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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 A 4πϵ0r1r2r1−r2 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=q4πϵ0r2−q4πϵ0r1=q4πϵ0[1r2−1r1] V=q4πϵ0(r1−r2r1r2) ...(i) Also, C=qV ∴C=4πϵ0r1r2r1−r2 using(i)

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