Q: A solid non-conducting sphere of radius $R$ has a uniform charge density $\rho$. Using Gauss' Law, what is the electric field at a distance $r < R$ from the center?

$E = \frac{\rho r}{3\epsilon_0}$

Q: Which of the following statements about electric potential energy is correct?

It can be positive or negative depending on the configuration of charges.

Q: A group of three point charges, $q_1$, $q_2$, and $q_3$, are assembled from infinity to form a triangle. Which expression gives the total electrostatic potential energy of the system?

$U = \frac{1}{4\pi\epsilon_0} \left( \frac{q_1 q_2}{r_{12}} + \frac{q_1 q_3}{r_{13}} + \frac{q_2 q_3}{r_{23}} \right)$

Question 1

A thin, uniformly charged rod of length $L$ carries a total charge $Q$. What is the magnitude of the electric field at a point $P$ located a distance $a$ from one end of the rod along the line extending from the rod (not perpendicular to it)?

Accepted Answer

$E = \frac{1}{4\pi\epsilon_0} \frac{Q}{a(a+L)}$

Question 2

Two point charges, $q_1 = +2\ \mu\mathrm{C}$ and $q_2 = -2\ \mu\mathrm{C}$, are placed 10 cm apart. What is the net electric field at the midpoint between them?

Accepted Answer

$E = \frac{1}{4\pi\epsilon_0} \frac{4q}{(0.05)^2}$

Question 3

A solid non-conducting sphere of radius $R$ has a uniform charge density $\rho$. Using Gauss' Law, what is the electric field at a distance $r < R$ from the center?

Accepted Answer

$E = \frac{\rho r}{3\epsilon_0}$

Question 4

Which of the following statements about electric potential energy is correct?

Accepted Answer

It can be positive or negative depending on the configuration of charges.

Question 5

A proton is released from rest at a point where the electric potential is $V_0$. What is its kinetic energy after moving to a point where the potential is zero?

Accepted Answer

$KE = eV_0$

Question 6

Which of the following best describes the relationship between electric field $\vec{E}$ and electric potential $V$?

Accepted Answer

$\vec{E} = -
abla V$

Question 7

A group of three point charges, $q_1$, $q_2$, and $q_3$, are assembled from infinity to form a triangle. Which expression gives the total electrostatic potential energy of the system?

Accepted Answer

$U = \frac{1}{4\pi\epsilon_0} \left( \frac{q_1 q_2}{r_{12}} + \frac{q_1 q_3}{r_{13}} + \frac{q_2 q_3}{r_{23}} \right)$

Question 8

A charge $q$ is moved from point $A$ to point $B$ in an electric field. The potential at $A$ is $V_A$ and at $B$ is $V_B$. What is the work done by the electric field?

Accepted Answer

$W = q(V_A - V_B)$

Question 9

A spherical shell of radius $R$ carries a uniform surface charge density $\sigma$. What is the electric field at a point outside the shell at distance $r > R$?

Accepted Answer

$E = \frac{1}{4\pi\epsilon_0} \frac{Q}{r^2}$

Question 10

Which of the following is a correct application of Gauss' Law?

Accepted Answer

The net electric flux through a closed surface is proportional to the net charge enclosed.

Question 11

A negative charge is released from rest in a region of increasing electric potential. What happens to its kinetic energy?

Accepted Answer

It increases.

Question 12

A point charge $q$ is placed at the center of a cube. What is the total electric flux through all six faces of the cube?

Accepted Answer

$\Phi_E = \frac{q}{\epsilon_0}$

Question 13

Which of the following best describes the gradient operator $
abla$ in the context of electric potential?

Accepted Answer

It gives the direction and rate of the steepest increase of the potential.

Question 14

A charge $q$ is placed in a uniform electric field $\vec{E}$. What is the potential difference between two points separated by a distance $d$ along the direction of the field?

Accepted Answer

$\Delta V = -Ed$

Question 15

A spacecraft must escape Earth's electric field. If the Earth's net charge is $Q$ and the spacecraft has charge $q$, what is the minimum work required to move the spacecraft from the Earth's surface (radius $R$) to infinity?

Accepted Answer

$W = \frac{1}{4\pi\epsilon_0} \frac{Qq}{R}$

Question 16

Which of the following is true about the electric field inside a conductor in electrostatic equilibrium?

Accepted Answer

The electric field is zero everywhere inside the conductor.

Question 17

A charge $q$ is moved in a circle of radius $r$ around a point charge $Q$. What is the work done by the electric field?

Accepted Answer

$W = 0$

Exam 01 Review: Electrostatics and Electric Potential (PHYS 2200)

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