AP® Physics C: E&M - Electric Flux - MCQs
Questions
A conducting spherical shell S has a charge Q distributed over its surface. The total electric flux through any imaginary concentric spherical shell of radius r that encloses S is
(A) inversely proportional to r
(B) inversely proportional to \(r^{2}\)
(C) directly proportional to r
(D) directly proportional to \(r^{2}\)
(E) independent of r
▶️Answer/Explanation
Ans: E
Questions
A charge is placed at the center of a cube. What is the flux of the electric field through one face of the cube?
(A) 0
(B) \(q/\epsilon _{\circ }\)
(C) \(q/6\epsilon _{\circ }\)
(D) \( 6\epsilon_{\circ }q \)
(E) The flux through one face cannot be determined from the information given.
▶️Answer/Explanation
Ans: C
Gauss’s law states that the total electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space \(\epsilon_0\):
\[ \Phi_{\text{total}} = \frac{q}{\epsilon_0} \]
In this problem, the charge \( q \) is placed at the center of a cube. The cube has 6 faces, and due to symmetry, the electric flux will be equally distributed through each face of the cube. Therefore, the flux through one face of the cube is:
\[ \Phi_{\text{one face}} = \frac{\Phi_{\text{total}}}{6} \]
Substituting the total flux:
\[ \Phi_{\text{one face}} = \frac{q}{6\epsilon_0} \]
Question
Which of the following must be true for a Gaussian surface through which the net flux is zero?
I. There are no charges inside the surface.
II. The net charge enclosed by the surface is zero.
III. The electric field is zero everywhere on the surface.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Answer/Explanation
Ans:BThe flux of an electric field through a closed surface is always zero if the net charge enclosed by the surface is zero. There could be charges inside the surface as long as they are equal and opposite charges. Also, there could be nonzero values of the electric field on the surface as long as the sum ΣE dA ⋅ is zero; thus, only II must be true.