Question

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

that the capacitance of a spherical capacitor is given by

where r₁ and r₂ are the radii of outer and inner spheres, respectively.

Answer 1

Radius of the outer shell = r₁ 

Radius of the inner shell = r₂ 

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,

Hence, proved.