An electron is projected from a distance d and with initial velocity u parallel to a uniformly charged flat conducting plate as shown. It strikes the plate after travelling a distance $\mathcal{l}$ along the direction of projection. The surface charge density $\sigma$ of the conducting plate is. 

For the motion of the electron along Y-axis
$\mathrm{d}=\frac{1}{2}\frac{\mathrm{eE}}{\mathrm{m}}{\mathrm{t}}^2$………………….(1)
where E is the electric field due to the charged plate given by 

$\mathrm{E}=\frac{\mathrm{\sigma }}{{\mathrm{\epsilon }}_0}$………………………….(2)
where $\sigma$ is the surface density of charge of the plate. 
The time taken by the electron is 
$\mathrm{t}=\frac{\mathrm{\ell }}{\mathrm{u}}$…………………………..(3)
From equations (1), (2) and (3), we obtain
$\begin{array}{l}\mathrm{d}=\frac{1}{2}\frac{\mathrm{e\sigma }}{{\mathrm{\epsilon }}_0\mathrm{m}}{\left(\frac{\mathrm{\ell }}{\mathrm{u}}\right)}^2\\ \Rightarrow \mathrm{\sigma }=\frac{2{\mathrm{d\epsilon }}_0{\mathrm{mu}}^2}{{\mathrm{e\ell }}^2}\end{array}$