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:

Options

A. Ape/(mv)
B. `Ape//(mv^(2))`
C. APV/(me)
D. Apm/(ev)

Answer

A

Explanation

Let n be the average no. of electrons per unit volume, present in the beam of electrons, then impulse-momentum theorem gives :
(nAv)(mv) = F, P = F/A, where A, v, m, F & P represents cross sectional area, drift velocity, mass of electron, force and pressure respectively.
`rArr n = P//(mv^(2))`
`therefore i = nAve = (APe)/(mv)`