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_(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)`