Three concentric spherical conductors A, B, and C of radii r, 2R, and 4R, respectively. A and C is shorted and B is uniformly charged (charge +Q).

Charge on conductor A is

Options

A. `Q//3`
B. `-Q//3`
C. `2Q//3`
D. `-2Q//3`

Answer

B

Explanation

`q_(1)+q_(2)=0`
`v_(A)=(kq_(1))/(R)+(kQ)/(2R)+(kq_(2))/(4R)`
`v_(C)=(kq_(1))/(4R)+(kQ)/(4R)+(kq_(2))/(4R)`
`v_(A)=v_(C)`
`q_(1)=-(Q)/(3)` and `q_(2)=(Q)/(3)`
`v_(A)=k[(-Q)/(3R)+(Q)/(2R)+(Q)/(12R)]=(Q)/(12piepsilon_(0)R)]=(Q)/(16piepsilon_(0)R)`
`v_(B)=k[(-Q)/(6R)+(Q)/(2R)+(Q)/(12R)]=(5Q)/(48piepsilon_(0)R)`