A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere si earthed and the inner sphere is given a charge of `2.5 muC`. The space between the concentric spheres is filled with a liquid of dielectric constant 32.
(a) Determine the capacitance of the capacitor. (b) What is the potential of the inner sphere ?
(c) Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm.Explain why the latter is much smaller ?

Explanation

Here, `r_(a) = 12cm = 12xx10^(-2) m, r_(b) = 13cm = 13xx10^(-2)m, q = 2.5 muC = 2.5xx10^(-6) C, in_(r) = 32`
(a) C = ?
As `C = 4pi in_(0) (in_(r) r_(a) r_(b))/(r_(b) - r_(a)) = (1)/(9xx10^(9)) (32xx12xx10^(-2)xx13xx10^(-2))/((13-12)10^(-2)) = 5.5xx10^(-9) farad`
(b) `V = ?, V = (q)/(C) = (2.5xx10^(-6))/(5.5xx10^(-9)) = 4.5xx10^(2) vol t`
(c) Capacity of an isolated sphere of radius
`R = 12xx10^(-2) m is C' = 4pi in_(0)R = (1)/(9xx10^(9)) xx12xx10^(-2) = 1.33xx10^(-11) farad`
The capacity of an isolated sphere is much smaller because in a capacitor, outer sphere si eartheed. potential difference decreases and capacitance increases.