The electron beam emerging from a certain high-energy electron accelerator has a

Question

The electron beam emerging from a certain high-energy electron accelerator has a circular cross-section of radius 1.00 mm.
(a) If the beam current is 8.00 µA, what is the current density in the beam, assuming that it is uniform throughout?
(b) The speed of the electrons is so close to the speed of light that their speed can be taken as c = 3.00 x 10^8 m/s with negligible error. Find the electron density in the beam.
(c) How long does it take for Avogadro’s number of electrons to emerge from the accelerator?

Explanation / Answer

Given that
The radius (r) =1.00 mm                       = 0.001m Area of cross-section(A) =r2                                           =3.14(0.001m)2                                          =3.14*10-6m2 a) The current in the beam(I) =8µA                                            =8*10-6A The current density is(J) =I/A a) The current in the beam(I) =8µA                                            =8*10-6A The current density is(J) =I/A b) Speed(v) =300 Mm/s                = 3*108m/s Where q is the charge of the electron=1.6*10-19C The current density(J) =nqv Electron density( n ) = J/qv c) Where NA is the Avagadro number =6.023*1023 Time interval is(t) =NAq / I Substitue all the given values you get the requiredanswer

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