Q: A $$7.5 C $$charge moves from $$(0,0) to$$ $$(6.0\ \text{m}, 6.0\ \text{m}) in a $$uniform electric field pointing in the positive x-direction. What is the component of displacement relevant for calculating the change in electric potential energy?

$$6.0$$\ m$$\ (\text{along x})$$

Question 1

A uniform electric field of magnitude $$3.8 	imes 10^4$ N/C points in the positive x-direction. What is the change in electric potential energy when a 7.5$ C charge moves from the origin to the point (6.0$$\ 	ext{m}, 0)$$?

Accepted Answer

$$1.71 	imes 10^6$\ J

Question 2

For the same electric field and charge, what is the change in electric potential energy when the charge moves from the origin to the point $$(0, 6.0\ 	ext{m})$$?

Accepted Answer

$$0$$\ J

Question 3

A $$7.5 C $$charge moves from the origin to $$(6.0\ 	ext{m}, 6.0\ 	ext{m}) in $$the same electric field. What is the change in electric potential energy?

Accepted Answer

$$1.71 	imes 10^6$\ J

Question 4

Which equation correctly expresses the change in electric potential energy $$\Delta U$$ for a charge $$q$$ moving a distance $$d in a $$uniform electric field $$E$$ along the direction of the field?

Accepted Answer

$$\Delta U = -qEd$$

Question 5

A proton ($$q = +1.6 	imes 10$$^{-19}$$ C) moves 2.0$ m in the direction of a uniform electric field of 5.0$$ 	imes $$10^3 N/C. $$What is the change in its electric potential energy?

Accepted Answer

$$-1.6 	imes 10$$^{-15}$$\ J

Question 6

If a $$7.5 C $$charge moves perpendicular to a uniform electric field of $$3.8 	imes 10^4$ N/C, what is the change in its electric potential energy?

Accepted Answer

$$0$$\ J

Question 7

A $$7.5 C $$charge moves from $$(0,0) to$$ $$(6.0\ 	ext{m}, 0) in a $$uniform electric field. If the field points in the negative x-direction, what is the change in electric potential energy?

Accepted Answer

$$-1.71 	imes 10^6$\ J

Question 8

Which of the following best describes why the change in electric potential energy is zero when a charge moves perpendicular to a uniform electric field?

Accepted Answer

No work is done by the field because the displacement is perpendicular to the field direction.

Question 9

A $$7.5 C $$charge moves from $$(0,0) to$$ $$(6.0\ 	ext{m}, 6.0\ 	ext{m}) in a $$uniform electric field pointing in the positive x-direction. What is the component of displacement relevant for calculating the change in electric potential energy?

Accepted Answer

$$6.0$$\ m$$\ (	ext{along x})$$

Question 10

A $$7.5 C $$charge moves $$6.0 m in $$the positive x-direction in a uniform electric field of $$3.8 	imes 10^4$ N/C. What is the electric potential difference $$\Delta V$$ experienced by the charge?

Accepted Answer

$$2.28 	imes 10^5$\ V

Question 11

Which formula relates the change in electric potential energy $$\Delta U to $$the electric potential difference $$\Delta V$$ for a charge $$q$$?

Accepted Answer

$$\Delta U = q \Delta V$$

Question 12

A $$7.5 C $$charge moves from $$(0,0) to$$ $$(6.0\ 	ext{m}, 0) in a $$uniform electric field. If the field magnitude is doubled, what happens to the change in electric potential energy?

Accepted Answer

It doubles.

Question 13

A $$7.5 C $$charge moves $$6.0 m in $$the positive x-direction in a uniform electric field. If the charge is negative, what is the sign of the change in electric potential energy?

Accepted Answer

Positive

Question 14

Which of the following best describes the physical meaning of electric potential energy in the context of a uniform electric field?

Accepted Answer

It is the energy a charge has due to its position in the electric field.

Question 15

A $$7.5 C $$charge moves $$6.0 m in $$the positive x-direction in a uniform electric field. If the field points in the positive x-direction, what is the direction of the force on the charge?

Accepted Answer

Positive x-direction

Question 16

A $$7.5 C $$charge moves $$6.0 m in $$the positive x-direction in a uniform electric field. If the charge moves against the field, what happens to its electric potential energy?

Accepted Answer

It increases.

Question 17

A $$7.5 C $$charge moves $$6.0 m in $$the positive x-direction in a uniform electric field. If the field points in the negative x-direction, what is the electric potential difference $$\Delta V$$?

Accepted Answer

$$-2.28 	imes 10^5$\ V

Question 18

A $$7.5 C $$charge moves from $$(0,0) to$$ $$(6.0\ 	ext{m}, 0) in a $$uniform electric field. If the charge moves at an angle of $$45^\circ to $$the x-axis, what is the change in electric potential energy?

Accepted Answer

$$1.21 	imes 10^6$\ J

Question 19

A $$7.5 C $$charge moves $$6.0 m in $$the positive x-direction in a uniform electric field. If the field is not uniform but varies with position, which formula should be used to calculate the change in electric potential energy?

Accepted Answer

$$\Delta U = -q \int_{x_1$}^{x_2$} E(x)\ dx$$

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