Question

A charge Q is distributed over two concentric hollow spheres of radii r and `R (gt r)` such that the surface charge densities are equal. Find the potential at the common centre.

Answer 1

Correct Answer - `(Q(R+r))/(4pi in_(0)(r^(2)+R^(2)))`
`q_(1)+q_(2)=Q`
`sigma4pir^(2)+sigma4piR^(2)=Q`
`sigma=Q/(4pi(r^(2)+R^(2)))`
`V_("centre")=1/(4pi in_(0))[(sigma4pir^(2))/r+(sigmapi R^(2))/R]`
`=(Q(r+R))/(4pi in_(0)(r^(2)+R^(2)))`