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A Spherical Capacitor Consists of Two Concentric Spherical Conductors, Held in Position by Suitable Insulating Supports - Physics

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

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Solution

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,

`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.

Concept: Capacitors and Capacitance
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APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 2 Electrostatic Potential and Capacitance
Q 29 | Page 90
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