Q: A 3 $$\muC $$and a -2 $$\muC $$charge are separated so that their potential energy is -100 mJ. What is the distance between them? (Use $$k = 8.99 \times 10^9$ N·m^2$/C^2$)

$$r = k \frac{q_1$ q_2$}{U} = \frac{8.99 \times 10^9$ \times 3 \times 10$$^{-6}$$ \times (-2 \times 10$$^{-6}$$)}{-0.1}$$

Q: A 1 $$\muC $$charge is placed in a uniform electric field of 1,000 N/C. What is the work done on the charge when it travels 2 m parallel to the field?

$$W = qEd = (1 \times 10$$^{-6}$$)(1000)(2) = 2 \times 10$$^{-3}$$ J

Q: What is the value of 1 electronvolt (eV) in joules?

$$1 \text{ eV} = 1.6 \times 10$$^{-19}$$ \text{ J}$$

Question 1

Consider three point charges arranged as shown in the first image. What is the total electric potential energy $$U_{tot} of $$this system of charges?

Accepted Answer

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

Question 2

Which of the following best describes the direction of the electric field lines in the second image (electric dipole)?

Accepted Answer

From the positive charge to the negative charge

Question 3

What is the electric potential $$V at a $$distance $$r$$ from a point charge $$q$$?

Accepted Answer

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

Question 4

A 3 $$\muC $$and a -2 $$\muC $$charge are separated so that their potential energy is -100 mJ. What is the distance between them? (Use $$k = 8.99 	imes 10^9$ N·m^2$/C^2$)

Accepted Answer

$$r = k \frac{q_1$ q_2$}{U} = \frac{8.99 	imes 10^9$ 	imes 3 	imes 10$$^{-6}$$ 	imes (-2 	imes 10$$^{-6}$$)}{-0.1}$$

Question 5

If a positive charge moves from a point of higher potential to a point of lower potential, what happens to its electric potential energy?

Accepted Answer

It decreases

Question 6

An electron is at rest between two points, A at 10 V and B at 0 V. Which point will the electron move to?

Accepted Answer

Point B (0 V)

Question 7

What is the relationship between electric field $$E$$ and electric potential $$V in a $$region where the field is uniform?

Accepted Answer

$$E = -\frac{\Delta V}{d}$$

Question 8

A 1 $$\muC $$charge is placed in a uniform electric field of 1,000 N/C. What is the work done on the charge when it travels 2 m parallel to the field?

Accepted Answer

$$W = qEd = (1 	imes 10$$^{-6}$$)(1000)(2) = 2 	imes 10$$^{-3}$$ J

Question 9

What is the potential at the center of a square formed by four equal charges $$q at $$each corner, with side length $$a$$?

Accepted Answer

$$V = 4k \frac{q}{a/\sqrt{2}}$$

Question 10

Which of the following statements about equipotential surfaces is correct?

Accepted Answer

The electric field is always perpendicular to equipotential surfaces

Question 11

A 5 g, 3 $$\muC $$point charge is moving with an initial speed of 20 m/s away from a –5 $$\muC $$charge. If they are initially 5 cm apart, how far can the 3 $$\muC $$travel before stopping?

Accepted Answer

Use energy conservation: $$\frac{1}{2}mv^2$ + k \frac{q_1$ q_2$}{r_i} = k \frac{q_1$ q_2$}{r_f}$$

Question 12

What is the value of 1 electronvolt (eV) in joules?

Accepted Answer

$$1 	ext{ eV} = 1.6 	imes 10$$^{-19}$$ 	ext{ J}$$

Question 13

Given the electric potential $$V(x, y) = 5x^2$y - 8xy^2$, what is the x$-component of the electric field E_x$?

Accepted Answer

$$E_x = -\frac{\partial V}{\partial x} = - (10xy - 8y^2$)$$

Question 14

A -2 C charge lies at rest. What is the potential difference between point A, 1.5 m from the charge, and point B, 4 m from the charge?

Accepted Answer

$$\Delta V = kq \left( \frac{1}{r_A} - \frac{1}{r_B} \right)$$

Question 15

Which of the following is true about the work done by the electric force when moving a charge between two points?

Accepted Answer

It depends only on the initial and final positions, not the path taken

Question 16

If the electric potential in a region is given by $$V(x, y, z) = 4xy - 7x^2$ + 3yz$$, what is the $$z-$$component of the electric field $$E_z$$?

Accepted Answer

$$E_z = -\frac{\partial V}{\partial z} = -3y$$

Electric Potential and Potential Energy – Study Notes (Ch. 23, Young & Freedman University Physics)

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