Rutgers Physics 385 Electromagnetism I (Fall15/Gershtein)

Homework 4 - Due October 1, 2015 in class

1) Find the potential inside and outside of a uniformly charged solid phere whose radius is R and total charge is q. Use infinity as a reference point. Sketch V(r). Compute the gradient in each region and check that it yields the correct electric field.

2) Find the energy stored in a uniformly charged solid sphere (previous problem). There are many ways of doing it, but use the following. Assemble the sphere like an onion, layer by layer, i.e. bring in a infinitesimal charge dq of the infinitesimal layer dr, simultaneously increasing charge and radius of the sphere, and keeping the charge density constant.

3) compare the result of the previous problem to a more general way of finding energy by calculating