# Potential of a spherical shell (non-uniform charge density)

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1. Sep 8, 2015

### SquidgyGuff

1. The problem statement, all variables and given/known data
Given a spherical shell of radius R and the surface charge density ( being the angle from the top of the sphere and being a constant) find the electric potential and the electric field inside and outside the sphere. Check that both the potential is continuous inside and outside the sphere and that inside and out. I made this little diagram to illustrate.

2. Relevant equations

3. The attempt at a solution
I can't even understand this problem. I feel like the point of interest shown in the diagram should be on the shell so that can return a meaningful value, but I need to find the potential and electric field everywhere, so it can't be on the sphere.

Last edited by a moderator: May 8, 2017
2. Sep 9, 2015

### BvU

Hello Guff,

I notice that your problem statement mentions a charge distribution on the surface of the sphere, but that there is no equation where charge or charge density plays a role. Is there something you can add to your 'toolbox' ?

3. Sep 9, 2015

### SquidgyGuff

If I looked at the charge distribution a point charge the field would look like this , but I know that isn't correct because I believe the total charge is zero. because half of the values of are negative and the other half are positive.

4. Sep 9, 2015

### BvU

I still don't see how you want to find the field or the potential at a point in space.
Where exactly on the sphere is $\cos\theta$ negative ?