Question 1

Which of the following best describes the electric flux $$\Phi_E$$ through a flat surface of area $$A$$ when the electric field $$\vec{E} is $$perpendicular to the surface?

Accepted Answer

$$\Phi_E = E \cdot A$$

Question 2

A point charge $$q is $$placed at the center of a spherical Gaussian surface of radius $$r. $$What is the electric flux $$\Phi_E$$ through the surface?

Accepted Answer

$$\Phi_E = \dfrac{q}{\$$epsilon_0$$}$$

Question 3

For a non-uniform electric field $$\vec{E}$$ passing through a curved surface, which integral correctly represents the total electric flux?

Accepted Answer

$$\Phi_E = \int \vec{E} \cdot d\vec{A}$$

Question 4

A long, straight wire carries a uniform line charge density $$\lambda. $$Using a cylindrical Gaussian surface of radius $$r$$ and length $$l$$, what is the magnitude of the electric field at distance $$r$$ from the wire?

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Two large, parallel conducting plates carry equal and opposite surface charge densities $$+\sigma$$ and $$-\sigma. $$What is the electric field in the region between the plates?

Accepted Answer

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

Question 7

Where is the electric field zero for a charged thin spherical shell?

Accepted Answer

Inside the shell

Question 8

A uniformly charged insulating sphere of radius $$R$$ and total charge $$Q$$ has a volume charge density $$\rho. $$What is the electric field at a distance $$r \u003c R$$ from the center?

Accepted Answer

$$E = \dfrac{Q r}{4\pi \$$epsilon_0$$ R^3$}$$

Question 9

Which statement about Gauss’s Law is correct?

Accepted Answer

The electric flux through any closed surface depends only on the charge inside the surface.

Question 10

A Gaussian surface encloses a net charge $$Q_{encl}. $$What is the total electric flux through the surface?

Accepted Answer

$$\Phi_E = \dfrac{Q_{encl}}{\$$epsilon_0$$}$$

Question 11

If the electric field $$\vec{E} is $$parallel to a surface, what is the electric flux $$\Phi_E$$ through the surface?

Accepted Answer

$$\Phi_E = 0$$

Question 12

A spherical shell of radius $$R$$ carries a total charge $$Q. $$What is the electric field at a point outside the shell at distance $$r \u003e R$$?

Accepted Answer

$$E = \dfrac{Q}{4\pi \$$epsilon_0$$ r^2$}$$

Question 13

Which symmetry is most useful for applying Gauss’s Law to a line charge?

Accepted Answer

Cylindrical symmetry

Question 14

A Gaussian surface is placed around a region with no net charge. What is the electric flux through the surface?

Accepted Answer

$$\Phi_E = 0$$

Question 15

A charged sphere of radius $$R$$ has a total charge $$Q$$ distributed uniformly throughout its volume. What is the electric field at the surface ($$r = R$$)?

Accepted Answer

$$E = \dfrac{Q}{4\pi \$$epsilon_0$$ R^2$}$$

Question 16

Which of the following is NOT a valid strategy for choosing a Gaussian surface?

Accepted Answer

Choose a surface that is not related to the symmetry of the charge distribution.

Question 17

A fluid analogy is often used to describe electric flux. Which quantity in fluid flow is analogous to electric flux?

Accepted Answer

Volume flow rate

Question 18

If a Gaussian surface encloses both positive and negative charges, what determines the net electric flux?

Accepted Answer

The net charge (algebraic sum) inside the surface

Question 19

A nonconducting plane sheet has a surface charge density $$\sigma. $$What is the electric field at a point very close to the sheet?

Accepted Answer

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

Question 20

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.

Gauss’s Law and Applications in Electrostatics

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