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The capacity of an isolated sphere is in...

The 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

`(n^(2))/(n-1)`

B

`(n)/(n-1)`

C

`(2n)/(n+1)`

D

`(2n+1)/(n+1)`

Text Solution

Verified by Experts

The correct Answer is:
B

Capacity of an isolated sphere
`C_(1)=4piepsi_(0)R_(1)`
and Capacity of a sphere when enclosed by an earthed concentric sphere
`C_(2)=4piepsi_(0)((R_(1)R_(2))/(R_(1)+R_(2)))`
Given that `C_(2)=nC_(1)`
or `(R_(2)R_(1))/(R_(2)-R_(1))=nR_(1)`
or `((R_(2))/(R_(1)))/((R_(2))/(R_(1))-1)=n`
or `(R_(2))/(R_(1))=(n)/(n-1)`
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