# Electric Potential of a Spherical Shell of Charge

Ok if you have a spherical shell of radius R with an even distribution of charge then outside the shell at a distance r where r>R I get that the shell can be treated as a point charge and inside the sphere (r<R) the electric potential will be constant.
All my notes cover when the shell has no thickness and I was thinking what happen if the spherical shell did have thickness (say inner radius a and outer radius b)? When r is greater then b can the shell still be treated as a point charge? How about when a<r<b?

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Doc Al
Mentor
If the charge is uniformly distributed throughout the (nonconducting) shell:

(r > b) Treat as a point charge

(r < a) potential will be constant

(a < r < b) the field (and potential) will vary throughout this range; you'll need to integrate. (The field at a radius r depends only on the charge within that radius; the field is that of a point charge, but only the charge within r contributes to the field.)

Thanks for just clearing that up for me. I've managed to find a question on this (I'm getting practise in before mid-year exams) however it deals in terms of charge density. Is it just as simple as finding Q in terms of the sphere (volume of shell at such and such density).

Doc Al
Mentor
Right. You should be able to work with either total charge Q or with the charge density. As an exercise, you might want to find the field as a function of radius for a uniform ball of charge density $\rho$.