Single Choice

An electron beam accelerated from rest through a potential difference of 5000 V in a 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$$1.1924\times 10^{-8}N$$
Correct Answer
B$$2.1\times 10^{-8}N$$
C$$1.6\times 10^{-8}N$$
D$$1.6\times 10^{-6}N$$

Solution

Total current is $$A=50\times 10^{-6}A$$
Charge of a electron $$e=1.6\times 10^{-19}C$$
Total number of electron per second $$n=\dfrac{A}{e}=3.125\times 10^{14}$$
Total energy $$KE =eV=1.6\times 10^{-19}\times 5000=8\times 10^{-16}J$$
Force on wall will be equal to change in momentum of n electron in one second
Let P = momentum and m be the mass of electron
So $$KE=\dfrac{P^2}{2m}$$
So $$P^2=2m\times KE$$
$$P=3.8\times 10^{-23}$$
Total force is $$F=nP=3.125\times 10^{14}\times 3.8\times 10^{-23}=1.19\times 10^{-8} N$$

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