Q: The differential form of Gauss's Law is given by which equation?

$$\nabla \cdot \vec{E} = \frac{\rho}{\$$epsilon_0$$}$$

Question 1

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

Accepted Answer

$$\Phi_E = E A \cos	heta$$

Question 2

For a non-uniform electric field passing through a curved surface, how is the total electric flux $$\Phi_E$$ calculated?

Accepted Answer

$$\Phi_E = \sum_{i=1}^n \vec{E}_i \cdot \Delta \vec{A}_i$$

Question 3

According to Gauss's Law, what is the net electric flux through a closed surface that encloses a net charge $$Q_{encl}$$?

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

If the net electric flux through a closed surface is zero, which of the following must be true?

Accepted Answer

The net charge enclosed by the surface is zero.

Question 6

A solid insulating sphere of radius $$r_0$$ carries 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

$$E = \frac{Q r}{4\pi\$$epsilon_0$$ r_0$^3}$$

Question 7

A long, straight wire has a uniform linear charge density $$\lambda. $$Using Gauss's Law, what is the electric field at a distance $$R$$ from the wire?

Accepted Answer

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

Question 8

A large, flat, non-conducting sheet has a uniform surface charge density $$\sigma. $$What is the magnitude of the electric field just outside the sheet?

Accepted Answer

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

Question 9

Which of the following statements about the direction of the area vector $$d\vec{A}$$ for a closed surface is correct?

Accepted Answer

It is always directed outward from the enclosed volume.

Question 10

The differential form of Gauss's Law is given by which equation?

Accepted Answer

$$
abla \cdot \vec{E} = \frac{ho}{\$$epsilon_0$$}$$

Question 11

A conducting spherical shell carries a net charge $$Q. $$What is the electric field inside the shell (but outside the center)?

Accepted Answer

$$E = 0$$

Question 12

Which of the following best describes the physical meaning of electric flux?

Accepted Answer

It is proportional to the number of electric field lines passing through a surface.

Question 13

If a closed surface encloses both positive and negative charges such that the total enclosed charge is zero, what is the net electric flux through the surface?

Accepted Answer

$$\Phi_E = 0$$

Question 14

A non-conducting solid sphere of radius $$r_0$$ has a uniform charge density $$\rho. $$What is the total charge $$Q$$ contained in the sphere?

Accepted Answer

$$Q = \frac{4}{3}\pi r_0$^3 \rho$$

Question 15

Which of the following is a correct application of Gauss's Law for a closed surface $$S$$?

Accepted Answer

$$\oint_S \vec{E} \cdot d\vec{A} = Q_{encl} / \$$epsilon_0$$

Question 16

A spherical Gaussian surface of radius $$r is $$placed outside a uniformly charged solid sphere of radius $$r_0$$ and total charge $$Q. $$What is the electric field at distance $$r \u003e r_0$?

Accepted Answer

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

Question 17

Which of the following is NOT a valid consequence of Gauss's Law?

Accepted Answer

The electric field inside a conductor in electrostatic equilibrium is nonzero.

Gauss's Law and Electric Flux: Concepts, Applications, and Mathematical Formulation

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