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A small ball is suspended over an infini...

A small ball is suspended over an infinite horizontal conducting plane by means of an insulating elastic thread of stifiness `k`. As soon as the ball was charged it decended by `x cm` and its separation from the plane become equal to `l`. Find the charge of the ball.

Text Solution

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When the ball is charged, for the equilibrium of ball, electric force on it must counter balance the excess spring force, extered, on the ball due to the extension in the spring.
Thus `F_(el) = F_(spr)`
or, `(q^(2))/(4pi epsilon_(0) (2l)^(2)) = k x`, (The force on the charge `q` might be considered as arised from attraction by the eletrical image).
or, `q = 4l sqrt(pi epsilon_(0) k x)`,
sought charge on the sphere,
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Knowledge Check

  • Statement-1: A small metal ball is suspended in a uniform electric field with an insulated thread. If high energy X-rays beam falls on the ball, the ball will be declected in the electric field. Statement-2: X-rays emit photoelectrons and metal and metal becomes negatively charged.

    A
    Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation of Statement-1.
    B
    Statement-1 is true, Statement-2 is true, but Statement-2 is not a correct explanation of Statement-1.
    C
    Statement-1 is true, but Statement-2 is false
    D
    Statement-1 is false, but Statement-2 is true.

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