Q: In a uniform electric field $$\vec{E}$$, a charge $$q$$ moves from point A to point B along a path that makes an angle $$\theta$$ with the field direction (see the second image). What is the potential difference $$V_B - V_A$$?

$$V_B - V_A = -E d \cos \theta$$

Question 1

A positive test charge $$q_0 is $$moved from point A to point B in a uniform electric field $$\vec{E}$$, as shown in the first image. If the distance between A and B is $$d$$, what is the change in electric potential energy $$\Delta U of $$the charge-field system?

Accepted Answer

$$\Delta U = -q_0$ E d$$

Question 2

In a uniform electric field $$\vec{E}$$, a charge $$q$$ moves from point A to point B along a path that makes an angle $$	heta$$ with the field direction (see the second image). What is the potential difference $$V_B - V_A$$?

Accepted Answer

$$V_B - V_A = -E d \cos 	heta$$

Question 3

A positive charge is released from rest in a uniform electric field between two parallel plates (see the third image). Which of the following statements is correct as the charge moves from A to B?

Accepted Answer

Its electric potential energy decreases and its kinetic energy increases.

Question 4

A charge $$q_0 is $$moved from point a to point b along two different paths in a uniform electric field (see the fourth image). What can be said about the work done by the electric field?

Accepted Answer

The work is the same for both paths.

Question 5

A positive charge moves in the direction of a uniform electric field $$\vec{E}$$ between two plates (see the fifth image, left panel). What happens to its potential energy $$U$$ and what type of work does the field do?

Accepted Answer

Potential energy decreases; field does positive work.

Question 6

A negative charge moves in the direction of a uniform electric field $$\vec{E} ($$see the sixth image, left panel). What happens to its potential energy $$U$$?

Accepted Answer

Potential energy increases.

Question 7

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 8

Which of the following best describes the equipotential surfaces around a single point charge (see image 15)?

Accepted Answer

They are concentric spheres centered on the charge.

Question 9

A charged conductor in electrostatic equilibrium has which of the following properties?

Accepted Answer

The electric potential is constant everywhere on the surface and inside the conductor.

Question 10

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

Accepted Answer

$$U = \dfrac{k q_1$ q_2$}{r}$$

Question 11

If a charge $$q is $$moved between two points on the same equipotential surface, what is the work done by the electric field?

Accepted Answer

It is zero.

Question 12

Which of the following is true about the electric field and equipotential surfaces?

Accepted Answer

The electric field is always perpendicular to equipotential surfaces.

Question 13

A Van de Graaff generator is used to accelerate protons. If a proton is accelerated through a potential difference of $$2 	imes 10^6$ V, what is the kinetic energy gained by the proton in electron-volts (eV)?

Accepted Answer

$$2 	imes 10^6$ eV

Question 14

In the Millikan oil-drop experiment, what is the significance of the observation that the charge on each oil drop is always a multiple of $$1.6 	imes 10$$^{-19}$$ C?

Accepted Answer

It demonstrates that charge is quantized.

Question 15

A parallel-plate capacitor has a potential difference $$V$$ across plates separated by distance $$d. $$What is the magnitude of the electric field $$E$$ between the plates?

Accepted Answer

$$E = \dfrac{V}{d}$$

Question 16

The electric potential at a point due to a continuous charge distribution is given by:

Accepted Answer

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

Question 17

Which of the following statements about the electric field inside a conductor in electrostatic equilibrium is correct?

Accepted Answer

The electric field is zero everywhere inside the conductor.

Question 18

A system consists of three point charges $$q_1$$, $$q_2$$, and $$q_3. $$The total electric potential energy of the system is:

Accepted Answer

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

Question 19

Which of the following is a correct expression for the relationship between electric field and electric potential in one dimension?

Accepted Answer

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

Electric Potential: Concepts, Calculations, and Applications

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