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A small conducting sphere of radius r is...

A small conducting sphere of radius `r` is lying concentrically inside a bigger hollow conducting sphere of radius `R`. The bigger and smaller spheres are charged with `Q` and `q(Q gt q)` and are insulated from each other. The potential difference between the spheres will be

A

`(1)/(4 pi epsilon_(0)) ((q)/(r ) - (Q)/(R) )`

B

`(1)/(4 pi epsilon_(0)) ((Q)/(R) + (q)/(r) )`

C

`(1)/(4 pi epsilon_(0)) ((q)/(r ) - (q)/(R))`

D

`(1)/(4 pi epsilon_(0)) ((q)/(R ) - (Q)/(r) )`

Text Solution

Verified by Experts

The correct Answer is:
3
`V_(A) = (1)/(4 pi in_(0)) [ (q)/( r) + (Q)/(R )]`
`V_(B) = (1)/(4 pi in_(0)) [ (q)/(R ) + (Q)/(R )]`
`V_(A) - V_(B) = (1)/(4 pi in_(0)) [ (q)/(r ) - (q)/(R )]`
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Knowledge Check

  • A conducting sphere of radius r has a charge . Then .

    A
    the charge is uniformly distributed over its surface if there is an external electric field .
    B
    Distribution of charge over its surface will be non uniform if no external electric field exist in space,
    C
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    D
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    A
    Q/3 amount of charge will flow from the sphere to the shell
    B
    20/3 amount of charge will flow from the sphere to the shell
    C
    Q amount of charge will flow from the sphere to the shell
    D
    `(kQ^2)/(4R)` amount of heat will be produced

  • A conducting sphere A of radius a ,with charge Q , is placed concentrically inside a conducting shell B of radius b . B is earthed. C is the common centre of the A and B

    A
    The field at a distance `r` from `C` , where `a le rle b` , is `k(Q)/(r^(2))`
    B
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    D
    All options are correct

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