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Question 29

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

spherical conductors

 

that the capacitance of a spherical capacitor is given by

capacitance of a spherical capacitor

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

Answer

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.

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