A particle of mass m and -q enters the region between the two charged plates initially moving along x-axis with speed Vx as shown in the given figure. The length of plate is L and a uniform electric field E is maintained between the plates. Find the vertical deflection of the particle at the far edge of the plate.

It is given that the charge on a particle of mass m is -q; the velocity of the particle is vx; the length of the plates is L; the magnitude of the uniform electric field between the plats is E.From the mechanical force, F, the acceleration a is given by F=ma⇒a=Fmbut we know that the electric force is F=q EHence, the acceleration can be given as a=qEmtime of travel= Lvx and displacement due to the electric field is 12at2Far edge of the plate is qEL2/(2mvx2).The motion of the particle mentioned in this problem can be compared with the motion of the horizontal projectiles under gravity.