I Two hemispheres, and a shell inside dielectric material

1. Jan 8, 2017

Phylosopher

Hello,

I am trying to solve two different questions, and I am having trouble finding the solution:

1- Spherical shell of radius R, have two hemispheres of different charge density. The northerns hemisphere is +σ and the southern hemisphere is -σ. Use direct integration to find V inside and outside the shell. (i.e V=k∫σ'/χ dr').

2- A spherical shell of radius a that have charge density of σcos(θ) is placed in a dielectric material that surround it and makes spherical shape around it with radius b. Find V in the whole space using separation of variables.[i.e shell of radius a attached from the inside to a dielectric material of radius a to b]

For (1), I solved it using separation of variables, and it does give me a series. The problem with direct integration is that there is no symmetry in the space so I cannot solve the problem on specific axis! more than that, I have no idea how to solve the problem inside the sphere.

For (2), I did solve the question but I am wondering, is the potential inside the shell is constant or not?

2. Jan 9, 2017

Phylosopher

I tried to be as clear and simple as possible. If anyone can help and didn't get fully what I wrote or my post seems vague, please comment.