Practice Problem #13: Using Gauss's Law with Two Thick Shells
Remarks:
Here we through thick shells at you, and one of these is a conductor.
Remember you do not need to "prove" that the electric field is zero
inside the conductor, you know it automatically and so you can use this
fact plus Gauss' Law to get the surface charges.
I actually gave this exact problem last year for the Second Hour Exam.
In retrospect it was a little too long. Still, a nice question, I think.