Q: Which of the following correctly expresses the work $W$ done by a constant force $\vec{F}$ over a displacement $\vec{s}$ at an angle $\theta$?

$W = F \cdot s \cdot \cos \theta$

Question 1

A proton is moved from point i to point f in a uniform electric field directed from left to right. If the displacement is to the left, which statement is correct about the work done and the change in electric potential energy?

Accepted Answer

The electric field does negative work on the proton, and its electric potential energy increases.

Question 2

Which of the following correctly expresses the work $W$ done by a constant force $\vec{F}$ over a displacement $\vec{s}$ at an angle $	heta$?

Accepted Answer

$W = F \cdot s \cdot \cos 	heta$

Question 3

A cow of mass $m = 50\,\mathrm{kg}$ is lifted to a height $h = 10\,\mathrm{m}$ above the ground. What is the gravitational potential energy gained by the cow? (Take $g = 9.8\,\mathrm{m/s^2}$)

Accepted Answer

$U_g = 4900\,\mathrm{J}$

Question 4

The electric potential $V$ at a distance $r$ from a point charge $q$ is given by which of the following expressions?

Accepted Answer

$V = \dfrac{kq}{r}$

Question 5

Which statement about equipotential surfaces is correct?

Accepted Answer

No work is required to move a charge along an equipotential surface.

Question 6

A charge $Q = 1\,\mathrm{C}$ is moved $10\,\mathrm{m}$ in a uniform electric field $E = 1\,\mathrm{N/C}$, parallel to the field. What is the change in electric potential energy?

Accepted Answer

$\Delta U = 10\,\mathrm{J}$

Question 7

The potential difference $\Delta V$ between two points in a uniform electric field $\vec{E}$ separated by displacement $\vec{d}$ is given by:

Accepted Answer

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

Question 8

If a test charge $+q$ moves from a region of lower potential to higher potential, what happens to its electric potential energy?

Accepted Answer

It increases.

Question 9

Which of the following is true about the electric potential inside a conducting shell?

Accepted Answer

It is constant everywhere inside the shell.

Question 10

For a group of point charges, the total electric potential at a point is:

Accepted Answer

The scalar sum of the potentials due to each charge.

Question 11

A ring of radius $a$ carries a total charge $Q$. What is the electric potential at a point on the axis of the ring, a distance $z$ from its center?

Accepted Answer

$V = \dfrac{kQ}{\sqrt{z^2 + a^2}}$

Question 12

Which of the following best describes the relationship between electric field $\vec{E}$ and electric potential $V$?

Accepted Answer

$\vec{E}$ is the gradient of $V$.

Question 13

A charged disk of radius $R$ has a uniform surface charge density $\sigma$. At a point on its axis a distance $z$ from the center, the potential is given by:

Accepted Answer

$V = 2\pi k \sigma \left( \sqrt{z^2 + R^2} - z \right)$

Question 14

Which of the following is true about the work required to move a charge along an equipotential surface?

Accepted Answer

No work is required to move a charge along an equipotential surface.

Question 15

A negative test charge is moved from point i to point f in a uniform electric field. What is the sign of the change in electric potential energy $\Delta U$?

Accepted Answer

It is negative.

Question 16

The potential difference between the plates of a parallel plate capacitor separated by distance $d$ and with electric field $E$ is:

Accepted Answer

$V = -Ed$

Question 17

Which of the following is a correct expression for the electric potential due to a continuous charge distribution?

Accepted Answer

$V = k \int \dfrac{dq}{r}$

Question 18

A charged rod of length $L$ and total charge $Q$ is placed along the x-axis. What is the potential at a point $P$ on the y-axis a distance $d$ from the origin?

Accepted Answer

$V = k \int_{0}^{L} \dfrac{\lambda dx}{\sqrt{x^2 + d^2}}$

Question 19

If the electric field at a point is zero, which of the following must be true about the electric potential at that point?

Accepted Answer

The electric potential is constant in the region around the point.

Electric Potential: Concepts, Calculations, and Applications

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