# Find the surface charge density of a perfect conductor

This is for extra credit not actual homework but I need the points and I would like to understand the subject matter as well so any help would be much obliged.

## Homework Statement

There is a sphere with radius R made up of a perfect conducting material in a constant and uniform electric field E. I am tasked to find the surface charge density ρ.

## Homework Equations

See #3 for the relevant equations that I used.

## The Attempt at a Solution

I am attempting to solve this problem by Gauss's Law. I am almost done, all I need to do is actually construct the sphere...I think.

Since the electric field, E, is 0 in in the sphere the surface charge density is going to be the charge due to the sphere being in the field E.

I assumed $\Phi$ = ERcos$\Theta$ and then assumed that $_{Q}A$ would be the surface charge density (the enclosed charge in the sphere) = $\Phi$*$_{\epsilon}0$

However this doesn't help because I didn't construct any sphere and that is where I am lost. That is assuming I am doing this correctly. If I am not please tell me.