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Question

Capacity of an isolated sphere is increased n times when it is enclosed by an earthed concentric sphere. The ratio of their radii is

A
nn1
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B
n2n1
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C
2nn+1
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D
2n+1n+1
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Solution

The correct option is B nn1
Let the radius of isolated sphere be a and that of earthed sphare be b.
Capacitance of isolated sphere C=4πϵoa
Capacitance of isolated sphere enclosed in earthed sphere nC=4πϵoabba
nC=C bba
Or nbna=b
Or (n1)b=na
ba=nn1

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