Question

An electron beam accelerated from rest through a potential difference of $500V$ in vacuum is allowed to impinge on a surface normally. The incident current is $50\mu A$ and if the electrons come to rest on striking the surface the force on it is

• A. $1.1924\times {10}^{-8}N$
• B. $2.1\times {10}^{-8}N$
• C. $1.6\times {10}^{-8}N$
• D. $1.6\times {10}^{-6}N$

Answer 1

The correct option is A $1.1924\times {10}^{-8}N$

Potential difference $=500V$

incident current $=50\times {10}^{-6}A$

Total current is $A=50\times {10}^{-6}A$

change of a electron $C=1.6\times {10}^{-19}C$

Total number of electron per second $n=\frac{A}{e}=3.125\times {10}^{14}$

Total energy $KE=eV$

$=1.6\times {10}^{-19}\times 5000$

$=8\times {10}^{-16}y$

force on wall will be equal to change in momentum of $n$ electron is one second.

Let, $P=$ moment and $m$ be the mass of electron

So, $KE=\frac{P^2}{2m}$

$P^2=2m\times KE$

$P=3.8\times {10}^{-23}$

Total force is $F=nP$

$=3.125\times {10}^{14}\times 3.8\times {10}^{-23}$

$=1.19\times {10}^{-8}N$