A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R=n r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is:

Let say inside shell has charge q1 and outside shell has charge q2.​Surface charge densities are equal for both shells.​⇒q14πr2=q24πR2 ⇒q1q2=r2R2→1​  &​ q1+q2=Q→2​∴q1=r2r2+R2Q    &    q2=R2R2+r2QPotential at common centre = V=Kq1r+Kq2R=KQrr2+R2+KQRR2+r2=KQr+Rr2+R2=KQr+nrr2+nr2=KQ1+nr1+n2