[UPSC CSE 2012] Electrostatics and Magnetostatics (Q140, 15M)

The volume between two concentric conducting spherical surfaces of radii $a$ and $b$ ( $a<b$ ) is filled with an inhomogeneous dielectric with $\epsilon=\epsilon_0/(1+cr)$ , where $c$ is a constant and $r$ is the radial coordinate. A charge $+Q$ is placed on the inner surface, while the outer surface is grounded. Determine-

(i) $\vec{D}$ in the region $a<r<b$ ;

(ii) capacitance of the device;