Question 1

Which of the following correctly expresses the work done by an electric field when moving a charge $$q$$ through a potential difference $$\Delta V$$?

Accepted Answer

$$W = q \Delta V$$

Question 2

What are the SI units of electric potential?

Accepted Answer

$$\mathrm{V} = \mathrm{J}/\mathrm{C}$$

Question 3

A charge $$q$$ moves a distance $$d in a $$uniform electric field $$E. $$What is the potential difference $$\Delta V$$ between the starting and ending points?

Accepted Answer

$$\Delta V = -E d$$

Question 4

The electric potential $$V at a $$distance $$r$$ from a point charge $$q is $$given by which formula?

Accepted Answer

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

Question 5

If two point charges $$q_1$$ and $$q_2$$ are separated by a distance $$r_{12}$$, what is the potential energy $$U of $$the system?

Accepted Answer

$$U = k \frac{q_1$ q_2$}{r_{12}}$$

Question 6

How is the electric field $$E_x$$ related to the electric potential $$V in $$one dimension?

Accepted Answer

$$E_x = -\frac{dV}{dx}$$

Question 7

A parallel plate capacitor has plates separated by distance $$d$$ and a uniform electric field $$E$$ between them. What is the potential difference $$\Delta V$$ between the plates?

Accepted Answer

$$\Delta V = E d$$

Question 8

A rod of length $$L$$ has a non-uniform linear charge density $$\lambda = a x$$, where $$a is a $$constant and $$x is $$the position along the rod. What are the units of $$a$$?

Accepted Answer

$$\mathrm{C}/\mathrm{m}^2$$

Question 9

For a continuous charge distribution, the electric potential at a point is given by:

Accepted Answer

$$dV = k \frac{dq}{r}$$

Question 10

A particle with charge $$+q is at $$the origin and a particle with charge $$-2q is at$$ $$x = 2.00\ \mathrm{m} on $$the $$x-$$axis. At what position $$x is $$the electric field zero?

Accepted Answer

$$x = -1.41\ \mathrm{m}$$

Question 11

A rod of length $$L$$ with uniform linear charge density $$\lambda is $$placed along the $$x-$$axis. What is the expression for the electric potential at a point $$P$$ located a distance $$a$$ from the origin on the $$y-$$axis?

Accepted Answer

$$V = k \lambda \$$int_0$$^L \frac{dx}{\sqrt{x^2$ + a^2$}}$$

Question 12

Which of the following statements about electric potential is correct?

Accepted Answer

Electric potential is a scalar quantity and can be negative or positive depending on the reference point.

Question 13

A charged particle is released from rest in a uniform electric field. Which of the following best describes its motion?

Accepted Answer

It accelerates in the direction of the electric field if its charge is positive.

Question 14

The potential energy $$U of a $$charge $$q in an $$electric potential $$V is $$given by:

Accepted Answer

$$U = q V$$

Question 15

In a uniform electric field, the potential difference between two points separated by a displacement $$\vec{d} is$$:

Accepted Answer

$$\Delta V = -\vec{E} \cdot \vec{d}$$

Question 16

A rod with linear charge density $$\lambda$$ and mass density $$\rho is $$released from rest in a uniform electric field $$E$$ perpendicular to the rod. What is the speed $$v of $$the rod after it has traveled a distance $$d$$?

Accepted Answer

$$v = \sqrt{\frac{2 \lambda E d}{\rho}}$$

Question 17

For a system of three point charges $$q_1$$, $$q_2$$, and $$q_3 at $$distances $$r_{12}$$, $$r_{13}$$, and $$r_{23}$$ from each other, what is the total potential energy $$U of $$the system?

Accepted Answer

$$U = k \left( \frac{q_1$ q_2$}{r_{12}} + \frac{q_1$ q_3$}{r_{13}} + \frac{q_2$ q_3$}{r_{23}} \right)$$

Question 18

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

Accepted Answer

$$\Delta V = - \int_A^B \vec{E} \cdot d\vec{l}$$

Electric Potential: Concepts, Calculations, and Applications

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