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Question

A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports as shown in figure. The capacitance C, of this spherical capacitor is:

A
4πϵ0r1r2r1r2
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B
4πϵ0(r2r1)r1r2
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C
r1r24πϵ0(r2r1)
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D
(r1r2)4πϵ0r1r2
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Solution

The correct option is C 4πϵ0r1r2r1r2

As shown in figure, +q charge spreads uniformly on inner surface of outer sphere of radius r1. The induced charge -q spreads uniformly on the outer surface of inner sphere of radius r2. The outer surface of outer sphere is earthen.
Due to electrostatic shielding
E = 0 for r < r2 and E = 0 for r > r1
In the space between the two spheres,
Potential difference between two spheres,
V=q4πϵ0r2q4πϵ0r1=q4πϵ0[1r21r1]
V=q4πϵ0(r1r2r1r2) ...(i)
Also, C=qV
C=4πϵ0r1r2r1r2 using(i)


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