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An electron of mass m is placed at the m...

An electron of mass m is placed at the mid point of line joining two fixed charges + Q coulomb each separated by a distance r. Calculate the escape velocity for the electron.

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As electron is placed at mid-point of two charges of +Q coulomb each, then potential energy of the electron is
`U = k[(-Qe)/(r//2) + (-Qe)/(r//2)]` (here, e is the charge of electron)
`rArr U = (kQ)/r (-4e)`
By energy conservation, Kinetic energy (KE) = U = `1/2 m_(e)v_(e)^(2) = (kQ)/r (-4e)`
(`m_(e)` is mass of electron, ve is escape velocity of electron) negative sign shows the attraction.
`rArr v_( e) = sqrt((2kQ)/(m_(e) r) (4e)) = sqrt((8kQe)/(m_(e) r))`
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