AP Physics 2: Algebra-Based Unit 2: Electric Force, Field, and Potential Practice Exam

Assessment for Unit 2: Electric Force, Field, and Potential

Estimated Time: 60 minutes

Exam Details

Questions: 23 total (23 multiple choice)
Time: 60 minutes (recommended)
Topics Covered: Unit 2: Electric Force, Field, and Potential
Format: Multiple Choice questions matching real exam difficulty
Scoring: Instant results with detailed explanations

A. Multiple-Choice Questions (23 Questions)

Select the one best answer for each question.

1. [Skill: 6.4 | Topic: 2.1] An experimenter is measuring the net electric charge on several small plastic beads. Which of the following measured values for the net charge $q$ on a bead is physically possible according to the principle of charge quantization?

(A)$q = 2.40 \times 10^{-19} \text{ C}$(B)$q = 4.00 \times 10^{-19} \text{ C}$(C)$q = 4.80 \times 10^{-19} \text{ C}$(D)$q = 7.20 \times 10^{-19} \text{ C}$

2. [Skill: 2.2 | Topic: 2.1] Two small spheres, each carrying a net charge, are separated by a distance $d$. The magnitude of the electrostatic force exerted by one sphere on the other is $F$. If the charge on the first sphere is doubled, the charge on the second sphere is kept constant, and the distance between them is tripled to $3d$, what is the magnitude of the new electrostatic force in terms of $F$?

(A)$\frac{2}{3} F$(B)$\frac{4}{9} F$(C)$\frac{2}{9} F$(D)$\frac{1}{18} F$

3. [Skill: 1.4 | Topic: 2.1] Two protons are held at a fixed distance from each other in a vacuum. Which of the following statements correctly compares the gravitational force $\vec{F}_G$ and the electric force $\vec{F}_E$ exerted by one proton on the other?

(A)The forces are in the same direction, and $|\vec{F}_E| > |\vec{F}_G|$.(B)The forces are in opposite directions, and $|\vec{F}_E| > |\vec{F}_G|$.(C)The forces are in the same direction, and $|\vec{F}_G| > |\vec{F}_E|$.(D)The forces are in opposite directions, and $|\vec{F}_G| > |\vec{F}_E|$.

Refer to the figure below.

4. [Skill: 1.1 | Topic: 2.1] Two point charges are placed a fixed distance apart. Initially, they are in a vacuum, and the magnitude of the electric force between them is $F_{vac}$. The space between the charges is then filled with a non-conducting material with an electric permittivity $\epsilon$ that is greater than the permittivity of free space $\epsilon_0$. Which of the following describes the change in the magnitude of the electric force and provides the correct justification?

(A)The force increases because the material becomes polarized and its internal field adds to the field of the charges.(B)The force increases because the higher permittivity allows the electric field lines to propagate more efficiently.(C)The force decreases because the material becomes polarized, creating an induced internal field that opposes the field of the charges.(D)The force remains the same because the electric force between two point charges depends only on the magnitude of the charges and the distance between them.

5. [Skill: 6.4 | Topic: 2.2] Two identical small metal spheres, $S_1$ and $S_2$, are mounted on insulating stands. Sphere $S_1$ carries a net charge of $+10 mu C$, and sphere $S_2$ carries a net charge of $-4 mu C$. The spheres are brought into contact with each other and then separated. Which of the following correctly describes the final charge on $S_1$ and the behavior of the system's total charge?

(A)The final charge on $S_1$ is $+3 mu C$, and the total charge of the system remains $+6 mu C$.(B)The final charge on $S_1$ is $+6 mu C$, and the total charge of the system remains $+6 mu C$.(C)The final charge on $S_1$ is $+3 mu C$, and the total charge of the system becomes $+3 mu C$.(D)The final charge on $S_1$ is $+7 mu C$, and the total charge of the system remains $+14 mu C$.

Refer to the figure below.

6. [Skill: 1.4 | Topic: 2.2] A student performs an experiment with a neutral, conducting sphere on an insulating stand. The following steps are performed in order: 1. A positively charged glass rod is brought near (but does not touch) the right side of the sphere. 2. A wire is connected from the left side of the sphere to the ground. 3. The ground wire is removed. 4. The glass rod is moved far away from the sphere. Which of the following best describes the final state of the sphere and the movement of charge during Step 2?

(A)The sphere is negatively charged because protons flowed from the sphere into the ground.(B)The sphere is negatively charged because electrons flowed from the ground onto the sphere.(C)The sphere remains neutral because the rod never touched it.(D)The sphere is positively charged because electrons were attracted toward the glass rod and then entered the ground.

7. [Skill: 7.2 | Topic: 2.2] An isolated system consists of three identical metal spheres: Sphere A ($Q_A = +3q$), Sphere B ($Q_B = -q$), and Sphere C ($Q_C = 0$). Sphere A is first touched to Sphere B and then separated. Next, Sphere B is touched to Sphere C and then separated. What is the final charge on Sphere C?

(A)+q(B)+0.5q(C)+1.5q(D)+2q

8. [Skill: 6.1 | Topic: 2.2] A positively charged rod is brought near a neutral metallic object that is connected to a large, neutral reservoir (ground). While the rod is held in place, the connection to the reservoir is broken. The rod is then removed. Which of the following statements is true regarding the system consisting of the metallic object and the rod?

(A)The net charge of the metallic object-rod system was conserved throughout the entire process.(B)The metallic object became positively charged because it was attracted to the positive rod.(C)The net charge of the metallic object-rod system changed because charge was transferred between the object and the reservoir.(D)The reservoir gained a net positive charge during the process because electrons moved from the reservoir to the rod.

9. [Skill: 2.A | Topic: 2.3] A small positive test charge $q_0$ is placed at a distance $r$ from a fixed source charge $+Q$. The test charge experiences an electric force of magnitude $F_E$. If the test charge is replaced by a new test charge with a magnitude of $+3q_0$ at the same location, which of the following best describes the change, if any, to the magnitude of the electric field $E$ produced by the source charge at that location?

(A)The magnitude of the electric field increases to $3E$.(B)The magnitude of the electric field decreases to $E/3$.(C)The magnitude of the electric field remains the same.(D)The magnitude of the electric field becomes zero because the test charges are no longer balanced.

Refer to the figure below.

10. [Skill: 1.C | Topic: 2.3] Two point charges of equal magnitude but opposite sign, $+Q$ and $-Q$, are fixed at two corners of an equilateral triangle, as shown in the diagram. Point $P$ is the third corner of the triangle. Which of the following vectors best represents the direction of the net electric field $\vec{E}_{net}$ at point $P$? [Image Cue]: [Diagram], [Equilateral triangle with $+Q$ at the bottom-left vertex, $-Q$ at the bottom-right vertex, and point $P$ at the top vertex. The distance between each vertex is $d$.]

(A)A vector pointing vertically upward, away from the base of the triangle.(B)A vector pointing vertically downward, toward the base of the triangle.(C)A vector pointing horizontally to the right, parallel to the base of the triangle.(D)A vector pointing horizontally to the left, parallel to the base of the triangle.

11. [Skill: 6.C | Topic: 2.3] A solid, neutral conducting sphere is placed in an external, uniform electric field $\vec{E}_{ext}$ that points to the right. Which of the following correctly describes the state of the sphere after it has reached electrostatic equilibrium?

(A)The electric field inside the sphere is equal to $\vec{E}_{ext}$ because the sphere is neutral.(B)Electrons move to the left side of the sphere, creating an internal field that cancels $\vec{E}_{ext}$ so that the net field inside is zero.(C)Protons move to the right side of the sphere, creating a net positive field inside the sphere pointing to the left.(D)The excess charge is distributed uniformly throughout the entire volume of the sphere to maintain a constant potential.

12. [Skill: 1.B | Topic: 2.3] An isolated, thin conducting spherical shell of radius $R$ carries a net charge of $+Q$. A point charge of $-q$ is placed at the center of the shell. Which of the following expressions correctly represents the magnitude of the electric field $E$ at a point a distance $r$ from the center, where $r < R$?

(A)$E = 0$(B)$E = \frac{kQ}{r^2}$(C)$E = \frac{kq}{r^2}$(D)$E = \frac{k(Q-q)}{r^2}$

Refer to the figure below.

13. [Skill: 5.B | Topic: 2.4] Three point charges are fixed at the vertices of an equilateral triangle with side length $L$, as shown in the figure. The charges have values $+q$, $+q$, and $-q$. Which of the following expressions represents the total electric potential energy $U_{E}$ of the system of three charges?

(A)$U_{E} = \frac{k q^{2}}{L}$(B)$U_{E} = -\frac{k q^{2}}{L}$(C)$U_{E} = -\frac{3k q^{2}}{L}$(D)$U_{E} = 0$

14. [Skill: 2.C | Topic: 2.4] A student is investigating the relationship between the electric potential energy of a system consisting of two point charges, $q_{1}$ and $q_{2}$, and the distance $r$ between them. The student creates a plot of the electric potential energy $U_{E}$ as a function of the reciprocal of the separation distance, $1/r$. The resulting graph is a straight line with a positive slope that passes through the origin. Which of the following must be true about the charges?

(A)The charges $q_{1}$ and $q_{2}$ must have the same sign.(B)The charges $q_{1}$ and $q_{2}$ must have opposite signs.(C)One of the charges must be significantly larger in magnitude than the other.(D)The net work done by an external force to bring the charges together from infinity was negative.

15. [Skill: 1.C | Topic: 2.4] Two point charges, $Q_{A} = +Q$ and $Q_{B} = +4Q$, are initially held at rest a distance $d$ apart. An external agent slowly moves charge $Q_{A}$ to a new position such that the distance between the charges is $2d$. Which of the following correctly describes the work $W_{ext}$ done by the external agent and the resulting change in the electric potential energy $\Delta U_{E}$ of the system?

(A)$W_{ext} < 0$ and $\Delta U_{E} < 0$(B)$W_{ext} > 0$ and $\Delta U_{E} > 0$(C)$W_{ext} < 0$ and $\Delta U_{E} > 0$(D)$W_{ext} > 0$ and $\Delta U_{E} < 0$

16. [Skill: 6.C | Topic: 2.5] A proton with charge $+e$ is moved by an external force at a constant speed from a location where the electric potential is $10 V$ to a location where the electric potential is $40 V$. Which of the following correctly identifies the work $W_{ext}$ done by the external force on the proton and the resulting change in the electric potential energy $\Delta U_E$ of the proton-field system?

(A)$W_{ext} = 30 eV$; $\Delta U_E = 30 eV$(B)$W_{ext} = -30 eV$; $\Delta U_E = 30 eV$(C)$W_{ext} = 30 eV$; $\Delta U_E = -30 eV$(D)$W_{ext} = -30 eV$; $\Delta U_E = -30 eV$

Refer to the figure below.

17. [Skill: 2.D | Topic: 2.5] [Image Cue]: A diagram shows three concentric circular equipotential lines. The innermost circle is labeled $100 V$, the middle circle is $50 V$, and the outermost circle is $25 V$. Based on the equipotential map, which of the following is a correct observation about the electric field $\vec{E}$ in this region?

(A)The electric field vectors point radially inward toward the center of the circles.(B)The electric field vectors point radially outward from the center of the circles.(C)The magnitude of the electric field is uniform because the potential decreases by a constant factor.(D)The electric field is strongest at the $25 V$ line because that is where the potential is lowest.

18. [Skill: 2.A | Topic: 2.6] A parallel-plate capacitor with plate area $A$ and separation distance $d$ is connected to a battery that maintains a constant potential difference $\Delta V$ across the plates. Which of the following modifications would lead to an increase in the magnitude of the charge $Q$ stored on each plate?

(A)Increasing the separation distance $d$ between the plates.(B)Decreasing the surface area $A$ of the plates.(C)Inserting a dielectric material with a dielectric constant $\kappa > 1$ between the plates.(D)Replacing the battery with one that has a lower potential difference.

19. [Skill: 1.C | Topic: 2.6] A parallel-plate capacitor is initially charged by a battery and then disconnected, leaving the plates electrically isolated. A student then pulls the plates further apart, increasing the separation distance $d$. Which of the following correctly describes the change in the electric potential energy $U_C$ stored in the capacitor and provides the correct physical justification?

(A)$U_C$ increases because the capacitance decreases and the charge remains constant, requiring work to be done to separate the oppositely charged plates.(B)$U_C$ decreases because the capacitance increases as the plates are moved further apart, reducing the energy density.(C)$U_C$ remains constant because the charge $Q$ is trapped on the isolated plates and cannot change.(D)$U_C$ increases because the electric field between the plates increases significantly as the distance increases.

Refer to the figure below.

20. [Skill: 5.D | Topic: 2.6] [Image Cue]: A linear graph with 'Charge Q' on the vertical axis and 'Potential Difference Delta V' on the horizontal axis. The line passes through the origin with a positive constant slope. A student performs an experiment to determine the properties of a specific parallel-plate capacitor. The student measures the charge $Q$ stored on the plates for several different potential differences $\Delta V$ and creates the graph described above. If the student were to repeat the experiment after doubling the area $A$ of the plates while keeping the distance $d$ constant, how would the slope of the graph change?

(A)The slope would remain the same because the slope represents the dielectric constant, which is a property of the material.(B)The slope would be halved because capacitance is inversely proportional to the plate area.(C)The slope would double because the slope represents the capacitance, which is directly proportional to the plate area.(D)The slope would quadruple because the energy stored depends on the square of the area.

21. [Skill: 1.4 | Topic: 2.7] An electron (charge $-e$) is released from rest at a location where the electric potential is $V_1 = -200\text{ V}$. It accelerates uniformly toward a region where the electric potential is $V_2 = -50\text{ V}$. Which of the following correctly describes the change in the electric potential energy $\Delta U_E$ of the electron-field system and the final kinetic energy $K_f$ of the electron when it reaches the second location?

(A)$\Delta U_E = -150\text{ eV}$ and $K_f = 150\text{ eV}$ (B)$\Delta U_E = +150\text{ eV}$ and $K_f = 150\text{ eV}$ (C)$\Delta U_E = -250\text{ eV}$ and $K_f = 250\text{ eV}$ (D)$\Delta U_E = +250\text{ eV}$ and $K_f = 250\text{ eV}$

22. [Skill: 2.2 | Topic: 2.7] Two particles, a proton (charge $+e$, mass $m_p$) and an alpha particle (charge $+2e$, mass $4m_p$), are both accelerated from rest through the same electric potential difference $\Delta V$. Let $v_p$ be the final speed of the proton and $v_\alpha$ be the final speed of the alpha particle. Which of the following is a correct expression for the ratio of their speeds, $v_\alpha / v_p$?

(A)$1/2$(B)$1/\sqrt{2}$(C)$\sqrt{2}$(D)

Refer to the figure below.

23. [Skill: 5.1 | Topic: 2.7] An object with a charge of $+2.0\text{ \mu C}$ is placed in a region of space where the electric potential $V$ as a function of position $x$ is shown in the provided description. The particle is released from rest at $x = 1.0\text{ m}$, where $V = 100\text{ V}$. It moves to $x = 3.0\text{ m}$, where $V = 40\text{ V}$. What is the kinetic energy of the particle at $x = 3.0\text{ m}$? [Image Cue]: A graph of Electric Potential $V$ (in Volts) on the y-axis vs Position $x$ (in meters) on the x-axis. The graph shows a linear decrease from $(1, 100)$ to $(3, 40)$.

(A)$8.0 \times 10^{-5}\text{ J}$(B)$1.2 \times 10^{-4}\text{ J}$(C)$2.0 \times 10^{-4}\text{ J}$(D)$2.8 \times 10^{-4}\text{ J}$

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