Figure shows a system of three concentric metal shells, A, B and C with radii a, 2a and 3a respectively. Shell B is earthed and shell C is given a charge Q. Now if shell C is connected to shell A, then find the final charge on the shell B

Answer

8

Explanation

From given conditions,
`V_(A) = V_(C )` and `V_(B) = 0 rArr V_(B) = (K(Q-q_(1)))/(3a) + (Kq_(2))/(2a) + (Kq_(1))/(2a) = 0`
`rArr 2Q + q_(1) + 3q_(2) = 0`………. (1)
Using `V_( C) = V_(A)`,
`(K(Q-q_(2)))/(3a) + (Kq_(2))/(3a) + (Kq_(1))/(3a) = (Kq_(1))/a + (K(Q-q_(1)))/(3a) + (Kq_(2))/(2a)`..........
`rArr q_(1) = -q_(2)/4`.......... (2)

Using it in (1), `q_(2) = -8/11 Q`