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Surface charge densities of two thin con...

Surface charge densities of two thin concentric spherical capacitors or shells are given as `sigma and -sigma`. The radii are R and 2R. The concentric capacitors are connected by a thin conducting wire. The entire charge on the inner miner transfers to the outer caspacitor and potential difference between them becomes zero. final potential of each capacitor will be

A

`-(3sigmaR)/(2epsi_(0))`

B

`-(2sigmaR)/(epsi_(0))`

C

`-(sigmaR)/(2epsi_(0))`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
A

On connecting the two spherical shells by a wire, charge from the inner shell flows to outer shell. Hence, net charge on the outer shell is `q=q_(1)+q_(0)`
`impliesq=(sigma)(4piR^(2))+(-sigma)(4pi)(2R)^(2)`
`=-12sigmaR^(2)`
`V=(1)/(4piepsi_(0))*(q)/((2R))=(-12sigmapiR^(2))/(8piepsi_(0)R)=-(3sigmaR)/(2epsi_(0))`
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