Q: The electric flux $$\Phi_E$$ through a flat surface of area $$A in a $$uniform electric field $$\vec{E} is $$given by which of the following equations?

$$\Phi_E = E \cdot A \cos \theta$$

Question 1

Which of the following best describes the direction of the area vector $$\vec{A}$$ for a flat surface when calculating electric flux?

Accepted Answer

It is perpendicular to the surface.

Question 2

The electric flux $$\Phi_E$$ through a flat surface of area $$A in a $$uniform electric field $$\vec{E} is $$given by which of the following equations?

Accepted Answer

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

Question 3

If the electric field is perpendicular to a flat surface and points into the surface, what is the sign of the electric flux through the surface?

Accepted Answer

Negative

Question 4

Which integral expression correctly represents the net electric flux through a general surface $$S in a $$non-uniform electric field?

Accepted Answer

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

Question 5

For a closed surface, if the net electric flux $$\Phi_E is $$positive, what does this indicate about the electric field lines?

Accepted Answer

More field lines leave the surface than enter.

Question 6

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

$$\Phi_E = \dfrac{Q}{\$$varepsilon_0$$}$$

Question 7

Which of the following is a necessary condition for using Gauss's law to easily calculate the electric field?

Accepted Answer

The electric field must be perpendicular and have the same magnitude everywhere on the Gaussian surface.

Question 8

For a uniformly charged non-conducting solid sphere of radius $$R$$ and total charge $$Q$$, what is the electric field at a distance $$r$$ from the center, where $$r \u003c R$$?

Accepted Answer

$$E = \dfrac{1}{4\pi \$$varepsilon_0$$} \dfrac{Qr}{R^3$}$$

Question 9

What is the electric field outside a uniformly charged non-conducting solid sphere (at $$r \u003e R$$)?

Accepted Answer

$$E = \dfrac{1}{4\pi \$$varepsilon_0$$} \dfrac{Q}{r^2$}$$

Question 10

A conductor is placed in a uniform external electric field. What is the electric field inside the conductor?

Accepted Answer

Zero

Question 11

If the electric field just outside the surface of a conductor is $$E$$ and the surface charge density is $$\sigma$$, what is the relationship between them?

Accepted Answer

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

Question 12

Which of the following statements about the electric field near a conductor with excess charge is correct?

Accepted Answer

The electric field is strongest at the points where the surface is most curved.

Question 13

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

Accepted Answer

$$\Phi_E = 0$$

Question 14

Which of the following is a correct application of Gauss's law?

Accepted Answer

Calculating the electric field inside a hollow conducting shell.

Question 15

If a surface is oriented such that the electric field is parallel to the surface, what is the electric flux through the surface?

Accepted Answer

Zero

Question 16

A spherical Gaussian surface of radius $$r$$ encloses a charge $$Q. If $$the radius is doubled, what happens to the electric flux through the surface?

Accepted Answer

It remains the same

Question 17

Which of the following best explains why the electric field outside a uniformly charged sphere is the same as if all the charge were concentrated at the center?

Accepted Answer

Because of the superposition principle and spherical symmetry

Study Notes on Gauss's Law and Electric Flux

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