Potential of particle - why is there a scalar product here?

AI Thread Summary
The discussion centers on the Lagrangian equation in the context of electromagnetism, specifically questioning the origin of the scalar product between magnetic potential and velocity in the potential energy term. The participant expresses confusion over this formulation, noting it is not commonly encountered in their studies. A suggestion is made to refer to a specific section of the electromagnetism notes for clarification. The conversation highlights the need for deeper understanding of how scalar products are applied in Lagrangian mechanics. Overall, the inquiry reflects a broader interest in the mathematical foundations of physics.
tarkin2
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I'm reading up on the Lagrangian equation, but what I'm asking is to do with electromagnetism.

In the first equation here: http://www.phys.ufl.edu/~pjh/teaching/phy4605/notes/chargelagrangiannotes.pdf

L equals the kinetic minus the potential energy. For the potential energy term, I just don't see where the scalar product of magnetic potential and velocity is coming from. I haven't seen it written in this way before, could someone explain?
 
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