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

Answer

1

Explanation

`V_(A)=(1)/(4piepsilon_(0))((4pia^(2)sigma)/(a)-(4pia^(2)sigma)/(b)+(4pic^(2)sigma)/(c))`
`rArr V_(A)=(sigma)/(epsilon_(0))(a-b+c)and `
`rArr V_(B)=(1)/(4piepsilon_(0))((4pia^(2)sigma)/(b)-(4pib^(2)sigma)/(b)+(4pic^(2)sigma)/(c))`
`rArr V_(B)=(sigma)/(epsilon_(0))((a^(2))/(b)-b+c)`