An electron of mass m and charge e is fired perpendicular to a uniform electric field of intensity E with an initial velocity u. If the electron traverses a distance x in the field in the direction of firing, find the transverse displacement y it suffers.

Explanation

Given `m_(e)=m, q=e, d=x, u_(x)=u, u_(y)=0`
electric field between the plates `=E`
Time taken travel in the field, `t=d/u_(x)=x/u`
force on electron `F=qE=eE`
Acceleration of electron, `a=F/m=(eE)/m`
Transverse displacement of electron `y=u_(y)t+1/2 at^(2)`
`=y=0+1/2 ((eE)/m)(x/u)^(2)`
`:. y=(eEx^(2))/(2 m u^(2))`