Question 1

Which of the following statements about electric potential energy $$U_e$$ for two point charges $$q_1$$ and $$q_2$$ separated by a distance $$r is $$correct?

Accepted Answer

$$U_e = \frac{k q_1$ q_2$}{r}$$ and depends only on the positions of the charges.

Question 2

A proton and an electron are brought closer together from a large separation. What happens to the electric potential energy of the system?

Accepted Answer

It decreases because $$\Delta U_e \u003c 0$$ when $$r$$ decreases for opposite charges.

Question 3

If two particles both have positive charge, what must be done to bring them closer together?

Accepted Answer

Work must be done by an external agent against the electric repulsion.

Question 4

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

Accepted Answer

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

Question 5

A charge $$q$$ moves through a potential difference $$\Delta V. $$What is the change in its potential energy?

Accepted Answer

$$\Delta U_e = q \Delta V$$

Question 6

A $$+2e$$ charge moves from point P ($$500.0 kV) to $$point S ($$200.0 kV) in a $$vacuum. What is the change in its kinetic energy?

Accepted Answer

$$+600$$ keV

Question 7

An electron is accelerated from rest through a potential difference and reaches a speed of $$7.26 	imes 10^6$ m/s. What is the potential difference required?

Accepted Answer

$$+150$$ Volts

Question 8

Which equation correctly relates the electric potential difference between two points $$a$$ and $$b to $$the electric field?

Accepted Answer

$$V_b - V_a = -\int_a^b \mathbf{E} \cdot d\mathbf{l}$$

Question 9

For a uniform electric field $$\mathbf{E} in $$the $$y-$$direction, what is the potential at position $$y if$$ $$V=0 at$$ $$y=0$$?

Accepted Answer

$$V = -E y$$

Question 10

Given three point charges $$q_1$$, $$q_2$$, $$q_3 at $$the vertices of a right triangle, how do you calculate the total electric potential energy of the system?

Accepted Answer

Sum the potential energies for each unique pair: $$U_e = \sum_{i\u003cj} \frac{k q_i q_j}{r_{ij}}$$

Question 11

What is the value of the electric field $$\mathbf{E}$$ inside a conductor in electrostatic equilibrium?

Accepted Answer

$$\mathbf{E} is $$zero.

Question 12

Which property is true for excess charge placed on an isolated conductor?

Accepted Answer

It resides entirely on the surface.

Question 13

What is the electric flux $$\Phi_E$$ through a closed surface surrounding a point charge $$q$$ according to Gauss's Law?

Accepted Answer

$$\Phi_E = \frac{q}{\$$epsilon_0$$}$$

Question 14

Which Gaussian surface is most appropriate for finding the electric field at a distance $$r$$ from a long, straight, uniformly charged rod?

Accepted Answer

A cylinder of radius $$r$$ and length $$L$$ coaxial with the rod.

Question 15

Why does Gauss's Law not simplify the calculation of the electric field near the ends of a finite rod?

Accepted Answer

Because the field lines are not radial and the flux through the end caps is not zero.

Question 16

If the electric field $$\mathbf{E} is $$known everywhere, how can you find the electric potential $$V at a $$point?

Accepted Answer

By integrating $$\mathbf{E}$$ along any path from a reference point: $$V = -\int \mathbf{E} \cdot d\mathbf{l}$$

Question 17

What is the relationship between the electric field and the gradient of the electric potential?

Accepted Answer

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

Question 18

A conducting spherical shell has a charge $$+q$$ placed at its center and no excess charge on the conductor. What is the induced charge per unit area on the inner and outer surfaces?

Accepted Answer

Inner: $$-q$$ per unit area, Outer: $$+q$$ per unit area

Question 19

Which of the following is true about equipotential surfaces?

Accepted Answer

The electric field is perpendicular to equipotential surfaces.

Electric Potential and Gauss’ Law – Study Notes for PHY 131

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