A particle of mass m and charge charge q enters the region . . .

 Question : A particle of mass m and charge charge q enters the region between two charged parallel plates, initially moving along x-axis with a speed V m/s . The length of the plate is L m and a uniform electric field E is maintained between the plates. Find the expression for vertical deflection at the far edge of the plate. Draw necessary diagram.

Doubt by Ridhi 

Solution : 

Here 

u_x=v

u_y=0 
The charge particle will experience the force only in the upward direction only due to the vertical electric field.
So F_x=0
E_x=0
a_x=0
But
F_y=qE_y

ma_y=qE [∵E_y=E]
a_y=qE/m

Horizontal distance covered by the charge particle  q

s=ut+½at²
x=vt+½a_xt²
x=vt+½(0)t²
L=v/t
t=v/L — (1) 

Vertical distance covered by the charge particle  q

s=ut+½at²
y=u_yt+½a_yt²
y=(0)t+½(qE/m)t²
y=½(qE/m)t²
y=½(qE/m)[v/L]² [Using equation (1)]

y=qEL²/2mv²

The vertical deflection at the edge of the plate is given by 

tanθ=y/x
tanθ=[qEL²/2mv²]/x

tanθ=[qEL²/2mv²]/L [∵x=L]
tanθ=qEL/2mv²

Similar Question : 

A particle of mass m and charge (–q) enters the region between the two charged plates initially moving along x-axis with speed vx. The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is qEL²/(2mv_x²). [NCERT Question]