(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A charge is distributed uniformly throughout a non-conducting spherical volume of radius R. Show, that the potential at distance r from center (r<R) is given by:

V=q(3*R^2-r^2)/(8*PI*e0*R^3)

2. Relevant equations

From Gauss low:

E(r)=q*r/(4*PI*e0*R^3)

E(r)=-grad(V(r))

3. The attempt at a solution

After integrating I got:

V(r)=-q*R^2/(8*PI*e0*R^3)

which is in fact stupid, as it yields V=0 at r=0. So probably I integrated with wrong limits.

How to obtain correct formula?

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# Potential inside of chrged non-conductive sphere

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