Question 1

A flat surface of area $$A is $$placed in a uniform electric field $$\vec{E}$$ such that the angle between the field and the normal to the surface is $$	heta. $$Which of the following correctly expresses the electric flux through the surface?

Accepted Answer

$$\Phi_E = EA \cos 	heta$$

Question 2

A rectangular surface of dimensions $$0.10\ \mathrm{m} 	imes 0.20\ \mathrm{m} is $$placed in a uniform electric field of $$200\ \mathrm{N/C} at an $$angle of $$30^\circ to $$the field. What is the electric flux through the surface?

Accepted Answer

$$3.5\ \mathrm{N \cdot m^2$/C}$$

Question 3

Which of the following statements about Gauss’s law is correct?

Accepted Answer

Gauss’s law is valid for any closed surface, regardless of shape.

Question 4

A point charge $$Q is $$placed at the center of a spherical Gaussian surface of radius $$r. $$What is the electric field at the surface?

Accepted Answer

$$E = \dfrac{Q}{4\pi \$$varepsilon_0$$ r^2$}$$

Question 5

A thin spherical shell of radius $$r_0$$ carries a total charge $$Q$$ uniformly distributed on its surface. What is the electric field at a point inside the shell ($$r \u003c r_0$)?

Accepted Answer

$$E = 0$$

Question 6

A nonconducting solid sphere of radius $$r_0$$ has a total charge $$Q$$ uniformly distributed throughout its volume. What is the electric field at a distance $$r \u003c r_0$ from the center?

Accepted Answer

$$E = \dfrac{Qr}{4\pi \$$varepsilon_0$$ r_0$^3}$$

Question 7

A very long straight wire carries a uniform positive charge per unit length $$\lambda. $$Using Gauss’s law, what is the magnitude of the electric field at a distance $$R$$ from the wire?

Accepted Answer

$$E = \dfrac{\lambda}{2\pi \$$varepsilon_0$$ R}$$

Question 8

A large, flat, nonconducting plane has a uniform surface charge density $$\sigma. $$What is the electric field just above the surface?

Accepted Answer

$$E = \dfrac{\sigma}{2\$$varepsilon_0$$}$$

Question 9

A conductor has a net charge $$+Q$$ and contains a cavity with a point charge $$+q$$ inside. What is the total charge on the inner surface of the cavity?

Accepted Answer

$$-q$$

Question 10

Which of the following is a necessary step when solving a Gauss’s law problem?

Accepted Answer

Choose a Gaussian surface that matches the symmetry of the charge distribution.

Question 11

A closed surface encloses several point charges. According to Gauss’s law, the net electric flux through the surface depends on:

Accepted Answer

The total charge enclosed by the surface.

Question 12

A metal ball is placed in contact with a charged metal cylinder and then removed. According to Gauss’s law, what happens to the charge on the ball?

Accepted Answer

It becomes zero.

Question 13

The electric field just outside the surface of a conductor with surface charge density $$\sigma is$$:

Accepted Answer

$$E = \dfrac{\sigma}{\$$varepsilon_0$$}$$

Question 14

Which of the following best explains why the electric field inside a conductor in electrostatic equilibrium is zero?

Accepted Answer

The charges move to the surface, canceling the internal field.

Question 15

A nonconducting sphere of radius $$r_0$$ has a total charge $$Q$$ uniformly distributed throughout its volume. What is the electric field at a point outside the sphere ($$r \u003e r_0$)?

Accepted Answer

$$E = \dfrac{Q}{4\pi \$$varepsilon_0$$ r^2$}$$

Question 16

A closed surface encloses no net charge. What is the net electric flux through the surface?

Accepted Answer

$$\Phi_E = 0$$

Question 17

Which of the following is a correct statement about the electric flux through a closed surface due to a charge located outside the surface?

Accepted Answer

The flux is zero.

Gauss’s Law and Electric Flux: Concepts, Applications, and Symmetry

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