E&M, Fall '10, Homework 7

Problems from UP Chapter 28

1. Problem 9 ("two spherical shells")

2. Problem 13 ("combo")

3. Problem 50 ("flashing lamp")

4. Use the divergence theorem to rewrite Gauss' Law (i.e., the book's equation 24-7) in "differential form". Hint: write "q_encl" as an integral of the charge density over the volume enclosed by the Gaussian surface. Another hint: the answer is that the divergence of the electric field ("del dot E") equals the charge density (rho) divided by epsilon_0. The point of the problem is just to make sure you know how to use the vector calc theorem to translate from the integral form to the differential form of Gauss' law.