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Consider two concentric spherical metal ...

Consider two concentric spherical metal shells of radii `r_(1)` and `r_(2) (r_(2) gt r_(1))`. Find the charge on the inner shell and charge distribution.

Text Solution

Verified by Experts

Let charge on inner shell be `q`.
The potential at `P`
`V_(P) = (1)/(4 pi in_(0)) ((q)/(r_(1)) + (Q)/(r_(2))) = 0`
`q = -(Qr_(1))/(r_(2))`
Charge on inner shell `= -Qr_(1)//r_(2)` and it will be on outer surface.
`(Qr_(1)//r_(2)` has been transferred to earth leaving negative charge on inner shell.)
Charge distribution : The facing will surfaces will have equal and opposite charges and total charge on outer shell `Q`.

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Knowledge Check

  • Consider two concentric spherical metal shells of radii r_(1) and r_(2) (r_(2) gt r_(1)) . If the outer shell has a charge q and the inner one is grounded, then the charge on the inner shell is

    A
    `(-r_(2))/r_(1) q`
    B
    zero
    C
    `(-r_(1))/r_(2) q`
    D
    `-q`

  • The capacitance of two concentric spherical shells of radii R_(1) and R_(2) (R_(2) gt R_(1)) is

    A
    `4pi epsi_(0)R_(2)`
    B
    `4pi epsi_(0) ((R_(2)-R_(1)))/(R_(1)R_(2))`
    C
    `4pi epsi_(0) (R_(1)R_(2))/((R_(2)-R_(1)))`
    D
    `4pi epsi_(0) R^(1)`

  • The radii of two concentric spherical conducting shells are r_(1) and r_(2)(gt r_(1)) . The change on the oute shell is q. The charge on the inner shell which is connected to the earth is

    A
    `q((r_(2))/(r_(1)))`
    B
    `q^(2)((r_(1))/(r_(2)))`
    C
    `-q(r_(1)//r_(2))`
    D
    `q^(2)((r_(2))/(r_(1)))`

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