Three concentric metallic shells A , B and C of radii a, b and c `(a lt b lt c)` have surface densities `+ sigma ,- sigma` and `+sigma` respectively as shown in Fig.

If shells A and C are at the same potential , obtain the relation between a , b and c.

Explanation

If `V_(A) = V_(C)` , then we have
`[(sigma)/(in_(0)) [a - b + c] = (sigma)/(in_(0)) [a^(2) - b^(2))/(c) + c] implies a - b + c = (a^(2) - b^(2))/(c) + c implies (a- b) = (a^(2) - b^(2))/(c) implies c = a + b`