Question

A charge q is uniformly distributed over the volume of a sphere of radius R. Assuming the permittivity to be equal to unity throughout, find the potential 

(a) at the centre of the sphere; 

(b) inside the sphere as a function of the distance r from its centre.

Answer 1

From Gauss’ theorem intensity at a point, inside the sphere at a distance r from the centre is given by,  and outside it, is given by 

(a) Potential at the centre of the sphere

(b) Now, potential at any point, inside the sphere, at a distance r from it s centre.