Q: For a cylindrical rod of radius $r_0$ with uniform volume charge density $\rho$, what is the magnitude of the electric field at a distance $r < r_0$ from the axis?

$E = \frac{\rho r}{2 \epsilon_0}$

Q: A cubical shell is centered on the origin with faces parallel to the axes and charge distributed on the surface. Which Gaussian surface(s) allow calculation of the electric field at point $P$ on the surface using only Gauss's law?

Cannot be calculated using either surface

Q: Why can't the electric field at point $P$ on the surface of a cubical shell with charge distributed on its surface be calculated using Gauss's law with a cube or sphere centered on the origin?

The electric field at $P$ is not equal to the field at all points on the Gaussian surface.

Q: In electrostatic equilibrium, what can be said about the electric field inside a conductor and at its surface?

The electric field is zero inside the conductor and perpendicular to the surface at the surface.

Q: A metal bucket with a metal lid has zero excess charge. A metal ball with charge $+q$ is placed inside the bucket (not touching the bucket). After equilibrium, what is the excess charge on the inner and outer surfaces of the bucket?

Inner surface: $-q$, Outer surface: $0$

Q: For a cylindrical rod with uniform charge density $\rho$, what is the direction of the electric field at a point outside the rod?

Radially outward from the axis of the rod

Q: In the context of Gauss's law, why is the electric field considered constant over the curved surface of a coaxial cylindrical Gaussian surface inside a uniformly charged rod?

Because of cylindrical symmetry, the field depends only on the distance from the axis.

Q: A metal bucket with zero excess charge contains a metal ball with charge $+q$ suspended inside. What is the electric field inside the metal of the bucket?

Zero everywhere inside the metal

Question 1

A cylindrical rod of radius $r_0$ has a uniform volume charge density $\rho$ and is aligned with the $x$ axis. Two coaxial cylindrical Gaussian surfaces are considered: Case 1 with radius $r_0$ and length $2l$, and Case 2 with radius $r_0/2$ and length $2l$. What is the ratio of electric flux through the Gaussian surface in Case 1 to that in Case 2, $\frac{\Phi_{e,1}}{\Phi_{e,2}}$?

Accepted Answer

$2$

Question 2

For a cylindrical rod of radius $r_0$ with uniform volume charge density $\rho$, aligned with the $x$ axis, consider a coaxial cylindrical Gaussian surface. Which of the following statements is correct about the electric flux through the surface?

Accepted Answer

The flux through the flat end surfaces is zero.

Question 3

A cylindrical rod of radius $r_0$ has uniform volume charge density $\rho$ and is aligned with the $x$ axis. What is the relationship between the magnitude of the electric field $E$ and $r$ for $r > r_0$ (outside the rod)?

Accepted Answer

$E \propto \frac{1}{r}$

Question 4

For a cylindrical rod of radius $r_0$ with uniform volume charge density $\rho$, what is the magnitude of the electric field at a distance $r > r_0$ from the axis?

Accepted Answer

$E = \frac{\rho r_0^2}{2 \epsilon_0 r}$

Question 5

A cylindrical rod of radius $r_0$ has uniform volume charge density $\rho$ and is aligned with the $x$ axis. What is the relationship between the magnitude of the electric field $E$ and $r$ for $r < r_0$ (inside the rod)?

Accepted Answer

$E \propto r$

Question 6

For a cylindrical rod of radius $r_0$ with uniform volume charge density $\rho$, what is the magnitude of the electric field at a distance $r < r_0$ from the axis?

Accepted Answer

$E = \frac{\rho r}{2 \epsilon_0}$

Question 7

A cubical shell is centered on the origin with faces parallel to the axes and charge distributed on the surface. Which Gaussian surface(s) allow calculation of the electric field at point $P$ on the surface using only Gauss's law?

Accepted Answer

Cannot be calculated using either surface

Question 8

Why can't the electric field at point $P$ on the surface of a cubical shell with charge distributed on its surface be calculated using Gauss's law with a cube or sphere centered on the origin?

Accepted Answer

The electric field at $P$ is not equal to the field at all points on the Gaussian surface.

Question 9

In electrostatic equilibrium, what can be said about the electric field inside a conductor and at its surface?

Accepted Answer

The electric field is zero inside the conductor and perpendicular to the surface at the surface.

Question 10

A metal bucket with a metal lid has zero excess charge. A metal ball with charge $+q$ is placed inside the bucket (not touching the bucket). After equilibrium, what is the excess charge on the inner and outer surfaces of the bucket?

Accepted Answer

Inner surface: $-q$, Outer surface: $0$

Question 11

A metal ball with charge $+q$ is placed inside a neutral metal bucket with a lid. The ball does not touch the bucket. What is the net charge enclosed by a Gaussian surface just inside the metal of the bucket?

Accepted Answer

$0$

Question 12

A cylindrical rod of radius $r_0$ has uniform volume charge density $\rho$ and is aligned with the $x$ axis. For a coaxial cylindrical Gaussian surface of radius $r$ and length $l$, what is the total charge enclosed when $r < r_0$?

Accepted Answer

$Q_{in} = \rho \pi r^2 l$

Question 13

For a cylindrical rod with uniform charge density $\rho$, what is the direction of the electric field at a point outside the rod?

Accepted Answer

Radially outward from the axis of the rod

Question 14

In the context of Gauss's law, why is the electric field considered constant over the curved surface of a coaxial cylindrical Gaussian surface inside a uniformly charged rod?

Accepted Answer

Because of cylindrical symmetry, the field depends only on the distance from the axis.

Question 15

A metal bucket with zero excess charge contains a metal ball with charge $+q$ suspended inside. What is the electric field inside the metal of the bucket?

Accepted Answer

Zero everywhere inside the metal

Question 16

If a conductor is in electrostatic equilibrium, where does any excess charge reside?

Accepted Answer

On the surface of the conductor

Question 17

A cylindrical rod of radius $r_0$ has uniform volume charge density $\rho$. For a Gaussian surface of radius $r < r_0$, what is the electric flux through the curved surface?

Accepted Answer

$\Phi_e = \frac{\rho \pi r^2 l}{\epsilon_0}$

Question 18

Which of the following is a necessary condition for applying Gauss's law to calculate the electric field at a point on a Gaussian surface?

Accepted Answer

The electric field must have the same magnitude at all points on the surface.

Electric Fields, Flux, and Conductors: Applications of Gauss's Law

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