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

Options

A. `(n^(2))/(n-1)`
B. `(n)/(n-1)`
C. `(2n)/(n+1)`
D. `(2n+1)/(n+1)`

Answer

B

Explanation

`C_(1)=4piepsi_(o)R_(1)`
`and C_(2)=4piepsi_(o)((R_(1)R_(2))/(R_(2)-F_(1)))`
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)`