Question

Two large conducting plates are placed parallel to each other with a separation of $2.00cm$ between them. An electron starting from rest near one of the plates reaches the other plate in $2.00$ microseconds. Find the surface charge density on the inner surfaces.

Answer 1

Given

Separation between the plates $=2.50cm$

Time taken by the electron is $=2\mu s$

Mass of the electron is $9.1\times {10}^{-31}jg$

The Charge of the electron is $1.6\times {10}^{-19}$

Permittivity of the vacuum $=8.84\times {10}^{-12}f/m$

So,

Using the equation:

$f=eE$

The electric field is given by:

$E=\frac{\sigma }{{\epsilon }_0}$

$\therefore f=\frac{e\sigma }{{\epsilon }_0}$

The distance covered by the accelerating charge particle is:

$d=\frac{a{t}^2}{2}$

Now using the equation $f=ma$.

$\Rightarrow a=\frac{2d}{t^2}$

$\frac{e\sigma }{{\epsilon }_0}=\frac{2dm}{t^2}$

$\sigma =\frac{2dm{\epsilon }_0}{e{t}^2}$