Particle in an Electromagnetic Field

[SpaceNerdz]

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 .

 

[BvU]

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 )

 

[SpaceNerdz]

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 ?