Particle in an Electromagnetic Field

AI Thread Summary
The discussion centers on the Lagrangian for a charged particle in an electromagnetic field, specifically the term qvA, where A represents the magnetic vector potential and v is the particle's velocity. Participants clarify that this term is crucial for understanding the magnetic effects on the particle's motion, linking it to the Lorentz Force Law. The expression qvA contributes to the overall energy dynamics of the particle, particularly in magnetic interactions. The conversation emphasizes the mathematical derivation from the Lorentz force to the Lagrangian form, reinforcing its validity in physics. Overall, the term qvA encapsulates the influence of magnetic fields on charged particles.
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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