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- Thread starter mlh3789
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The the correct expression for the Lorentz force on a relativistic particle in an EM field is no different than the same expression for a non-relativistic particle, i.e. in MKS units

This is not a 4-tensor equation though. If you're speaking about the tensor formulation then its taks on a different form. The tensor form is d

Pete

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In cgs gaussian units, just divide v by c, unless you have set c=1.

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Jonathan Scott

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I'm interested to see that someone is being taught about this way of getting the Lorentz force law from a Lagrangian. It makes it possible to see how adding the charge times the four-potential to the four-momentum (as in the Pauli "minimal electromagnetic coupling" assumption) gives a Lagrangian which results in exactly the same law of motion for charged particles as the Lorentz force law. That puzzled me for a long time until I worked it out for myself, which isn't difficult but I didn't see it mentioned in the text books which I used.

As mentioned in a previous response, the Lorentz force law is already relativistic. That means all you have to do is write out the Euler-Lagrange equations, recognize which partial derivatives of the four-potential correspond to the E and B fields and reorganize the result to show that it matches the Lorentz force law. I'm leaving the details as an exercise for the student.

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