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 charge on inner shell shell be `q` , charge on outer shell `= Q - q`.
Since surface charge densities are equal , we have
`(q)/( 4 pi r^(2)) = (Q - q)/(4 pi R^(2))`
`q = (Qr^(2))/(R^(2) + r^(2)) , Q - q = (QR^(2))/(R^(2) + r^(2))`
The electric potential at `O`
`V_(0) = (1)/(4 pi in_(0)) [ (q)/(r) + (Q - q)/(R )]`
`= (1)/(4 pi in_(0)) [ (Qr)/(R^(2) + r^(2)) + (QR)/(R^(2) + r^(2))]`
` = (1)/(4 pi in_(0)) (Q (R + r))/((R^(2) + r^(2)))`