Q: A charge moves $1.9$ m at $45^\circ$ to a uniform electric field of $7.0$ N/C. What is the potential difference $\Delta V$ experienced by the charge?

$\Delta V = -(E)(1.9\,\text{m})\cos(45^\circ)$

Question 1

Which equation gives the electric potential $V$ at a distance $r$ from a single point charge $q$ in vacuum?

Accepted Answer

$V = \frac{1}{4\pi\epsilon_0} \frac{q}{r}$

Question 2

A collection of point charges $q_i$ are located at distances $r_i$ from a point. What is the total electric potential $V$ at that point?

Accepted Answer

$V = \frac{1}{4\pi\epsilon_0} \sum_i \frac{q_i}{r_i}$

Question 3

Which of the following best describes an equipotential surface in an electric field?

Accepted Answer

A surface on which all points have the same electric potential.

Question 4

If a positive charge moves from a region of higher potential to a region of lower potential, what happens to its electric potential energy?

Accepted Answer

It decreases.

Question 5

An electron ($m = 9.11 	imes 10^{-31}$ kg, $q = -1.6 	imes 10^{-19}$ C) is accelerated through a potential difference of $5000$ V in a TV picture tube. What is its final speed?

Accepted Answer

$v = \sqrt{\frac{2q\Delta V}{m}}$

Question 6

Which of the following correctly relates the electric field $\vec{E}$ to the electric potential $V$ in one dimension?

Accepted Answer

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

Question 7

A charge moves $1.9$ m at $45^\circ$ to a uniform electric field of $7.0$ N/C. What is the potential difference $\Delta V$ experienced by the charge?

Accepted Answer

$\Delta V = -(E)(1.9\,	ext{m})\cos(45^\circ)$

Question 8

Which statement about equipotential surfaces and electric field lines is correct?

Accepted Answer

Equipotential surfaces are always perpendicular to electric field lines.

Question 9

A topographic map analogy is used to describe electrostatics. What do valleys/depressions represent?

Accepted Answer

Regions of negative electric potential.

Question 10

What is the work $W$ required to move a charge $q$ through a potential difference $\Delta V$?

Accepted Answer

$W = q\Delta V$

Question 11

A negative charge will naturally move from a region of ______ potential to a region of ______ potential to reduce its potential energy.

Accepted Answer

lower; higher

Question 12

Given a continuous distribution of charge, what is the expression for the electric potential $V$ at a point?

Accepted Answer

$V = \frac{1}{4\pi\epsilon_0} \int \frac{dq}{r}$

Question 13

If the electric field points to the right, which surface is at a higher potential: surface A (left) or surface B (right)?

Accepted Answer

Surface A

Question 14

Which of the following is true about the change in electric potential energy $\Delta U$ when a charge $q$ moves through a potential difference $\Delta V$?

Accepted Answer

$\Delta U = q\Delta V$

Question 15

Which mathematical operation relates the electric field $\vec{E}$ to the electric potential $V$ in three dimensions?

Accepted Answer

$\vec{E} = -
abla V$

Question 16

A positive test charge is placed at a point in an electric field. The electric potential at that point is determined by:

Accepted Answer

The work needed to bring a unit positive charge from infinity to that point.

Question 17

Which of the following is the correct expression for the potential difference $\Delta V$ between two points separated by distance $d$ in a uniform electric field $E$?

Accepted Answer

$\Delta V = -E d$

Question 18

In the context of electrostatics, what does the 'steepness' of equipotential lines on a topographic map analogy represent?

Accepted Answer

The magnitude of the electric field.

Question 19

Which of the following is true about the electric potential energy $U$ between two point charges $q_1$ and $q_2$ separated by distance $r$?

Accepted Answer

$U = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r}$

Electric Potential & Equipotential Surfaces (PHYS 133: Physics II, Ch. 23: 3-4)

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