Three concentric spherical metallic shells A, B and C of radii a, b and c (a lt b ltc) have surface charge densities `sigma`, `-sigma` and `sigma` respectively.
`(i) Find the potential of the three shells A, B and C.
(ii) If the shells A and C are at the same potential, obtain the relation between the radii a, b and c.

Answer

(i) `V_(A)=sigma/in_(0)(a-b+c), V_(B)=sigma/in_(0)(a^(2)/b-b+c), V_(C)=sigma/in_(0)(a^(2)/c-b^(2)/c+c)` (ii) `a+b=c`

Explanation