Question

A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig.). Show that the capacitance of a spherical capacitor is given by 

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

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Updated on : 2022-09-05
Solution
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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,

Where,

= Permittivity of free space


Capacitance of the given system is given by,

Hence, proved.

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Physics Part-I
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