Particle in an Electromagnetic Field

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SUMMARY

The discussion centers on the Lagrangian formulation of a charged particle in an electromagnetic field, specifically the expression L = ½mv² - qφ + qAv. The term qAv represents the interaction between the charged particle's velocity (v) and the magnetic vector potential (A), which is crucial for understanding the Lorentz Force Law. Participants clarify that while ½mv² denotes kinetic energy and qφ indicates the electric potential, the term qvA encapsulates the magnetic effects on the particle's motion. This formulation effectively links classical mechanics with electromagnetism.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with the Lorentz Force Law
  • Knowledge of electromagnetic potentials, specifically magnetic vector potential (A)
  • Basic concepts of kinetic energy and electric potential energy
NEXT STEPS
  • Study the derivation of the Lorentz Force Law from the Lagrangian perspective
  • Explore the physical significance of the magnetic vector potential (A) in electromagnetism
  • Learn about the implications of the term qvA in the context of charged particle dynamics
  • Investigate applications of Lagrangian mechanics in electromagnetic systems
USEFUL FOR

Physicists, students of classical mechanics and electromagnetism, and anyone interested in the mathematical formulation of particle dynamics in electromagnetic fields.

SpaceNerdz
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Using the Lagrangian : L = ½mv^2 - qφ + qAv

What is the physical intuition of Av ? I know that A is the magnetic vector potential and that v is the velocity of the charged particle. I just don't know what their dot product means physically .
 
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Hi,

I find your expression hard to read/interpret. Fortunately, it's all chewed out thoroughly here . With the 'explanation':
we can solve .. for ##\vec F##: ... which is just the correct expression for the Lorentz Force Law

In other words: if you start with the Lorentz force law and do the math backwards (ahem) you (can) end up with this form for the Lagrangian.

"It works" is a also a good argument for a physicist ( I try to avoid the word intuition )
 
Well, 1/2mv^2 is kinetic energy of the particle , qφ is the coulomb potential of electricity . So we know what the other components of the equations are. So my question really is what does the term qvA mean ? It's something to do with magnetism, but what exactly ?
 

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