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Three conducting concentric shell sA,B, ...


Three conducting concentric shell s`A,B, and C` of radius `a,2a,3a` are as shown in the figure.The charge on shell `B` is `Q`..The switch `S` is closed.Then after closing the switch
The charge on innermost shell is

A

`(Q)/(4)`

B

`(-Q)/(4)`

C

`(Q)/(2)`

D

`(-Q)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B

when switcj is closed the inner and most and outer most shells will acquire same potential.
Let the charge on outer shell be `q` and that on the inner shell be `-q` the total charge on inner and outer shell is zero.
`V_(A)=V_(C)`
`(1)/(4piepsilon_(0))((q)/(2a)+(Q)/(2a)-(q)/(3a))=(1)/(4piepsilon_(0))(Q)/(3a)`
`q-(q)/(3)+(Q)/(2)=(Q)/(3)(2q)/(3)=(Q)/(3)-(Q)/(2)=(-Q)/(6)`
`=q=(-Q)/(4) rArr q_(A)=(-Q)/(4)`
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