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Three concentric metallic shells A, B an...

Three concentric metallic shells A, B and C of radii a b and c `(a lt blt c)` have surface charge densities to `+sigma and- sigma` to `+sigma` respectively. The potential of shell B is

A

`(sigma)/(epsilon_(0))[(a^(2)+b^(2))/(b)+c]`

B

`(sigma)/(epsilon_(0))[(a^(2)-b^(2))/(b)]`

C

`(sigma)/(epsilon_(0))[(b^(2)-a^(2))/(b)+c]`

D

`(sigma)/(epsilon_(0))[(a^(2)-b^(2))/(b)+c]`

Text Solution

Verified by Experts

The correct Answer is:
D
Potential at B
`V_(B)=(kQ_(A))/(b)+(kQ_(B))/(b)+(kQ_(c))/(c)`
`=k[(sigma(4pia^(2)))/(b)-(sigmaxx4pib^(2))/(b)+(sigmaxx4pic^(2))/(c)]`
`=(sigma)/(4piepsilon_(0))4pi[(a^(2)-b^(2))/(b)+c]=(sigma)/(epsilon_(0))[(a^(2)-b^(2))/(b)+c]`
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