Gauss's law

Suppose the radius of the sphere in Example 24.1 (radius 1.00 m, with a charge of +1.00 μC at its center) is changed to 0.500 m. What happens to the flux through the sphere and the magnitude of the electric field at the surface of the sphere?

• The flux and field both increase.

• The flux and field both decrease.

• The flux increases and the field decreases.

• The flux decreases and the field increases.

• The flux remains the same and the field increases.

In a charge-free region of space, a closed container is placed in an electric field. A requirement for the total electric flux through the surface of the container to be zero is that

• the field must be uniform

• the container must be symmetric

• the container must be oriented in a certain way

• The requirement does not exist – the total electric flux is zero no matter what.

If the net flux through a gaussian surface is zero, the following four statements could be true. Which of the statements must be true?

(I) There are no charges inside the surface.

(III) The electric field is zero everywhere on the surface.

(IV) The number of electric field lines entering the surface equals the number leaving the surface.

• I & IV

• II & III

• II & IV

• I & II

• All

Consider the charge distribution shown in the figure. The charges contributing to the total electric flux through surface S’ are ...

• q1 only

• q4 only

• q2 and q3

• all four charges

• none of the charges

Your little brother likes to rub his feet on the carpet and then touch you to give you a shock. While you are trying to escape the shock treatment, you discover a hollow metal cylinder in your basement, large enough to climb inside. In which of the following cases will you not be shocked?

• You climb inside the cylinder, making contact with the inner surface, and your charged brother touches the outer metal surface.

• Your charged brother is inside touching the inner metal surface and you are outside, touching the outer metal surface.

• Both of you are outside the cylinder, touching its outer metal surface but not touching each other directly.

A solid non-conducting sphere has a radius R and a charge of +Q uniformly distributed throughout its volume. Which graph below describes the electric field as a function of distance r from the center of the sphere?

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A conducting sphere has a charge +Q and a radius R. Which graph below describes the electric field as a function of distance r from the center of the sphere?

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A spherical conductor is given a positive charge. Under electrostatic conditions, which of the following is TRUE of the electric field just beneath the surface of the sphere?

• The electric field is directed away from the center of the sphere.

• The electric field in infinitely large.

• The electric field is zero.

• The electric field depends on the radius of the sphere.

• The electric field is directed tangential to the surface of the sphere.

A conducting sphere of radius R has a charge +Q.

If the electric field at a point 2R from the center has an electric field of E, what is the electric field at a point R/2 from the center?

• 0

• 1/4 E

• 1/2 E

• 2E

• 4E

In the figure, it shows four point charges and the cross section of a Gaussian surface:

Which of the following statements is true concerning the situation depicted?

• The net electric flux through the Gaussian surface depends on all four charges shown, but the electric field at point P depends only on charges Q2 and Q3

• The net electric flux through the Gaussian surface depends on charges Q2 & Q3, but the electric field at point P depends on all charges.

• The net electric flux through the Gaussian surface depends on charges Q2 & Q3 and the electric field at point P depends on charges Q2, Q3 and Q4

• The net electric flux through the Gaussian surface depends on charges Q1 & Q4 and the electric field at point P depends on charges Q2 and Q3

• Both the net electric flux through the Gaussian surface and the electric field at point P depend on all four charges.