Question

Two large conducting plates are placed parallel to each other with a separation $d \,cm$ between them. An electron of mass $m$ starting from rest near one of the plates reaches the other plate in $t \sec$. The surface charge density on the inner surfaces $x \times \frac{m \varepsilon_{0} d}{\text { et }^{2}}$. Find the value of $x$ is

Answer 1

$d =2 \times 10^{-2} m$
$t =2 \times 10^{-6} s$

force on electron $= eE$
acceleration of electron
$a=\frac{e E}{m}=\frac{e \sigma}{m \varepsilon_{0}}$
$d=\frac{1}{2} a t^{2} ; d=\frac{1}{2} \frac{e \sigma}{m \varepsilon_{0}} t^{2}$
or $\sigma=\frac{2 m \varepsilon_{0} d }{\text { et }^{2}}$