Comparing Flux of a Closed Cylinder

[tuggler]

Homework Statement

A closed cylinder consists of two circular end caps and a curved side. A negatively charged particle is placed outside the left end of the cylinder, on its axis. Compare the flux through the left end of the cylinder with that through the right.


2. The attempt at a solution

I know the field points out of the cylinder on the left end, and into the cylinder on the right, so the flux through the left end is positive while that through the right end is negative. But what above the sides of the curves?

 

[Simon Bridge]

Does the question ask you about the curved sides?
What law tells you how the electric flux from a point charge, through a fixed area, changes with distance?

 

[rude man]

Let
charge located at x = 0
near end locared at x = d
length of cylinder = L
R = radius of ends

1. Compute the flux through a differential annulus for the near end. Integrate from r = 0 to r = R parametrically using θ = arc tan r/d.
2. Do the same for the far end. Realize θ will range from 0 to a smaller number than for the near end.
3. Compare.

 

[tuggler]

Thanks !