#### Question

A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig. 2.36). Show

what the capacitance of a spherical capacitor is given by

`C=(4piin_0r_1r_2)/(r_1-r_2)`

where *r*_{1} and *r*_{2} are the radii of outer and inner spheres, respectively.

#### Solution

Radius of the outer shell = *r*_{1}

Radius of the inner shell = *r*_{2}

The inner surface of the outer shell has charge +*Q*.

The outer surface of the inner shell has induced charge −*Q*.

Potential difference between the two shells is given by,

`V=Q/(4piin_0)[1/r_2-1/r_1]`

Where,

`in_0` = Permittivity of free space

`V=Q/(4piin_0)[1/r_2-1/r_1]`

`=Q(r_1-r_2)/(4piin_0r_2r_1]`

Capacitance of the given system is given by

`C="Charge(Q)"/"Potenstial difference(V)"`

`=(4piin_0r_2r_1)/(r_1-r_2)`

Hence, proved.