# Point Charge Inside Cylinder

1. Sep 20, 2011

### JohanM

1. The problem statement, all variables and given/known data
A point charge Q is on the axis of a short cylinder at its center. The diameter of the cylinder is equal to its length L (see figure). What is the total flux through the curved sides of the cylinder? [Hint First calculate the flux through the ends.

2. Relevant equations
$E=\frac{kQ}{r^{2}}\widehat{r}$

$\phi=\oint\vec{E}\cdot d \vec{A}=\frac{q}{\epsilon_{0}}$

3. The attempt at a solution
I see that the angle between the electric field and the normal vector of the two ends varies as one goes from 0 to R0 because the direction of the electric field changes as well. I just don't know how (or what) to integrate in order to calculate the flux through the two end disks.

If R1 is the distance between the point charge and a point on the end disk, the angle that R1 makes with the axis is what determines the location on the disk. This tells me that converting to polar coordinates might be a good option as well...

I just can't piece it all together, so any help would be greatly appreciated!

2. Sep 20, 2011

### Delphi51

Make a circle of radius r and another of radius r + dr.
Figure out the flux dϕ through that area dA = 2πr*dr (don't forget the angle of the flux to the surface). Integrate from r = 0 to Ro.