I have no clue how they got the answer for this question. Could someone get me started in the right direction?

when it says "Find E everywhere" it means find an equation that gives the electric field both inside and outside the sphere. So you'll need to do two regions (notice that the answer shows two different formulas.... one for r < radius of the sphere, and one for r > radius of the sphere).

Next you'll need to manipulate Maxwell's equations. You can probably do it with just Gauss's Law. I don't have the time to help at the moment though. I might be able to help later tonight though.

This post was edited by bentherdonethat on Oct 20 2013 02:06pm

Ok, I'm pretty sure I found out how to derive that answer. The professor also said to make note of the direction of the electric field, the surfaces over which you can expect the field to be normal to and constant on.

As for the direction, isn't it pointed radially outward from the surface of the sphere? If that's the case, how would I describe the surface that it's normal to? But I still don't see where it would be constant, since the magnitude always depends on r, the distance from the center of the sphere.