Q: A $$1\ \mathrm{e}$$ charge moves through a $$1\ \mathrm{V}$$ potential difference. What is the change in its potential energy in joules?

$$1.6 \times 10$$^{-19}$$\ \mathrm{J}$$

Question 1

A battery supplies 9 J of energy to every coulomb of charge that passes through a circuit. What is the potential difference across the battery?

Accepted Answer

$$9\ \mathrm{V}$$

Question 2

Which equation correctly expresses the potential energy change $$\Delta U_{AB}$$ for moving a charge $$q$$ from point A to point B in an electric field $$\vec{E}$$?

Accepted Answer

$$\Delta U_{AB} = -q \int_A^B \vec{E} \cdot d\vec{r}$$

Question 3

An electron moves through a uniform electric field of $$300\ \mathrm{kN/C}$$ over a distance of $$0.10\ \mathrm{m}. $$What is the potential difference experienced by the electron?

Accepted Answer

$$30\ \mathrm{kV}$$

Question 4

Which of the following best describes the relationship between electric field $$\vec{E}$$ and electric potential $$V in $$three dimensions?

Accepted Answer

$$\vec{E} = -
abla V$$

Question 5

A point charge $$q$$ creates an electric potential $$V at a $$distance $$r. $$Which equation gives the potential at that point?

Accepted Answer

$$V = \dfrac{q}{4\pi\$$epsilon_0$$ r}$$

Question 6

If the electric field strength in a region doubles, what happens to the potential difference across a fixed distance in that region?

Accepted Answer

It doubles

Question 7

A charge $$q$$ moves a distance $$\Delta r$$ opposite to the direction of a uniform electric field $$\vec{E}. $$What is the change in its potential energy?

Accepted Answer

$$\Delta U = qE \Delta r$$

Question 8

Which of the following is the correct unit for electric potential difference?

Accepted Answer

$$\mathrm{J/C}$$

Question 9

A wire with a radius of $$1\ \mathrm{m}$$ hangs $$22\ \mathrm{m}$$ above the ground and has a uniform linear charge density $$\lambda. $$What is the potential difference between the ground and the wire?

Accepted Answer

$$\Delta V = \dfrac{\lambda}{2\pi\$$epsilon_0$$} \ln\left(\dfrac{r_{	ext{ground}}}{r_{	ext{wire}}}ight)$$

Question 10

Which of the following integrals correctly gives the electric potential difference between points A and B in a non-uniform electric field?

Accepted Answer

$$\Delta V_{AB} = -\int_A^B \vec{E} \cdot d\vec{r}$$

Question 11

A charged particle moves in a straight line from point A to point B in a uniform electric field. If the displacement vector $$\Delta \vec{r} is $$perpendicular to $$\vec{E}$$, what is the potential difference between A and B?

Accepted Answer

It is zero

Question 12

Which of the following statements about electric potential is correct?

Accepted Answer

Electric potential is a scalar quantity

Question 13

A $$1\ \mathrm{e}$$ charge moves through a $$1\ \mathrm{V}$$ potential difference. What is the change in its potential energy in joules?

Accepted Answer

$$1.6 	imes 10$$^{-19}$$\ \mathrm{J}$$

Question 14

Which of the following best describes the physical meaning of electric potential difference?

Accepted Answer

The change in potential energy per unit charge between two points

Question 15

A dipole consists of charges $$+q$$ and $$-q$$ separated by distance $$d. $$What is the dipole moment $$\vec{p}$$?

Accepted Answer

$$\vec{p} = 2qd$$

Question 16

In a region where the electric potential $$V(x, y, z) is $$given, what is the expression for the electric field $$\vec{E}$$?

Accepted Answer

$$\vec{E} = -\left( \dfrac{\partial V}{\partial x} \hat{i} + \dfrac{\partial V}{\partial y} \hat{j} + \dfrac{\partial V}{\partial z} \hat{k} \right)$$

Question 17

A charged ring of radius $$a$$ carries a total charge $$Q. $$What is the electric potential at a point on the axis of the ring at a distance $$x$$ from its center?

Accepted Answer

$$V = \dfrac{kQ}{\sqrt{x^2$ + a^2$}}$$

Question 18

If a positive test 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

Electric Potential and Potential Difference

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