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
Answer & explanation
Correct answer: option 4
$\text{Let charge on the two spheres are }Q_1 \text{ and }Q_2 \text{ respectively.}$
$ Q_1 + Q_2 = Q$
$ \frac{Q_1}{4\pi r^2} = \frac{Q_2}{4\pi R^2}$
$ Q_2 = \frac{Q_1 R^2}{r^2}$
$Q_1(1+ \frac{R^2}{r^2}) = Q , Q_1 = \frac{Qr^2}{r^2+R^2} , Q_2 = \frac{QR^2}{r^2+R^2}$
$ V = \frac{1}{4\pi \epsilon_0}(\frac{Q_1}{r}+\frac{Q_2}{R}) = \frac{Q(R+r)}{4\pi \epsilon_0(r^2+R^2)}$