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.

Explanation

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,