Practice Problem #13: Using Gauss's Law with a non-uniform charge density

Remarks:

Here we complicate life by asking you to work out the field for a spherical distribution that is not uniform in some region. This means that you need to explicitly integrate to get the charge enclosed. This is not really so difficult but you need to keep track of "housekeeping" especially when you work out the voltage.

This problem is just a little too hard to be on an hour exam. I might put it on a final exam though.