A particle of mass m and charge(-q) enters the region between the two charged plates intially moving along x - axis with speed `V_(x)` . The length of plate is L and a uniform electric field E is maintained between the plates . Show that the verticles deflection of the particle at the far edge of the palte is `qEL^(2)//(2m v_(x)^(2))`.

Explanation

Let us assume that y is the deflection along Y-axis when the particle travels distance L along X-axis. Initial velocity given for the particle is `v_x` and is perpendicular to the electric field intensity E.
`S=1/2at^2rArr y=1/2 ((qE)/m)(L/v_x)^2`
The role of gravity is played by the electric force. The electric force is acting along Y-axis, hence the velocity along X-axis remains constant.