Question

A particle of mass m and charge$(-q)$ enters the region between the two charged plated initially moving along x-axis with speed $V_X$ in the given figure. The length of plate is $L$ and an uniform electric field $E$ is maintained between the plates. Find the vertical deflection of the particle at the far edge of the plate (neglecting gravity).

• A. $qE{L}^2/\left(m{V}_X^2\right)$
• B. $qE{L}^2/\left(2m{V}_X^2\right)$
• C. $qE{L}^2/\left(4m{V}_X^2\right)$
• D. Zero

Answer 1

The correct option is B $qE{L}^2/\left(2m{V}_X^2\right)$

As we know that acceleration of particle along y axis $a_y=\frac{qE}{m}$
Time taken by particle to cross the length of plate $t=\frac{L}{V_X}$

where $V_X$ is the velocity of particle along x axis.
And also, second equations of motion :
$S=u_{y}t+\frac{1}{2}{a}_y{t}^2$
Initially, velocity of particle along y axis $u_y=0$
$\therefore S=0+\frac{1}{2}\frac{qE}{m}\times (\frac{L}{V_X}{)}^2$
$\therefore S=qE{L}^2/\left(2m{V}_X^2\right)$