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

Answer

D

Explanation

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

Similarly `V_(B)= 4pi k sigma ((a^(2))/(b)- b+ c)`
`V_(C )= 4pi k sigma ((a^(2))/(c )- (b^(2))/(c )+ c)`
`=4pi k sigma ((a^(2)-b^(2))/(c ) + c)`
`=4pi k sigma (((a+b) (a-b))/(c ) + c)`
`=4pi k sigma [(a-b) +c]`
`=4pi k sigma (a-b+c)`
So, `V_(A ) = V_(C ) ne V_(B)`