Q: A solid insulating sphere of radius $a$ carries a net positive charge $Q$ uniformly distributed throughout its volume. What is the electric field at a distance $r < a$ from the center?

$E = \frac{1}{4\pi\epsilon_0} \frac{Q}{a^3} r$

Q: For a conducting sphere in electrostatic equilibrium, which statement is true?

The electric field inside the conductor is zero.

Q: A long, straight line of charge has a linear charge density $\lambda$. What is the magnitude of the electric field at a distance $r$ from the line?

$E = \frac{1}{2\pi\epsilon_0} \frac{\lambda}{r}$

Q: A plane of charge has a surface charge density $\sigma$. What is the electric field just outside the surface?

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

Question 1

Refer to the first image. Why is the magnitude of the electric field greater on surface A than on surface B?

Accepted Answer

Because the electric field lines are denser (closer together) at surface A, indicating a stronger field.

Question 2

In the second image, what does the pattern of electric field lines between the two charges represent?

Accepted Answer

An electric dipole, with field lines originating from the positive charge and terminating on the negative charge.

Question 3

Which of the following statements about electric field lines is correct?

Accepted Answer

Electric field lines never cross each other.

Question 4

Refer to the fourth image. Rank the magnitude of the electric field at points A, B, and C.

Accepted Answer

$E_A > E_B > E_C$

Question 5

An electron is projected horizontally into a uniform electric field between two plates, as shown in the fifth image. What is the direction of the electron's acceleration?

Accepted Answer

Downward, opposite to the direction of the electric field.

Question 6

Which equation correctly expresses the electric flux $\Phi_E$ through a flat surface of area $A$ in a uniform electric field $E$ at an angle $	heta$ to the normal?

Accepted Answer

$\Phi_E = E A \cos 	heta$

Question 7

If the electric field is parallel to the surface (as in image 15), what is the electric flux through that surface?

Accepted Answer

Zero, because $\cos 90^\circ = 0$.

Question 8

Which of the following is the correct mathematical statement of Gauss's Law?

Accepted Answer

$\Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{q_{in}}{\epsilon_0}$

Question 9

A solid insulating sphere of radius $a$ carries a net positive charge $Q$ uniformly distributed throughout its volume. What is the electric field at a distance $r < a$ from the center?

Accepted Answer

$E = \frac{1}{4\pi\epsilon_0} \frac{Q}{a^3} r$

Question 10

For a conducting sphere in electrostatic equilibrium, which statement is true?

Accepted Answer

The electric field inside the conductor is zero.

Question 11

A long, straight line of charge has a linear charge density $\lambda$. What is the magnitude of the electric field at a distance $r$ from the line?

Accepted Answer

$E = \frac{1}{2\pi\epsilon_0} \frac{\lambda}{r}$

Question 12

A plane of charge has a surface charge density $\sigma$. What is the electric field just outside the surface?

Accepted Answer

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

Question 13

For an insulating spherical shell with inner radius $a$, outer radius $b$, and uniform charge density $\rho$, what is the electric field at a point $r$ such that $a < r < b$?

Accepted Answer

$E = \frac{\rho}{3\epsilon_0} \frac{r^3 - a^3}{r^2}$

Question 14

Which of the following best describes the direction of the electric field at the surface of a conductor in electrostatic equilibrium?

Accepted Answer

Perpendicular to the surface.

Question 15

A Gaussian surface encloses a net charge of $-2Q$. What is the net electric flux through the surface?

Accepted Answer

$\Phi_E = \frac{-2Q}{\epsilon_0}$

Question 16

Which of the following is NOT a valid Gaussian surface for applying Gauss's Law to a point charge?

Accepted Answer

A surface that does not enclose the charge.

Question 17

If the electric field at a point is zero, which of the following must be true?

Accepted Answer

The net electric field from all sources at that point cancels out.

Question 18

Which of the following is a correct statement about the electric field inside a uniformly charged insulating sphere?

Accepted Answer

It increases linearly with distance from the center.

Question 19

Which symmetry is most appropriate for using Gauss's Law to find the electric field of an infinite plane of charge?

Accepted Answer

Planar symmetry

Electric Field Lines, Electric Flux, and Gauss’s Law

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