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Three concentric metal shells A, B, and ...

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

A

`(sigma)/(epsilon_0)[(b^(2)-c^(2))/b +a]`

B

`(sigma)/(epsilon_0)[(b^(2)-c^(2))/(c)+a]`

C

`(sigma)/(epsilon_0)[(a^(2)-b^(2))/(a)+c]`

D

`(sigma)/(epsilon_0)[(a^(2)-b^(2))/(b)+c]`

Text Solution

Verified by Experts

The correct Answer is:
D

The potential of shell B,
`V_(B) = 1/(4 pi epsilon_0)[((+sigma)4pia^(2))/(b) + ((-sigma)4pib^(2))/(b) + ((+sigma)4pic^(2))/(c )]`
`= (sigma)/(epsilon_0)[(a^(2)-b^(2))/b + c]`.
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