Question 1

A rectangular loop of area $$A is $$placed in a uniform electric field $$\vec{E}$$ such that the normal to the loop makes an angle $$	heta$$ with the field. What is the expression for the electric flux through the loop?

Accepted Answer

$$\Phi_E = EA \cos 	heta$$

Question 2

Which of the following best describes Gauss’s Law?

Accepted Answer

The electric flux through any closed surface is equal to the total charge enclosed divided by $$\$$epsilon_0$$.

Question 3

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

$$\Phi_E = q/\$$epsilon_0$$

Question 4

A very long straight wire carries a uniform charge per unit length $$\lambda. $$Using Gauss’s Law, what is the magnitude of the electric field at a distance $$r$$ from the wire (outside the wire)?

Accepted Answer

$$E = \dfrac{\lambda}{2\pi \$$epsilon_0$$ r}$$

Question 5

A non-conducting sphere of radius $$r_0$$ carries a uniform charge $$Q$$ distributed throughout its volume. What is the electric field at a distance $$r \u003c r_0$ from the center?

Accepted Answer

$$E = \dfrac{Qr}{4\pi \$$epsilon_0$$ r_0$^3}$$

Question 6

A large, thin, non-conducting plane has a uniform surface charge density $$\sigma. $$What is the electric field just above the surface?

Accepted Answer

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

Question 7

A conducting shell is in electrostatic equilibrium. What is the electric field inside the conductor?

Accepted Answer

$$E = 0$$

Question 8

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

Accepted Answer

$$-q$$

Question 9

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

Accepted Answer

The charge distribution must have a high degree of symmetry (spherical, cylindrical, or planar).

Question 10

A Faraday cage is used to shield sensitive electronic equipment from external electric fields. Which principle explains why the electric field inside the cage is zero?

Accepted Answer

Gauss’s Law: The net flux through a closed conducting surface is zero if no charge is enclosed.

Question 11

A cylindrical piece of insulating material is placed in a uniform external electric field. What is the net electric flux through the surface of the cylinder?

Accepted Answer

Zero

Question 12

A closed surface encloses several point charges. According to Gauss’s Law, what determines the net electric flux through the surface?

Accepted Answer

The sum of all charges inside the surface

Question 13

A metal sphere is placed in a uniform electric field and reaches electrostatic equilibrium. What is the direction of the electric field just outside the surface?

Accepted Answer

Perpendicular to the surface

Question 14

A charge $$Q is $$distributed uniformly over the surface of a conducting sphere of radius $$R. $$What is the electric field just outside the surface?

Accepted Answer

$$E = \dfrac{Q}{4\pi \$$epsilon_0$$ R^2$}$$

Question 15

A cone with base radius $$R$$ and height $$h is $$placed in a uniform horizontal electric field. What is the electric flux entering the left side of the cone?

Accepted Answer

$$\Phi_E = E \pi R^2$

Question 16

A parallel-plate capacitor is surrounded by a conducting box (Faraday cage). What happens to the electric field inside the box?

Accepted Answer

It is zero everywhere inside the box.

Question 17

Which of the following is the correct expression for the electric field just outside the surface of a conductor with surface charge density $$\sigma$$?

Accepted Answer

$$E = \dfrac{\sigma}{\$$epsilon_0$$}$$

Question 18

A non-conducting sphere of radius $$r_0$$ has a total charge $$Q$$ distributed uniformly throughout its volume. What is the electric field at a point outside the sphere ($$r \u003e r_0$)?

Accepted Answer

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

Electric Flux and Gauss’s Law: Concepts, Applications, and Conductors

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