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. `V_(A)=(a+b+c)(sigma)/(epsilon_(0))`
B. `V_(B)=((a^(2))/b-b+c)(sigma)/(epsilon_(0))`
C. `V_(C)=((a^(2)+b^(2))/b+c)(sigma)/(epsilon_(0))`
D. `V_(A)=V_(B)=V_(C)=(a+b+c)(sigma)/(epsilon_(0))`

Answer

B

Explanation

Potential due to a charged shell
at an outside point `=1/(4 pi epsilon_(0))xxQ/r`
while that inside the shell `=(sigmaR)/(epsilon_(0))` where R is the radius of the shell.
Add potential due to all the shells at a given point.