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A Spherical Capacitor Consists of Two Concentric Spherical Conductors, Held in Position by Suitable Insulating Supports - CBSE (Science) Class 12 - Physics

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

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.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Physics Textbook for Class 12 (2018 to Current)
Chapter 2: Electrostatic Potential and Capacitance
Q: 29 | Page no. 90

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Solution A Spherical Capacitor Consists of Two Concentric Spherical Conductors, Held in Position by Suitable Insulating Supports Concept: Capacitors and Capacitance.
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