Practicing Success
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. |
$\frac{1}{4\pi\epsilon_0}\frac{Q(R+r)}{R^2+ r^2}$ $\frac{1}{4\pi\epsilon_0}\frac{Q(R-r)}{R^2+ r^2}$ $\frac{1}{4\pi\epsilon_0}\frac{Q(R+r)}{R^2 - r^2}$ $\frac{1}{4\pi\epsilon_0}\frac{Q(R+r)^2}{R^2+ r^2}$ |
$\frac{1}{4\pi\epsilon_0}\frac{Q(R+r)}{R^2+ r^2}$ |
$ q_1 + q_2 = Q$ .......(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}$ $V_c = V_1 + V_2 = \frac{1}{4\pi\epsilon_0} (\frac{q_1}{r} + \frac{q_2}{R}) = \frac{1}{4\pi\epsilon_0}\frac{Q(R+r)}{R^2+ r^2}$ |