CUET Preparation Today
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. |
$\frac{1}{4\pi \epsilon_0} \frac{Q(R+r)}{R^2+r^2}$ $\frac{1}{4\pi \epsilon_0} \frac{Q(R-r)}{R^2+r^2}$ $\frac{1}{4\pi \epsilon_0} \frac{Q(R+r)^2}{R^2+r^2}$ None of the above |
$\frac{1}{4\pi \epsilon_0} \frac{Q(R+r)}{R^2+r^2}$ |
$ 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}$ $V_{centre} = V_1 + V_2 = \frac{1}{4\pi \epsilon_0} (\frac{q_1}{r} + \frac{q_2}{R}) = \frac{1}{4\pi \epsilon_0} \frac{Q(R+r)}{R^2+r^2}$ |
