Three concentric spherical shells have radii `a, b` and `c(a lt b lt c)` and have surface charge densities `sigma, -sigam` and `sigma` respectively. If `V_(A), V_(B)` and `V_(C)` denote the potentials of the three shells, then for `c = q + b`, we have

Options

A. `V_(C) = V_(B) ne V_(A)`
B. `V_(C) ne V_(B) ne V_(A)`
C. `V_(C) = V_(B)= V_(A)`
D. `V_(C) = V_(A) ne V_(B)`

Answer

D

Explanation

`V _(A) = (1)/(4 pi epsi_(0)) ((q_(A))/(a) + (q_(B))/(b) + (q_(C))/(c))`
`V_(B) = (1)/(4 pi epsi_(0)) ((q_(A))/(b) + (q_(B))/(b) + (q_(C))/(c))`
`V_(C) = (1)/( 4 pi epsi_(0)) ( (q_(A))/(c) + (q_(B))/(c) + (q_(C))/(c))`