Question

We typically consider cases in class where charge is distributed completely uniformly, but it's not always that way - let's consider an insulating sphere (radius R) with surface charge density s =s0 sin2(q) cos2(f).

(a) Describe briefly in words and a picture what this charge distribution "looks like"

– i.e. where on the sphere is there more charge and where is there is less charge.

(b) Set up an integral for the total charge on this sphere in terms of R and s0 .

Evaluate the integral to show that the total charge is 4

5?R2s0.

(c) Briefly but clearly, describe a procedure to find E(x,0,0) (for x>R)?

Answer 1