Q: Four identical charges $$q$$ are placed at the corners of a rectangle with sides $$L$$ and $$W. $$What is the total potential energy of the configuration?

$$U_{\text{total}} = k_e q^2$ \left( \frac{2}{L} + \frac{2}{W} + \frac{4}{\sqrt{L^2$ + W^2$}} \right)$$

Q: A $$12.0\ \mu\text{C}$$ charge moves in a uniform electric field of $$250\ \text{V/m}$$ from $$(0,0) to$$ $$(0.20\ \text{m}, 0.50\ \text{m}). $$What is the change in potential energy?

$$\Delta U = -qEd = -12.0 \times 10$$^{-6}$$ \times 250 \times 0.20$$

Question 1

Which of the following best describes the relationship between electric potential energy and electric potential for a point charge $$q at a $$location with potential $$V$$?

Accepted Answer

$$U = qV$$

Question 2

A proton is released from rest at a location where the electric potential is $$+50\ 	ext{V}. $$What will happen to the proton?

Accepted Answer

It will move toward lower potential with increasing speed.

Question 3

The potential energy of a charge $$q in a $$uniform electric field $$E$$ after moving a distance $$x is $$given by:

Accepted Answer

$$U = qEx$$

Question 4

If a $$+q$$ charge is moved closer to another $$+Q$$ charge, what happens to the electrostatic potential energy of the system?

Accepted Answer

It increases.

Question 5

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

Accepted Answer

$$V = k_e \frac{Q}{r}$$

Question 6

Four identical charges $$q$$ are placed at the corners of a rectangle with sides $$L$$ and $$W. $$What is the total potential energy of the configuration?

Accepted Answer

$$U_{	ext{total}} = k_e q^2$ \left( \frac{2}{L} + \frac{2}{W} + \frac{4}{\sqrt{L^2$ + W^2$}} ight)$$

Question 7

A $$12.0\ \mu	ext{C}$$ charge moves in a uniform electric field of $$250\ 	ext{V/m}$$ from $$(0,0) to$$ $$(0.20\ 	ext{m}, 0.50\ 	ext{m}). $$What is the change in potential energy?

Accepted Answer

$$\Delta U = -qEd = -12.0 	imes 10$$^{-6}$$ 	imes 250 	imes 0.20$$

Question 8

What is the ratio of electric potentials $$V_B/V_A at $$points B and A, where B is 3 mm and A is 1 mm from a point charge?

Accepted Answer

1/3

Question 9

Which statement about equipotential surfaces is correct?

Accepted Answer

No work is done by the field when moving a charge along an equipotential surface.

Question 10

A proton is brought to rest by an electric field after moving from an initial speed of $$800,000\ 	ext{m/s}. $$Did the proton move into a region of higher or lower potential?

Accepted Answer

Lower potential

Question 11

The work done by the electric field to move a charge $$q$$ through a potential difference $$\Delta V is$$:

Accepted Answer

$$W = -q\Delta V$$

Question 12

Which of the following is true about the direction of the electric field relative to equipotential surfaces?

Accepted Answer

The electric field is always perpendicular to any equipotential surface.

Question 13

An electron is accelerated from rest through a potential difference of $$1\ 	ext{V}. $$What is its final speed?

Accepted Answer

$$v = \sqrt{\frac{2eV}{m_e}}$$

Question 14

For two point charges $$q_1$$ and $$q_2$$ separated by distance $$r$$, the potential energy of the system is:

Accepted Answer

$$U = k_e \frac{q_1$ q_2$}{r}$$

Question 15

Which of the following is a correct interpretation of the electric potential at the center of a square with charges $$+q$$, $$+q$$, $$-q$$, $$-q at $$the corners?

Accepted Answer

The electric potential at the center is zero.

Question 16

A charged particle moves from a region of high potential to low potential. What happens to its potential energy if the charge is positive?

Accepted Answer

Its potential energy decreases.

Question 17

Which of the following sources has the highest electric potential difference?

Accepted Answer

Transmission lines

Question 18

In the figure below, the charges have equal magnitude but opposite sign. The electric field and electric potential at the midpoint is:

Accepted Answer

$$\vec{E} = 0, V = 0$$

Question 19

A $$4\ 	ext{nC}$$ charge is brought from infinity to the bottom right corner of a rectangle with three other $$2\ 	ext{nC}$$ charges at the other corners. What is the work required?

Accepted Answer

$$W = qV_{	ext{corner}}$$

Chapter 22: Electric Potential – Physics II Study Notes

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