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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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Knowledge Check

  • 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 outermost shell is

    A
    `(Q)/(4)`
    B
    `(-Q)/(4)`
    C
    `(Q)/(2)`
    D
    `(-Q)/(2)`

  • 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 If sigma_(A),sigma_(B) and sigma_(C) are the surface charge densities on A,B and C respectively then sigma_(A):sigma(B):sigma(C) is

    A
    `9:9:1`
    B
    `9:-9:1`
    C
    `-9:9:1`
    D
    `1:1:1`

  • Find the charge flown when the switch S is closed.

    A
    zero
    B
    `(epsilon_0A)/dV`
    C
    `3/2 (epsilon_0A)/d V`
    D
    `(epsilon_0A)/(2d)V`

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