E&M - flux encircled by orbit of particles is conserved

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SUMMARY

The discussion focuses on proving the conservation of magnetic flux encircled by particle orbits in a magnetic mirror configuration, specifically when the magnetic field varies. The magnetic flux is defined as BA, where A represents the area of the circular orbits determined by the radius R. Participants suggest rescaling the magnetic field B to B' = aB and demonstrate that the flux remains independent of the scaling factor "a". This establishes that the flux is conserved despite variations in the magnetic field strength.

PREREQUISITES
  • Understanding of magnetic fields and their properties
  • Familiarity with the concept of magnetic flux
  • Knowledge of circular motion and geometry of circles
  • Basic principles of particle dynamics in magnetic fields
NEXT STEPS
  • Study the principles of magnetic flux conservation in electromagnetic theory
  • Learn about magnetic mirror configurations and their applications
  • Explore the mathematical derivation of flux in varying magnetic fields
  • Investigate the relationship between magnetic field strength and particle orbits
USEFUL FOR

This discussion is beneficial for physicists, electrical engineers, and students studying electromagnetism, particularly those interested in particle dynamics in magnetic fields and magnetic confinement systems.

Qyzren
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Prove that in a magnetic mirror the flux encircled by the orbit of the particles is conserved when the magnetic field varies.

How do you do this? i have no idea how to approach/start this!
 
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The flux is BA for the circular orbits (as you change the direction of the B field, the orbits adjust direction so that the flux is clearly the same) where A=area for a circle, found from the radius R. You can relate the radius R to the value of the B-field (and other quantities). Rescale B to B'=aB everywhere in your equations and show that the flux is independent of "a".
 

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