In the above diagram, a particle of mass m and charge (- q) initially moving along X-axis with velocity `v_x` enters the region between two charged plates. The length of the plate system is L and uniform electric field between the plates is E. What is the vertical deflection of the particle at the far edge of the plate?

Explanation

Mass of particle = m, velocity of particle= `v_(x)` charge on particle = -q, length of plates -L and electric field between the plates = E.
Let vertical deflection is y, because force is applied in the +y-direction and direction of force from negative plate towards positive plate.

Initial velocity, u = 0 Acceleration, `a=F/m = +(qE)/m`
Time,`t = L/v_(x)`
Second equation of motion,
` s= ut + 1/2 at^(2)`
Putting the values,
`y = 0 + 1/2 xx (+(qE)/m).L^(2)/V_(x)^(2) (V_(y)=0)`
`rArr y =(qEL^(2))/(2mv_(x)^(2))`
So, the vertical deflection of the particle at the far edge of the plate is `(qEL^(2))/(2mv_(x)^(2))`