Question

Two large conducting plates are placed parallel to each other with a separation $dcm$ 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 $x\times \frac{m{\epsilon }_{0}d}{{\text{ et }}^2}$. Find the value of $x$ is

Answer 1

Answer: 2.00

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

force on electron $=eE$
acceleration of electron
$a=\frac{eE}{m}=\frac{e\sigma }{m{\epsilon }_0}$
$d=\frac{1}{2}a{t}^2;d=\frac{1}{2}\frac{e\sigma }{m{\epsilon }_0}{t}^2$
or $\sigma =\frac{2m{\epsilon }_{0}d}{{\text{ et }}^2}$