Question 1

Which of the following best describes Gauss's law?

Accepted Answer

It states that the electric flux through a closed surface is proportional to the amount of charge enclosed within the surface.

Question 2

A spherical Gaussian surface encloses a point charge $$q. $$What is the electric flux through the surface?

Accepted Answer

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

Question 3

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

Accepted Answer

Cylindrical symmetry

Question 4

The electric field inside a conductor in electrostatic equilibrium is:

Accepted Answer

Zero

Question 5

A closed box has an outward-pointing electric field passing through every surface. What can you conclude about the net charge inside the box?

Accepted Answer

The box contains net positive charge.

Question 6

The electric flux through a surface of area $$A in a $$uniform electric field $$E at an $$angle $$	heta to $$the normal is given by:

Accepted Answer

$$\Phi_E = EA\cos	heta$$

Question 7

Which of the following is NOT a property of conductors in electrostatic equilibrium?

Accepted Answer

The external electric field is parallel to the surface.

Question 8

A Gaussian surface is most useful when:

Accepted Answer

It matches the shape and symmetry of the electric field.

Question 9

If the electric field is everywhere tangent to a closed surface, what is the electric flux through the surface?

Accepted Answer

It is zero.

Question 10

A charged metal sphere of radius $$R$$ carries a total charge $$Q. $$What is the electric field just outside its surface?

Accepted Answer

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

Question 11

A parallel-plate capacitor has plates of area $$A$$ separated by distance $$d$$, with charge $$+Q on $$one plate and $$-Q on $$the other. What is the electric flux through a surface of area $$A$$ placed between the plates and perpendicular to the field?

Accepted Answer

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

Question 12

Which of the following statements about electric flux is correct?

Accepted Answer

Electric flux through a closed surface depends only on the net charge enclosed.

Question 13

A cylindrical Gaussian surface of length $$L$$ and radius $$r$$ surrounds an infinite line of charge with linear charge density $$\lambda. $$What is the electric field at distance $$r$$ from the line?

Accepted Answer

$$E = \dfrac{\lambda}{2\pi\$$varepsilon_0$$ r}$$

Question 14

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

Accepted Answer

Calculating the electric field for charge distributions with high symmetry.

Question 15

A non-conducting sphere of radius $$R$$ has a uniform charge density $$\rho. $$What is the electric field at a distance $$r \u003c R$$ from the center?

Accepted Answer

$$E = \dfrac{\rho r}{3\$$varepsilon_0$$}$$

Question 16

A point charge $$q is $$placed at the center of a hollow, neutral, conducting sphere. What is the net charge induced on the inner surface of the sphere?

Accepted Answer

$$-q$$

Question 17

Which of the following best describes the area vector $$\vec{A}$$ for a surface?

Accepted Answer

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

Question 18

A flat surface of area $$A is $$placed in a uniform electric field $$E. If $$the surface is tilted so that the angle between the field and the normal to the surface is $$90^\circ$$, what is the electric flux through the surface?

Accepted Answer

$$0$$

Question 19

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

Accepted Answer

$$E = \dfrac{\sigma}{\$$varepsilon_0$$}$$, perpendicular to the surface

Gauss's Law, Symmetry, and Electric Flux: Foundations and Applications

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