Two spherical conductors A and B of radii a and b (`b gt a`) are placed concentrically in air. A is given charged +Q while B is earthed. Then the equivalent capacitance of the system is

Options

A. `4pi epsilon_0(ab)/(b-a)`
B. `4pi epsilon_0 (a+b)`
C. `4pi epsilon_0 b`
D. `4pi epsilon_0 (b^2)/(b-a)`

Answer

D

Explanation

When inner sphere is earthed
`C=4piepsilon_0b+4piepsilon_0((ab)/(b-a))`
`=4piepsilon_0(b^2/(b-a))`