AP Physics C: Electricity and Magnetism Unit 1 Practice Test & Exam | 18 Questions

Questions 1-3 refer to the following information.

1. What is the direction of the net electric field at point P, the center of the triangle?

(A)To the left(B)To the right(C)Upward, toward the $+2Q$ charge(D)Downward, away from the $+2Q$ charge

2. What is the magnitude of the net electrostatic force exerted on the $+2Q$ charge by the two $-Q$ charges?

(A)$\frac{1}{4\pi\epsilon_0}\frac{2Q^2}{s^2}$(B)$\frac{1}{4\pi\epsilon_0}\frac{2\sqrt{3}Q^2}{s^2}$(C)$\frac{1}{4\pi\epsilon_0}\frac{4Q^2}{s^2}$(D)$\frac{1}{4\pi\epsilon_0}\frac{Q^2}{s^2}$

3. A fourth charge, $+q$, is placed at point P. The distance from each vertex to the center P is $r$. Which of the following expressions represents the magnitude of the net electric force on the charge $+q$ at point P?

(A)Zero(B)$\frac{1}{4\pi\epsilon_0}\frac{2Qq}{r^2}$(C)$\frac{1}{4\pi\epsilon_0}\frac{3Qq}{r^2}$(D)$\frac{1}{4\pi\epsilon_0}\frac{4Qq}{r^2}$

Questions 4-5 refer to the following information.

4. The spheres are brought into contact with each other and are then separated. What is the final charge on Sphere 2?

(A)$0$(B)$+3Q$(C)$+6Q$(D)$-6Q$

5. Now consider a different process. Sphere 1 (with charge $+6Q$) is held fixed. Neutral Sphere 2 is brought near Sphere 1 but does not touch it. A grounding wire is then momentarily connected to Sphere 2 and then removed. Finally, Sphere 1 is moved far away. This process is known as charging by induction. What is the final charge on Sphere 2?

(A)$0$(B)$+3Q$(C)A net negative charge(D)A net positive charge

6. A solid conducting sphere of radius $R$ is given a net positive charge $+Q$. Which of the following correctly describes the electric field $\vec{E}$ and the charge distribution after the sphere reaches electrostatic equilibrium?

(A)The charge is uniformly distributed throughout the volume, and $\vec{E}=0$ for $r<R$.(B)The charge resides on the surface, and $\vec{E}$ is constant but non-zero for $r<R$.(C)The charge resides on the surface, and $\vec{E}=0$ for $r<R$.(D)The charge is uniformly distributed throughout the volume, and $\vec{E}$ points radially inward for $r<R$.

Questions 7-8 refer to the following information.

7. An infinitesimal segment of the rod of length $dy$ is located at a height $y$ above the origin. Which of the following integrals correctly represents the magnitude of the total electric field $E$ at point P, located at a distance $x$ from the rod on the x-axis?

(A)$E = \int_{-\infty}^{\infty} \frac{k\lambda}{x^2+y^2} dy$(B)$E = \int_{-\infty}^{\infty} \frac{k\lambda x}{(x^2+y^2)} dy$(C)$E = \int_{-\infty}^{\infty} \frac{k\lambda y}{(x^2+y^2)^{3/2}} dy$(D)$E = \int_{-\infty}^{\infty} \frac{k\lambda x}{(x^2+y^2)^{3/2}} dy$

8. Due to the symmetry of the charge distribution, the net electric field at point P must point in which direction?

(A)In the positive y-direction(B)In the negative y-direction(C)Radially away from the rod (positive x-direction)(D)At a 45-degree angle from the x-axis

9. A uniform electric field $\vec{E} = E_0 \hat{i}$ exists in a region of space. What is the electric flux through a square surface of side length $L$ that lies in the xy-plane?

(A)$E_0 L^2$(B)$E_0 L$(C)Zero(D)$-E_0 L^2$

10. The same square surface from the previous question is now rotated so that its area vector $\vec{A}$ makes an angle of 60° with the uniform electric field $\vec{E}$. What is the electric flux through the surface?

(A)$E_0 L^2$(B)$E_0 L^2 \cos(60^\circ)$(C)$E_0 L^2 \sin(60^\circ)$(D)Zero

11. A closed cubical surface of side length $L$ is placed in a region with a uniform electric field. What is the net electric flux through the entire surface of the cube?

(A)$E_0 L^2$(B)$2E_0 L^2$(C)$6E_0 L^2$(D)Zero

Questions 12-14 refer to the following information.

12. To use Gauss's Law to find the electric field inside the cylinder ($r<R$), what is the total charge $q_{enc}$ enclosed by the Gaussian surface of radius $r$ and length $L$?

(A)$\rho \pi R^2 L$(B)$\rho \pi r^2 L$(C)$\rho (2\pi r L)$(D)$\frac{\rho \pi r^2 L}{R}$

13. Which expression correctly represents the electric flux $\oint \vec{E} \cdot d\vec{A}$ through the Gaussian surface of radius $r$ and length $L$? (Assume the field is radially outward with magnitude $E$.)

(A)$E(\pi r^2)$(B)$E(2\pi R L)$(C)$E(2\pi r L)$(D)$E(\pi r^2 L)$

14. A student correctly derives the electric field inside the cylinder to be $E = \frac{\rho r}{2\epsilon_0}$. A second student argues that Gauss's Law cannot be used to find the electric field outside a finite-length insulating cylinder. The second student's argument is correct primarily because:

(A)The charge distribution is not symmetric.(B)The electric field is not constant in magnitude over a chosen cylindrical Gaussian surface.(C)The electric field is not perpendicular to the end caps of a chosen cylindrical Gaussian surface.(D)The electric field outside an insulator is always zero.

15. An electron and a proton are separated by a distance $r$. Let $FE$ be the magnitude of the electrostatic force between them and $FG$ be the magnitude of the gravitational force between them. Which statement is true?

(A)$FE \gg FG$(B)$FG \gg FE$(C)$FE = FG$(D)The relationship depends on the distance $r$.

Refer to the figure below.

16. A large, thin, nonconducting sheet has a uniform surface charge density $+\sigma$. Which of the following graphs best represents the magnitude of the electric field $E$ as a function of distance $z$ from the sheet?

(A)Graph A(B)Graph B(C)Graph C(D)Graph D

17. A point charge $+q$ is located at the center of a spherical, uncharged, conducting shell of inner radius $R1$ and outer radius $R2$. What is the net charge on the outer surface of the conducting shell?

(A)$-q$(B)$0$(C)$+q$(D)$+q \frac{R2^2}{R1^2}$

18. An electric dipole consists of a charge $+q$ at $y = +a$ and a charge $-q$ at $y = -a$. What is the approximate magnitude of the electric field at a point on the x-axis very far away (i.e., $x \gg a$)? The field is known to be proportional to $1/x^n$. What is the value of $n$?

(A)1(B)2(C)3(D)4

AP Physics C: Electricity and Magnetism Unit 1: Electric Charges, Fields, and Gauss's Law Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)

AP Physics C: Electricity and Magnetism Unit 1: Electric Charges, Fields, and Gauss's Law Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)