Q: A positive charge $$q is $$moved a distance $$s$$ from the negative plate toward the positive plate in a parallel-plate capacitor. Which equation correctly represents the increase in electric potential energy?

$$\Delta U_{\text{elec}} = qEs$$

Question 1

Which of the following statements best describes electric potential energy in the context of a uniform electric field, such as inside a parallel-plate capacitor?

Accepted Answer

It is the interaction energy between a charge and the source charges creating the field.

Question 2

A positive charge $$q is $$moved a distance $$s$$ from the negative plate toward the positive plate in a parallel-plate capacitor. Which equation correctly represents the increase in electric potential energy?

Accepted Answer

$$\Delta U_{	ext{elec}} = qEs$$

Question 3

In the analogy between gravitational and electric fields, which property couples with the field to determine the change in potential energy?

Accepted Answer

Mass for gravity, charge for electricity

Question 4

A proton is released from rest at the surface of a sphere charged to $$+1000\ 	ext{V}. $$What is the charge $$Q of $$the sphere if its radius is $$r = 0.005\ 	ext{m}$$?

Accepted Answer

$$Q = 4\pi\$$epsilon_0$$ r V$$

Question 5

Which of the following is true about the electric potential $$V$$ created by a point charge $$q at a $$distance $$r$$?

Accepted Answer

$$V$$ decreases inversely with distance: $$V = \frac{q}{4\pi\$$epsilon_0$$ r}$$

Question 6

A negative charge moves toward the negative plate in a uniform electric field. What happens to its electric potential energy and kinetic energy?

Accepted Answer

Potential energy increases (becomes less negative), kinetic energy decreases.

Question 7

Which equation gives the electric potential at a point on the axis of a thin, uniformly charged ring of radius $$R$$ and total charge $$Q$$, at a distance $$z$$ from the center?

Accepted Answer

$$V = \frac{Q}{4\pi\$$epsilon_0$$ \sqrt{R^2$ + z^2$}}$$

Question 8

A proton is accelerated from rest through a potential difference of $$30,000\ 	ext{V} in a $$cathode ray tube. What is its final kinetic energy in electron-volts?

Accepted Answer

$$30,000\ 	ext{eV}$$

Question 9

If a positive charge is released from rest, it moves in the direction of:

Accepted Answer

Lower electric potential and weaker electric field.

Question 10

The electric potential energy $$U of $$two point charges $$q_1$$ and $$q_2$$ separated by distance $$r is$$:

Accepted Answer

$$U = \frac{q_1$ q_2$}{4\pi\$$epsilon_0$$ r}$$

Question 11

Which of the following is a correct statement about conservative forces?

Accepted Answer

The work done by a conservative force depends only on the initial and final positions, not the path taken.

Question 12

A proton moves from a region of lower electric potential to higher electric potential. What happens to its kinetic energy?

Accepted Answer

It decreases.

Question 13

The electric field inside a parallel-plate capacitor with plate separation $$d$$ and voltage $$\Delta V is$$:

Accepted Answer

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

Question 14

Which of the following best describes equipotential surfaces?

Accepted Answer

Mathematical surfaces where the electric potential $$V is $$constant at every point.

Question 15

The electric potential at a point due to multiple point charges is:

Accepted Answer

The sum of the potentials due to each charge, added as scalars.

Question 16

A system of three electrons spaced equally along a line has the center electron displaced horizontally. What type of equilibrium is this?

Accepted Answer

Unstable equilibrium

Question 17

Which unit is equivalent to the electric field strength $$E$$?

Accepted Answer

Volt per meter ($$	ext{V/m})$$

Question 18

A positive and a negative charge are released from rest in vacuum and move toward each other. As they do, their potential energy:

Accepted Answer

A negative potential energy becomes less negative.

Question 19

If a charge $$q is $$placed in an electric potential $$V$$, what is its electric potential energy?

Accepted Answer

$$U = qV$$

Question 20

Which of the following is true about the electric field vectors and equipotential surfaces inside a parallel-plate capacitor?

Accepted Answer

The electric field vectors are perpendicular to the equipotential surfaces.

Chapter 25: The Electric Potential – Study Notes

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