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 $$+3\ \muC $$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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