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

Let the charges on spheres of radii r and R be q1 and q2 respectively. Then Q = q1+ q2. The potential at the centre will be V=14πε0q1r+q2RAs surface densities are equal, henceσ=q14πr2=q24πR2  or  q2=q1R2/r2∴ V=14πε0q1r+q1Rr2=14πε0×q1r2[r+R]Now,  q1+q2=Q  or  q1+q1R2r2=Q∴ q1r2=QR2+r2So,   V=Q4πε0R+rR2+r2