Two conducting concentric, hollow spheres A and B have radii a and b respectively, with A inside B. Their common potentials is V. A is now given some charge such that its potential becomes zero. The potential of B will now be

Options

A. 0
B. `V(1-(a)/(b))`
C. `((V)/(ab))`
D. `V((b-a))/((b+a))`

Answer

B

Explanation

Let initial charge on B be Q. Then , V = kQ/b. There is no initial charge on A, as A and B are at the same potential. Let q charge be now given to A. Potential of A now is
`k(q)/(a) + k(Q)/(b) = 0` or `q = -(Qa)/(b)` …(i)
Potential of B now is
`k((Q+q)/(b)) = (k)/(b)[Q-(Qa)/(b)] = k(Q)/(b)(1-(a)/(b)) = V(1-(a)/(b))` (Using (i))