Slab Beam of electrons through Neutralising Ions

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SUMMARY

The discussion focuses on calculating the electric and magnetic fields generated by a slab beam of electrons with charge density (-ρb) and velocity vbez as it passes through a channel of neutralizing ions with charge density f*ρb. The objective is to determine the value of f that results in no net force acting on the electrons in the beam. Participants reference the Biot-Savart law for magnetic field calculations and the Lorentz force equation F = q(E + v x B) to analyze the forces involved. Clarification is sought regarding the behavior of the neutralizing ions within the lab frame.

PREREQUISITES
  • Understanding of electric and magnetic fields in charged particle dynamics
  • Familiarity with the Biot-Savart law for magnetic field calculations
  • Knowledge of the Lorentz force equation F = q(E + v x B)
  • Concept of charge density and its implications in electromagnetic theory
NEXT STEPS
  • Study the application of the Biot-Savart law in different geometries
  • Explore the concept of charge neutrality in plasma physics
  • Learn about the dynamics of charged particle beams in electromagnetic fields
  • Investigate the effects of varying charge densities on particle motion
USEFUL FOR

Students and researchers in physics, particularly those focusing on electromagnetism, charged particle dynamics, and plasma physics, will benefit from this discussion.

Remembrandt
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Homework Statement


A slab beam of electrons of thickness a, width w >> a, charge density
(-ρb ), (Take ρb to be positive.) and velocity vbez passes through a channel of
neutralizing ions with charge density f*ρb where f is some number between zero and one
(all parameters given above apply in the "lab" frame).
  1. Calculate the electric and magnetic fields produced by this combination of charges and currents in the region y << w / 2 .
  2. Find f such that there is no net force on any electron in the beam.

Homework Equations


F[/B] = q(E + v x B)

The Attempt at a Solution


I have an idea as how to begin. But I am not very sure about it.

At any instant of time the new current flowing is given by (ρb - f *ρb)*w*a*vb. If this is the current, then the magnetic field is given by Biot Savarts law (μo/4π)*I/2R ? I just don't get this .

Can anybody guide me on how to start ?
 
Physics news on Phys.org
I'm not sure what "channel of neutralizing ions" means, but I don't think those ions move in our lab frame.
How did you apply Biot-Savart to your disk of electrons?
 

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