AP Physics C: Electricity and Magnetism Unit 3 Practice Test & Exam | 18 Questions

Questions 1-3 refer to the following scenario.

1. After electrostatic equilibrium is reached, which of the following best describes the distribution of charge on the sphere?

(A)Positive charge accumulates on the left side and negative charge on the right side.(B)Negative charge accumulates on the left side and positive charge on the right side.(C)A net positive charge is induced on the entire surface of the sphere.(D)The sphere remains completely uncharged on its surface and in its interior.

2. What is the magnitude of the electric field at the very center of the conducting sphere?

(A)$E_0$(B)Greater than $E_0$(C)Less than $E_0$ but greater than zero(D)Zero

3. Which of the following statements about the electric potential of the sphere is correct?

(A)The potential is highest on the right side of the sphere.(B)The potential is highest on the left side of the sphere.(C)The potential is zero at the center of the sphere.(D)The potential is constant throughout the entire sphere.

4. A hollow conducting spherical shell has an inner radius $a$ and an outer radius $b$. A point charge $+Q$ is placed at the center of the shell. The shell itself has a net charge of $-3Q$. What is the charge on the outer surface of the conducting shell (at radius $r=b$)?

(A)$-3Q$(B)$-2Q$(C)$-Q$(D)$+Q$

5. Two isolated conducting spheres, Sphere 1 with radius $R1$ and Sphere 2 with radius $R2$, are given charges $Q1$ and $Q2$, respectively. They are then connected by a thin conducting wire. If $R1 > R2$, which of the following must be true after the spheres reach electrostatic equilibrium?

(A)The charge on Sphere 1 is greater than the charge on Sphere 2.(B)The surface charge density on Sphere 1 is greater than on Sphere 2.(C)The electric field at the surface of Sphere 1 is greater than at the surface of Sphere 2.(D)The final charge on each sphere is $(Q1+Q2)/2$.

6. A neutral conducting sphere is held near a positively charged rod, and a student grounds the sphere with their finger. The student then removes their finger and, after that, removes the rod. Which of the following describes the final state of the sphere?

(A)The sphere is polarized but has no net charge.(B)The sphere has a net positive charge.(C)The sphere has a net negative charge.(D)The sphere remains neutral.

7. A parallel-plate capacitor has a capacitance $C_0$. If the area of the plates is doubled and the distance between the plates is halved, what is the new capacitance?

(A)$C_0/4$(B)$C_0$(C)$2C_0$(D)$4C_0$

8. A capacitor with capacitance $C$ is connected to a battery of voltage $V$ until it is fully charged with charge $Q$. The energy stored in the capacitor is $U$. The battery is disconnected, and the charge remains on the plates. The plates are then pulled apart to twice their original separation. What is the new energy stored in the capacitor?

(A)$U/2$(B)$U$(C)$2U$(D)$4U$

Questions 9-10 refer to the following graph.

9. What is the capacitance of the capacitor?

(A)0.5 µF(B)2.0 µF(C)4.0 µF(D)32 µF

10. How much energy is stored in the capacitor when the potential difference across it is 4.0 V?

(A)4.0 µJ(B)8.0 µJ(C)16 µJ(D)32 µJ

11. An air-filled parallel-plate capacitor is charged by a battery to a voltage $V_0$. The battery remains connected as a slab of dielectric material with dielectric constant $\kappa > 1$ is inserted between the plates, completely filling the space. Which of the following correctly describes the changes in the charge $Q$ on the plates and the energy $U$ stored in the capacitor?

(A)$Q$ increases and $U$ increases.(B)$Q$ increases and $U$ decreases.(C)$Q$ remains the same and $U$ decreases.(D)$Q$ decreases and $U$ remains the same.

12. Which of the following best explains why inserting a dielectric material between the plates of an isolated, charged capacitor decreases the potential difference?

(A)The dielectric material is a conductor, allowing charge to flow between the plates and reduce the potential.(B)The dielectric material increases the effective distance between the plates.(C)The polarization of the dielectric creates an internal electric field that opposes the original field from the plate charges.(D)The dielectric constant increases the permittivity of free space, which reduces the potential.

13. A parallel-plate capacitor with capacitance $C$ is charged to a potential difference $V$. The charging battery is disconnected. A dielectric slab with constant $\kappa = 3$ is then inserted, completely filling the space between the plates. The magnitude of the electric field between the plates is now $E$. What was the magnitude of the electric field, $E_0$, before the dielectric was inserted?

(A)$E/9$(B)$E/3$(C)$3E$(D)$9E$

14. A solid conducting sphere is given a net positive charge. Which of the following correctly describes the electric potential $V$ and the magnitude of the electric field $E$ as a function of the distance $r$ from the center of the sphere?

(A)$V$ is constant inside the sphere; $E$ is constant inside the sphere.(B)$V$ is constant inside the sphere; $E$ decreases as $1/r^2$ inside the sphere.(C)$V$ increases linearly from the center to the surface; $E$ is zero inside the sphere.(D)$V$ is constant inside the sphere; $E$ is zero inside the sphere.

15. The electric field between the plates of an air-filled parallel-plate capacitor is $E = Q/(\epsilon0 A)$. The potential difference is given by $\Delta V = -\int \vec{E} \cdot d\vec{l}$. From these, the capacitance is $C = Q/\Delta V = \epsilon0 A / d$. What is the primary reason this derivation is an approximation for a real capacitor?

(A)The charge $Q$ is not uniformly distributed on the plates.(B)The derivation neglects the fringing field at the edges of the plates.(C)The permittivity of air is not exactly equal to the permittivity of free space.(D)The plates are not perfect conductors.

16. A capacitor is charged and then isolated. A student inserts a dielectric slab with constant $\kappa$ between the plates. Which quantity must remain constant during this process?

(A)The charge on the capacitor plates.(B)The potential difference across the capacitor.(C)The electric field between the plates.(D)The energy stored in the capacitor.

17. Two conducting spheres are connected by a wire. Sphere A has a radius twice that of Sphere B ($RA = 2RB$). The entire system is given a net charge $+Q{total}$. After reaching equilibrium, what is the relationship between the charges $QA$ and $Q_B$ on the spheres?

(A)$QA = QB$(B)$QA = 2QB$(C)$QA = 4QB$(D)$QA = QB / 2$

18. Electrostatic shielding, as demonstrated by a Faraday cage, works because the charges on the outer conducting surface rearrange themselves. This rearrangement causes which of the following? Section II: Free-Response Directions:Show all your work. Your grade will be determined by the clarity of your methods as well as the correctness of your answers. FRQ 1[Skills: 2.D, 2.E, 6.B, 7.A | Topics: 10.1] A solid conducting sphere of radius $a$ has a net charge of $+Q$. It is surrounded by a concentric, uncharged, conducting spherical shell with inner radius $b$ and outer radius $c$. i. The surface of the solid sphere at $r=a$. ii. The inner surface of the spherical shell at $r=b$. iii. The outer surface of the spherical shell at $r=c$. [Image Cue]: A blank graph with the vertical axis labeled "Electric Field, E" and the horizontal axis labeled "Radial Distance, r". Vertical dashed lines are present at r=a, r=b, and r=c. FRQ 2[Skills: 2.D, 6.B, 7.C | Topics: 10.2] Two isolated conducting spheres are separated by a large distance. Sphere 1 has radius $R1 = 2.0$ cm and an initial charge $Q1 = +3.0$ nC. Sphere 2 has radius $R2 = 4.0$ cm and is initially uncharged ($Q2 = 0$). i. Describe the relationship between the final electric potential of Sphere 1 and Sphere 2. Justify your answer. ii. Calculate the final charge, $Q{1f}$ and $Q{2f}$, on each sphere. FRQ 3[Skills: 2.E, 6.B | Topics: 10.3] Consider an ideal parallel-plate capacitor with plate area $A$ and separation distance $d$. The capacitor is given a charge $+Q$ on one plate and $-Q$ on the other. Assume the dimensions of the plates are much larger than the separation distance $d$. FRQ 4[Skills: 6.B, 7.C | Topics: 10.4] A parallel-plate air-gap capacitor with capacitance $C0$ is connected to a battery with potential difference $V0$. The capacitor becomes fully charged, storing a charge $Q0$ and energy $U0$. Two separate procedures are then performed. Procedure 1:The battery is disconnected from the capacitor. Then, a dielectric slab with dielectric constant $\kappa$ is inserted, completely filling the space between the plates. i. The new capacitance $C_1$. ii. The charge on the plates $Q_1$. iii. The potential difference across the plates $V_1$. iv. The energy stored in the capacitor $U_1$. Procedure 2:The dielectric slab is inserted while the battery remains connected to the capacitor. i. The new capacitance $C_2$. ii. The charge on the plates $Q_2$. iii. The potential difference across the plates $V_2$. iv. The energy stored in the capacitor $U_2$.

(A)For Procedure 1, determine the following quantities after the dielectric is inserted, in terms of $C0, V0, Q0, U0$, and $\kappa$.(B)For Procedure 2, determine the following quantities after the dielectric is inserted, in terms of $C0, V0, Q0, U0$, and $\kappa$.(C)Justify your answer for the change in stored energy in each procedure. Specifically, explain the source of the energy change (work done by an external agent, work done by the battery, etc.) for both Procedure 1 and Procedure 2.(D)The work done to add a small amount of charge $dq$ to a capacitor with potential difference $v$ is $dW = v \, dq$. By integrating this expression, derive the total potential energy $U_C$ stored in the capacitor when it has a final charge $Q$. Express your answer in terms of $Q$ and $C$.

AP Physics C: Electricity and Magnetism Unit 3: Conductors and Capacitors Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)

AP Physics C: Electricity and Magnetism Unit 3: Conductors and Capacitors Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)