A charge Q is distributed over two concentric hollow spheres of radii r and R (R >r) such that the surface densities are equal. Find the potential at the common centre.
Answer & explanation
Correct answer: option 1
$ Q = q_1 + q_2$ ..............(1)
$\sigma = \frac{q_1}{4\pi r^2} = \frac{q_2}{4\pi R^2}$ ..........(2)
From (1) and (2)
$ q_1 = \frac{Qr^2}{r^2+R^2} , q_2 = \frac{QR^2}{r^2+R^2}$
$V_{centre} = V_1 + V_2 = \frac{1}{4\pi \epsilon_0} (\frac{q_1}{r} + \frac{q_2}{R}) = \frac{1}{4\pi \epsilon_0} \frac{Q(R+r)}{R^2+r^2}$