Two concentric spherical shells have radii a and `b (gt a)`. Write the capacitance of the system in following cases.
(a) Positive terminal of the battery is connected to the outer shell and its other terminal and the inner shell are grounded.
(b) Positive terminal of the battery is connected to the inner shell and its negative terminal is grounded.
(c) A terminal of the battery is connected to the inner shell and the other terminal along with the outer shell is grounded.
(d) A terminal of the battery is connected to the outer shell and the other terminal is grounded.

Answer

(a) `4 pi in_(0)((b^(2))/(b-a))`
(b) `4 pi in_(0)a`
(c) `4 pi in_(0)((ab)/(b-a))`
(d) `4 pi in_(0) b`