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Assuming an expression for the potential...

Assuming an expression for the potential of an isolated conductor, show that the capacitance of such a sphere will be increased by a factor n, if it is enclosed within an earthed concentric sphere, the ration of the spheres being `n/(n - 1)`.

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
`C_(1)=4piepsi_(0)R_(1)`
`C_(2)=4piepsi_(0) (R_(1)R_(2))/(R_(2)-R_(1))=nC_(1)`
`therefore (R_(1)R_(2))/(R_(2)-R_(1))=nR_(1) or R_(2)=nR_(2)-nR_(1)`
`or nR_(1)=(n-1)r_(2) therefore R_(2)/R_(1)=(n)/(n-1)`
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