Question 1

A ring of radius $$a$$ carries a uniformly distributed positive total charge $$Q. $$What is the electric field at a point $$P$$ located a distance $$x$$ from the center along the axis perpendicular to the plane of the ring?

Accepted Answer

$$E = \frac{k x Q}{(x^2$ + a^2$)^{3/2}$$}$

Question 2

If a negative charge is placed at the center of a positively charged ring and displaced slightly along the axis, what type of motion does it exhibit when released?

Accepted Answer

Simple harmonic motion

Question 3

A positive charge $$Q is $$uniformly distributed along a line of length $$2a. $$What is the electric field at a point $$x on $$the axis if $$x \gg a$$?

Accepted Answer

$$E = \frac{k Q}{x^2$}$$

Question 4

A disk of radius $$R$$ has a uniform surface charge density $$\sigma. $$What is the electric field at a point $$x$$ along the central perpendicular axis very close to the disk ($$x \ll R$$)?

Accepted Answer

$$E = \frac{\sigma}{2 \$$epsilon_0$$}$$

Question 5

What is the electric field between two infinite parallel sheets, one with surface charge density $$+\sigma$$ and the other with $$-\sigma$$, separated by a distance $$d$$?

Accepted Answer

$$E = \frac{\sigma}{\$$epsilon_0$$}$$

Question 6

For a solid conductor in electrostatic equilibrium, where does any excess charge reside?

Accepted Answer

On the surface of the conductor

Question 7

A solid conductor with a cavity carries a total charge of $$+7 nC. $$Inside the cavity is an insulated point charge of $$-5 nC. $$What is the charge on the inner surface of the cavity?

Accepted Answer

$$+5 nC$$

Question 8

What is the electric field a distance $$r$$ from an infinite line of charge with linear charge density $$\lambda$$?

Accepted Answer

$$E = \frac{\lambda}{2 \pi \$$epsilon_0$$ r}$$

Question 9

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 10

A thin, flat, infinite non-conducting sheet has a uniform positive charge per unit area $$\sigma. $$What is the electric field just outside the sheet?

Accepted Answer

$$E = \frac{\sigma}{2 \$$epsilon_0$$}$$

Question 11

If a charge $$Q is $$uniformly distributed throughout a volume $$V$$, what is the volume charge density $$\rho$$?

Accepted Answer

$$\rho = \frac{Q}{V}$$

Question 12

A solid conductor with a cavity contains a point charge $$-5 nC $$and the conductor itself has a net charge of $$+7 nC. $$What is the charge on the outer surface of the conductor?

Accepted Answer

$$+2 nC$$

Question 13

Which of the following best describes the electric field just outside a charged conductor?

Accepted Answer

It is perpendicular to the surface and has magnitude $$\frac{\sigma}{\$$epsilon_0$$}$$

Question 14

A charge $$Q is $$uniformly distributed on a surface of area $$A. $$What is the surface charge density $$\sigma$$?

Accepted Answer

$$\sigma = \frac{Q}{A}$$

Question 15

Which experiment provided early experimental evidence for Gauss’s Law?

Accepted Answer

Faraday’s ice pail experiment

Question 16

If a charge $$Q is $$uniformly distributed along a line of length $$l$$, what is the linear charge density $$\lambda$$?

Accepted Answer

$$\lambda = \frac{Q}{l}$$

Question 17

On an irregularly shaped conductor, where does charge tend to accumulate?

Accepted Answer

At locations where the radius of curvature is smaller (sharp points)

Question 18

A solid conductor with a cavity contains a point charge $$q_{cavity}$$ and the conductor itself has a net charge $$q_{total}. $$What is the charge on the outer surface of the conductor?

Accepted Answer

$$q_{total} - (-q_{cavity})$$

Continuous Charge Distributions and Gauss’s Law

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