Formulating Lorentz's force law

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SUMMARY

The discussion centers on the derivation and implications of Lorentz's force law, expressed as F = Bvq, where F represents the force on a charged particle in an electromagnetic field. It is established that this formula emerges from relativistic electrodynamics and can be derived using the Euler-Lagrange equation, which combines the action of a free particle with an interaction term. Participants confirm that while Maxwell's equations remain unchanged under relativity, the Lorentz force law requires modification, highlighting its experimental foundation.

PREREQUISITES
  • Understanding of relativistic electrodynamics
  • Familiarity with Maxwell's equations
  • Knowledge of the Euler-Lagrange equation
  • Basic concepts of electromagnetic fields
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  • Study the derivation of the Lorentz force law from the Euler-Lagrange equation
  • Explore the implications of relativistic effects on Maxwell's equations
  • Investigate experimental validations of the Lorentz force law
  • Learn about the action principle in classical mechanics and its applications in electrodynamics
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Physicists, electrical engineers, and students of electromagnetism seeking to deepen their understanding of the relationship between force, charge, and electromagnetic fields in the context of relativity.

antoon
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How did sir Hendric Antoon Lorentz got to his formula:
F= B v q

Was i just experimental? or is this something witch follows out of the maxwell equesions or wath?
 
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You mean

[tex]\vec{F}=q \vec{v}\times\vec{B}[/tex]

,surely. I don't know the answer to the first question, but i do for the second. It follows in relativistic electrodynamics as a motion equation for a relativistic electrically charged particle in an electromagnetic field. Such equation can be derived as the Euler-Lagrange equation for the action obtained by adding the action for a free particle and the interaction term.

Daniel.
 
Without invoking the action principle, yeah it's a fundamental axiom of the theory of EM and its justification is certainly experimental. Turns out that in relativity, Maxwell's equations don't need changing, but the Lorentz force law does.
 

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