How Is the Electric Flux Calculated for a Point Charge Inside a Cylinder?

[JohanM]

Homework Statement

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.

Homework Equations

E=\frac{kQ}{r^{2}}\widehat{r}

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

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!

 

[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.