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

(a) `V_(A) = K( sigma4pi a^(2))/(a) + K((-sigma)4pib^(2))/(b) + K( sigma4pi c^(2))/(c )`
`= K sigma 4pi ( a-b+=c)`

`V_(B) = K ( 4pia^(2) sigma) /(b) - K(4pi b^(2) sigma)/(b) + K ( 4pi c^(2) sigma)/(c )`
` (sigma)/( epsilon_(0))[(a^(2))/(b) - a + c]`
`V_ ( C ) = ( K4pi a^(2) sigma- K4pi b^(2) sigma + K4pi c^(2 ) sigma)/( c )`
`= ( sigma)/(epsilon_(0)) ((a^(2) - b^(2) + c^(2))/( c))`