# 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