Q: A uniform electric field $$\vec{E}$$ points to the right. A square surface of area $$A is $$oriented so that its area vector $$\vec{A}$$ makes an angle $$\theta$$ with $$\vec{E}. $$What is the electric flux through the surface?

$$\displaystyle \Phi_E = EA \cos \theta$$

Question 1

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

$$\displaystyle \frac{q}{\$$epsilon_0$$}$$

Question 2

A uniformly charged infinite plane has a surface charge density $$\sigma. $$What is the magnitude of the electric field just above the surface?

Accepted Answer

$$\displaystyle \frac{\sigma}{2\$$epsilon_0$$}$$

Question 3

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

Accepted Answer

$$\displaystyle \frac{\lambda}{2\pi \$$epsilon_0$$ d}$$

Question 4

A conducting shell is electrically neutral. A charge $$+3 nC is $$placed in a cavity inside the shell. What is the total charge on the exterior surface of the shell?

Accepted Answer

The exterior surface has a charge of $$+3 nC.$$

Question 5

Which symmetry is most appropriate for applying Gauss’s Law to a charged spherical shell?

Accepted Answer

Spherical symmetry

Question 6

A non-conducting rod of length $$L is $$bent into a half-circle of radius $$r$$ and carries a total charge $$+Q$$ uniformly distributed. What is the direction of the electric field at the center of the half-circle?

Accepted Answer

It points directly to the right (along the axis of symmetry).

Question 7

A plastic rod with uniformly distributed charge $$-Q is $$bent into a circular arc of radius $$r$$ that subtends an angle of $$\pi/3$$ radians. What is the correct expression for the linear charge density $$\lambda$$?

Accepted Answer

$$\displaystyle \lambda = \frac{Q}{r \pi/3}$$

Question 8

Which of the following statements about electric flux is correct?

Accepted Answer

The net electric flux through a closed surface depends only on the total charge enclosed.

Question 9

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

Accepted Answer

Zero

Question 10

A metal sphere is in electrostatic equilibrium. What is the electric field inside the sphere?

Accepted Answer

Zero everywhere inside the sphere

Question 11

A uniform electric field $$\vec{E}$$ points to the right. A square surface of area $$A is $$oriented so that its area vector $$\vec{A}$$ makes an angle $$	heta$$ with $$\vec{E}. $$What is the electric flux through the surface?

Accepted Answer

$$\displaystyle \Phi_E = EA \cos 	heta$$

Question 12

Which of the following is true about the electric field produced by an infinite plane of charge?

Accepted Answer

The field is perpendicular to the plane and has the same magnitude everywhere.

Question 13

A Gaussian surface is chosen to match the symmetry of a charge distribution. Why is this important for applying Gauss’s Law?

Accepted Answer

It simplifies the calculation of the dot product $$\vec{E} \cdot d\vec{A}.$$

Question 14

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 15

A conducting box (Faraday cage) is placed in a uniform electric field. What is the electric field inside the box?

Accepted Answer

Zero

Question 16

A sphere has a charge $$q$$ uniformly distributed through its volume, except for a spherical hole filled with a uniformly charged sphere of charge $$-q. $$What is the net electric flux out of the large sphere?

Accepted Answer

Zero

Question 17

A charge $$Q is $$placed at the center of a conducting shell. What is the total charge induced on the inner surface of the shell?

Accepted Answer

$$-Q$$

Question 18

Which of the following is a correct statement about the area vector $$\vec{A}$$ for a surface?

Accepted Answer

It is perpendicular to the surface and has magnitude equal to the area.

Gauss's Law and Electric Fields: A Comprehensive Study Guide

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