Question

a beam of fast moving electrons having cross-sectional area a falls normally on a flat surface. the electrons are absorbed by the surface and the average pressure exerted by the electrons on this surface is found to be p. if the electrons are moving with a speed v, then the effective current through any cross-section of the electron beam is

Answer 1

The current through any cross-section of the electron beam is i = PeA  /  meV

Explanation:

Given data:

• Cross-sectional area =A  
• Average pressure exerted by the electrons =P.
• Let the number of electrons in the beam be n.  

Change in momentum Δmv = n.mev

Forces is given as

F = PA

Now, we know

F×t = Δmv

F×t=nm  

F x t = nmeV

PA x t = nmeV

t = nmeV / PA

We know,

Current, i =    q/t

q = ne

i = ne / nmeV / PA

i = PeA  /  meV

Thus the current through any cross-section of the electron beam is i = PeA  /  meV.

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