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

Options

A. `Q/(4 pi epsilon_0) xx ((r + R))/((R + r)^2)`
B. `(Q(R^2 + r)^2)/(4pi epsilon_0(r + R))`
C. `(Q(r + R))/(4pi epsilon_0(R^2 + r^2))`
D. none of these

Answer

C

Explanation

Let charge on smaller sphere be x
`x/(4pi r^2) = (Q - x)/(4 pi R^2) implies x = (Qr^2)/(R^2 + r^2)`
and `V = (Kx)/(r) + (K(Q - x))/(R)`