A cylinder contains a charge Q. The flux through the curved side of the container is 3πkQ. What is the flux through the ends of the cylinder?
A) 3π kQ
B) 5π kQ
C) 9π kQ
D) π kQ
E) 0.0

Question

Quizplus · Accepted Answer

The flux through the ends of the cylinder can be found using Gauss's law. Since the cylinder is closed, the total flux through the closed surface is equal to the charge enclosed divided by the permittivity of free space.

Φ_total = Q/ε

The flux through the curved side is given as 3πkQ, which is one-third of the total flux. Therefore,

3πkQ = Φ_curved = (1/3) Φ_total

Solving for Φ_total gives

Φ_total = 9πkQ

Substituting this into Gauss's law gives

9πkQ = Q/ε + Φ_ends

Since the cylinder has no net charge, Q = 0, so

Φ_ends = - 9πkQ

Therefore, the flux through the ends of the cylinder is in the opposite direction to the flux through the curved side, with a magnitude of 9πkQ. However, since the question is asking for the absolute value of the flux, the answer is D, πkQ.

A Cylinder Contains a Charge Q