Q: Which of the following is the correct general form of Gauss’s law?

$$\displaystyle \oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{encl}}}{\$$varepsilon_0$$}$$

Question 1

Which of the following best describes the concept of electric flux through a surface?

Accepted Answer

The product of the electric field and the area of the surface, considering only the component of the field perpendicular to the surface.

Question 2

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

Accepted Answer

$$\displaystyle \frac{q}{\$$varepsilon_0$$}$$

Question 3

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

Accepted Answer

The net electric flux through a closed surface depends only on the net charge enclosed within the surface.

Question 4

A flat disk of radius $$r = 0.10\ \mathrm{m} is $$placed in a uniform electric field $$E = 2.0 	imes 10^3$\ \mathrm{N/C}$$ such that the normal to the disk makes an angle of $$30^\circ$$ with the field. What is the electric flux through the disk?

Accepted Answer

$$54\ \mathrm{N \cdot m^2$/C}$$

Question 5

A solid conductor contains a hollow cavity with no charge inside. What is the net charge on the surface of the cavity?

Accepted Answer

Zero

Question 6

Which of the following is the correct expression for the electric flux $$\Phi_E$$ through a surface when the electric field $$\vec{E} is $$not perpendicular to the surface?

Accepted Answer

$$\Phi_E = EA \cos \phi$$

Question 7

A long, straight wire carries a uniform linear charge density $$\lambda. $$Using Gauss’s law, what is the magnitude of the electric field at a distance $$r$$ from the wire?

Accepted Answer

$$\displaystyle \frac{\lambda}{2\pi\$$varepsilon_0$$ r}$$

Question 8

A conducting box is placed in a uniform external electric field. What happens to the electric field inside the box?

Accepted Answer

It becomes zero due to electrostatic shielding.

Question 9

A Gaussian surface encloses a charge $$+2q. If $$the electric flux through the surface is $$\Phi$$, what would be the flux if the enclosed charge were $$+4q$$?

Accepted Answer

$$2\Phi$$

Question 10

Which of the following is NOT a valid Gaussian surface for applying Gauss’s law?

Accepted Answer

A surface that is not closed

Question 11

A solid insulating sphere of radius $$R$$ has a uniform charge density $$\rho. $$What is the total charge $$Q$$ contained in the sphere?

Accepted Answer

$$Q = \rho \frac{4}{3}\pi R^3$

Question 12

A charged conductor is in electrostatic equilibrium. Where is the excess charge located?

Accepted Answer

Entirely on the surface of the conductor

Question 13

A small charge $$q is $$placed inside a cavity within a neutral conductor. What is the charge induced on the inner surface of the cavity?

Accepted Answer

$$-q$$

Question 14

Which of the following best explains why the electric field just outside a charged conductor is perpendicular to the surface?

Accepted Answer

If the field were not perpendicular, charges would move along the surface until equilibrium is reached.

Question 15

A thin, infinite sheet has a uniform surface charge density $$\sigma. $$What is the magnitude of the electric field just outside the sheet?

Accepted Answer

$$\displaystyle \frac{\sigma}{2\$$varepsilon_0$$}$$

Question 16

Which of the following is the correct general form of Gauss’s law?

Accepted Answer

$$\displaystyle \oint \vec{E} \cdot d\vec{A} = \frac{Q_{	ext{encl}}}{\$$varepsilon_0$$}$$

Question 17

A box contains equal amounts of positive and negative charges. What is the net electric flux through the surface of the box?

Accepted Answer

Zero

Question 18

Which of the following is the SI unit for electric flux?

Accepted Answer

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

Question 19

A non-uniform electric field passes through a surface. Which mathematical operation is required to calculate the total electric flux through the surface?

Accepted Answer

A surface integral: $$\displaystyle \int \vec{E} \cdot d\vec{A}$$

Gauss’s Law and Electric Flux: Study Notes for Physics with Calculus

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