Q: If two particles both have positive charge, what must be done to bring them closer together?

Work must be done by an external agent against the electric repulsion.

Q: Which equation correctly relates the electric potential difference between two points $a$ and $b$ to the electric field?

$V_b - V_a = -\int_a^b \mathbf{E} \cdot d\mathbf{l}$

Q: Given three point charges $q_1$, $q_2$, $q_3$ at the vertices of a right triangle, how do you calculate the total electric potential energy of the system?

Sum the potential energies for each unique pair: $U_e = \sum_{i<j} \frac{k q_i q_j}{r_{ij}}$

Q: Which property is true for excess charge placed on an isolated conductor?

It resides entirely on the surface.

Q: What is the electric flux $\Phi_E$ through a closed surface surrounding a point charge $q$ according to Gauss's Law?

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

Q: Which Gaussian surface is most appropriate for finding the electric field at a distance $r$ from a long, straight, uniformly charged rod?

A cylinder of radius $r$ and length $L$ coaxial with the rod.

Q: Why does Gauss's Law not simplify the calculation of the electric field near the ends of a finite rod?

Because the field lines are not radial and the flux through the end caps is not zero.

Q: If the electric field $\mathbf{E}$ is known everywhere, how can you find the electric potential $V$ at a point?

By integrating $\mathbf{E}$ along any path from a reference point: $V = -\int \mathbf{E} \cdot d\mathbf{l}$

Question 1

Which of the following statements about electric potential energy $U_e$ for two point charges $q_1$ and $q_2$ separated by a distance $r$ is correct?

Accepted Answer

$U_e = \frac{k q_1 q_2}{r}$ and depends only on the positions of the charges.

Question 2

A proton and an electron are brought closer together from a large separation. What happens to the electric potential energy of the system?

Accepted Answer

It decreases because $\Delta U_e < 0$ when $r$ decreases for opposite charges.

Question 3

If two particles both have positive charge, what must be done to bring them closer together?

Accepted Answer

Work must be done by an external agent against the electric repulsion.

Question 4

What is the formula for the electric potential $V$ at a distance $r$ from a point charge $Q$?

Accepted Answer

$V = \frac{k Q}{r}$

Question 5

A charge $q$ moves through a potential difference $\Delta V$. What is the change in its potential energy?

Accepted Answer

$\Delta U_e = q \Delta V$

Question 6

A $+2e$ charge moves from point P ($500.0$ kV) to point S ($200.0$ kV) in a vacuum. What is the change in its kinetic energy?

Accepted Answer

$+600$ keV

Question 7

An electron is accelerated from rest through a potential difference and reaches a speed of $7.26 	imes 10^6$ m/s. What is the potential difference required?

Accepted Answer

$+150$ Volts

Question 8

Which equation correctly relates the electric potential difference between two points $a$ and $b$ to the electric field?

Accepted Answer

$V_b - V_a = -\int_a^b \mathbf{E} \cdot d\mathbf{l}$

Question 9

For a uniform electric field $\mathbf{E}$ in the $y$-direction, what is the potential at position $y$ if $V=0$ at $y=0$?

Accepted Answer

$V = -E y$

Question 10

Given three point charges $q_1$, $q_2$, $q_3$ at the vertices of a right triangle, how do you calculate the total electric potential energy of the system?

Accepted Answer

Sum the potential energies for each unique pair: $U_e = \sum_{i<j} \frac{k q_i q_j}{r_{ij}}$

Question 11

What is the value of the electric field $\mathbf{E}$ inside a conductor in electrostatic equilibrium?

Accepted Answer

$\mathbf{E}$ is zero.

Question 12

Which property is true for excess charge placed on an isolated conductor?

Accepted Answer

It resides entirely on the surface.

Question 13

What is the electric flux $\Phi_E$ through a closed surface surrounding a point charge $q$ according to Gauss's Law?

Accepted Answer

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

Question 14

Which Gaussian surface is most appropriate for finding the electric field at a distance $r$ from a long, straight, uniformly charged rod?

Accepted Answer

A cylinder of radius $r$ and length $L$ coaxial with the rod.

Question 15

Why does Gauss's Law not simplify the calculation of the electric field near the ends of a finite rod?

Accepted Answer

Because the field lines are not radial and the flux through the end caps is not zero.

Question 16

If the electric field $\mathbf{E}$ is known everywhere, how can you find the electric potential $V$ at a point?

Accepted Answer

By integrating $\mathbf{E}$ along any path from a reference point: $V = -\int \mathbf{E} \cdot d\mathbf{l}$

Question 17

What is the relationship between the electric field and the gradient of the electric potential?

Accepted Answer

$\mathbf{E} = -
abla V$

Question 18

A conducting spherical shell has a charge $+q$ placed at its center and no excess charge on the conductor. What is the induced charge per unit area on the inner and outer surfaces?

Accepted Answer

Inner: $-q$ per unit area, Outer: $+q$ per unit area

Question 19

Which of the following is true about equipotential surfaces?

Accepted Answer

The electric field is perpendicular to equipotential surfaces.

Electric Potential and Gauss’ Law – Study Notes for PHY 131

Study Guide - Practice Questions

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