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.

Explanation

`V_(A) = (1)/(4pi in_(0)) [ (sigma . 4 pi a^(2))/(a) + (-sigma . 4pi b^(2))/(b) + (sigma . 4 pi c^(2))/(c )]`
`V_(C) = (1)/(4pi in_(0)) [ (sigma . 4 pi a^(2))/(c ) + (-sigma . 4pi b^(2))/(c ) + (sigma . 4 pi c^(2))/(c )]`
`V_(A) = V_(C )`
`a - b = (a^(2))/(c ) - (b^(2))/(c ) = (a^(2) - b^(2))/(c )`
`= ((a + b) (a - b))/(c )`
`c = a + b`