An electron (mass `m_(e )`)falls through a distance d in a uniform electric field of magnitude E.
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The direction of the field is reversed keeping its magnitudes unchanged, and a proton(mass `m_(p)`) falls through the same distance. If the times taken by the electrons and the protons to fall the distance d is `t_("electron")` and `t_("proton")` respectively, then the ratio `t_("electron")//t_("proton")`.

Explanation

The acceleration experienced by a charged particle under the action of an electric field E is
`a=(eE)/(m)`
If it falls through a distance h, stating form rest,
`h=(1)/(2)at^(2)` (as u=0)
or, `t^(2)=(2h)/(a)=(2h)/(eE//m)=(2mh)/(eE)`
or `t prop sqrt(m)` ...(i)
From eq (i) the time of fall will be
`(t_("electron"))/(t_("proton"))=sqrt((m_(e)/(m_(p)))`
Now since `m_(p)gtm_(e)`, so `t_(p)gtt_(e)`, i.e., time of fall through the same distance is greater for a heavier particle, which is in constrant with the situation of free fall under gravity where the time of fall is independent of the mass of the body.