Q: Which of the following statements best describes the relationship between electric potential energy and the work done by a conservative force, such as the electric force?

$\Delta U = -W_{\text{conservative, initial} \to \text{final}}$

Question 1

Which of the following statements best describes the relationship between electric potential energy and the work done by a conservative force, such as the electric force?

Accepted Answer

$\Delta U = -W_{	ext{conservative, initial} 	o 	ext{final}}$

Question 2

A proton is released from rest in a region of uniform electric field. Which of the following best describes its motion?

Accepted Answer

It moves from high to low electric potential, gaining kinetic energy.

Question 3

What is the electric potential energy of two point charges $q_1$ and $q_2$ separated by a distance $r_{12}$?

Accepted Answer

$U = k \frac{q_1 q_2}{r_{12}}$

Question 4

If two protons are separated by a distance $2 	imes 10^{-15}$ m, what does the positive sign of their electric potential energy indicate?

Accepted Answer

Work must be done to bring them together from infinity.

Question 5

Which equation correctly relates the electric potential $V$ at a distance $r$ from a point charge $q$?

Accepted Answer

$V = \frac{1}{4\pi\epsilon_0} \frac{q}{r}$

Question 6

A $+3\ \mu$C charge is brought from infinity to a point $P$ where the electric potential is $-4.2 	imes 10^3$ V. How much work is done by the external force?

Accepted Answer

$-1.26 	imes 10^{-3}$ J

Question 7

Which of the following is true about equipotential surfaces in an electric field?

Accepted Answer

They are always perpendicular to electric field lines.

Question 8

What is the potential difference $\Delta V$ between two parallel plates separated by distance $d$ with a uniform electric field $E$ between them?

Accepted Answer

$\Delta V = Ed$

Question 9

A proton moves a distance $d$ in a uniform electric field $E$. What is the work done by the field on the proton?

Accepted Answer

$W = qEd$

Question 10

Which of the following best describes the unit 'electron volt' (eV)?

Accepted Answer

The energy required to move one electron through a potential difference of one volt.

Question 11

A system consists of three point charges $q_1$, $q_2$, and $q_3$ at distances $r_{12}$, $r_{13}$, and $r_{23}$ from each other. What is the total electric potential energy of the system?

Accepted Answer

$U = k \left( \frac{q_1 q_2}{r_{12}} + \frac{q_1 q_3}{r_{13}} + \frac{q_2 q_3}{r_{23}} \right)$

Question 12

Which of the following is true about the electric potential $V$ inside a charged conducting sphere of radius $R$?

Accepted Answer

$V = \frac{1}{4\pi\epsilon_0} \frac{Q}{R}$

Question 13

A thin rod of length $\ell$ lies along the x-axis and carries a total charge $Q$ uniformly distributed. What is the electric potential at a point $P$ on the y-axis at a perpendicular distance $a$ from the origin?

Accepted Answer

$V = kQ \ln \left( \frac{\ell + \sqrt{\ell^2 + a^2}}{a} \right) / \ell$

Question 14

If the electric field is zero everywhere in a region, what can you say about the electric potential in that region?

Accepted Answer

The electric potential is constant throughout the region.

Question 15

A ring of radius $a$ carries a total charge $Q$ uniformly distributed along its circumference. What is the electric potential at a point $P$ located on the axis of the ring at a distance $x$ from the center?

Accepted Answer

$V = k \frac{Q}{\sqrt{a^2 + x^2}}$

Question 16

Which of the following best describes the difference between electric potential and electric potential energy?

Accepted Answer

Electric potential is a property of the field, while electric potential energy is a property of the charge-field system.

Question 17

A long, charged conducting cylinder with charge per unit length $\lambda$ has radius $R$. What is the electric potential at a distance $r \geq R$ from the axis, taking $V = 0$ at $r = R$?

Accepted Answer

$V = \frac{\lambda}{2\pi\epsilon_0} \ln \left( \frac{R}{r} \right)$

Question 18

Which of the following is a correct statement about the work done by an external force when assembling a system of charges?

Accepted Answer

It is equal to the change in the system's electric potential energy.

Electric Potential and Electric Potential Energy: Concepts, Calculations, and Applications

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