Question

An electron beam after being accelerated from rest through a potential difference of 500V in vacuum is allowed to impinge normally on a fixed surface. If the incident current is $100\mu A$, the force exerted on the surface is $\frac{3x}{2}\times {10}^{-9}N$ assuming that it brings the electrons to rest. Find $x$. $(e=1.6\times {10}^{-19}C;m=9.0\times {10}^{-31}C)$

Answer 1

Energy of electron is $eV$

$dq/dt=A=100\times {10}^{-6}A$

So, total charge in $1$ second is $100\times {10}^{-6}C={10}^{-4}C$

number of electron is $n={10}^{-4}/1.6\times {10}^{-19}=6.25\times {10}^{14}$

Velocity of electron is $m{v}^2/2=eV\Rightarrow v=\sqrt{2eV/m}$

so, force is $F=n\times m\times \sqrt{2eV/m}=\frac{15}{2}\times {10}^{-9}N$

So, $x=15$