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anizet
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Homework Statement
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)
Homework Equations
From Gauss low:
E(r)=q*r/(4*PI*e0*R^3)
E(r)=-grad(V(r))
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?