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.

Explanation

Let the charges on the spheres be `q_(1) and q_(2)` such that `Q=q_(1)+q_(2)`
`=4pi sigma(r^(2)+R^(2)) or sigma=(Q)/(4pi(r^(2)+R^(2)))`
Now potential at the common centre
`V=V_(1)+V_(2)`
`V=(1)/(4pi epsilon_(0))((q_(1))/(r )+(q_(2))/(R ))=(1)/(4pi epsilon_(0))((4pi r^(2)sigma)/(r )+(4pi R^(2)sigma)/(R ))`
`V=((r+R)sigma)/(epsilon_(0))`
Substituting for `sigma`, we have
`V=(1)/(4pi epsilon_(0)) (Q(r+R))/((r^(2)+R^(2)))`