its surface. If the sphere's radius is reduced to $$R/3$$ while the charge $$Q$$ remains constant, what is the new potential at the surface?

- (A) $$V_s/9$$
- (B) $$V_s/3$$
- (C) $$3V_s$$
- (D) $$9V_s$$

**Answer: (C)** The potential at the surface of a conducting sphere is $$V = kQ/R$$. Reducing $$R$$ by a factor of 3 increases the potential by a factor of 3.

### Question 8

Two positive point charges $$+Q$$ are separated by a distance $$2x$$. The electric potential at the midpoint between them is $$V_0$$. If the distance between the charges is increased to $$4x$$, what is the new potential at the midpoint?

- (A) $$V_0/4$$
- (B) $$V_0/2$$
- (C) $$2V_0$$
- (D) $$4V_0$$

**Answer: (B)** The potential at the midpoint is $$V = 2(kQ/x)$$. If the separation doubles to $$4x$$, the distance from midpoint to charge becomes $$2x$$, reducing $$V$$ to $$2(kQ/2x) = V_0/2$$.

### Question 9

A circular arc of radius $$R$$ subtends an angle $$\theta$$ at its center and carries a uniform linear charge density $$\lambda$$. The potential at the center is $$V_0$$. If the angle is increased to $$2\theta$$ while $$R$$ and $$\lambda$$ remain constant, what is the new potential?

- (A) $$V_0/2$$
- (B) $$V_0$$
- (C) $$2V_0$$
- (D) $$4V_0$$

**Answer: (C)** The potential is $$V = \int k dq/R = k(R\theta\lambda)/R = k\lambda\theta$$. Doubling the angle $$\theta$$ doubles the total charge and thus doubles the potential.

### Question 10

A spherical shell of radius $$R$$ carries charge $$+Q$$. A second concentric shell of radius $$2R$$ carries charge $$+Q$$. The potential at the center is $$V_{center}$$. If the outer shell is removed, what is the new potential at the center?

- (A) $$1/3 V_{center}$$
- (B) $$2/3 V_{center}$$
- (C) $$3/4 V_{center}$$
- (D) $$4/3 V_{center}$$

**Answer: (B)** Initial potential is $$V = kQ/R + kQ/2R = 1.5 kQ/R$$. Removing the outer shell leaves $$V = kQ/R$$. The ratio is $$1/1.5 = 2/3$$.

## Review the Unit

- [9.1 Electric Potential Energy](/ap-physics-c-e-m/unit-9/1-electric-potential-energy/study-guide/InqS68GlgFXEOpRi)
- [9.2 Electric Potential](/ap-physics-c-e-m/unit-9/2-electric-potential/study-guide/NRfC3T6m1ZWgp69A)
- [9.3 Conservation of Electric Energy](/ap-physics-c-e-m/unit-9/3-conservation-of-electric-energy/study-guide/UJ3tt1NL0NomtBVo)

## Other Unit Tests

- [Unit 8: Electric Charges & Fields: Gauss's Law](/ap-physics-c-e-m/unit-test/8)
- [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)
- [Unit 13: Electromagnetic Induction](/ap-physics-c-e-m/unit-test/13)

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