Three concentric spherical metallic spheres `A,B` and `C` of radii `a , b` and `c(a lt b lt c)` have surface charge densities `sigma , -sigma` and `sigma` respectively.

Options

A. The potential of shell `A`:
`V_(A) = (sigma)/(epsilon_(0)) (a + b + c)`
B. The potential of shell `B`:
`V_(B) = (sigma)/(epsilon_(0)) ((a^(2))/(b) - b + c)`
C. The potential of shell `C`:
`V_(C ) = (sigma)/(epsilon_(0)) ((a^(2) - b^(2))/(c ) + c)`
D. All options are correct

Answer

4

Explanation

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