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In Ampere's circuit law we have the current density which is separated in bound and free current. Bound current is due to the atom's internal structure and free current is well that is the question actually.

Suppose I have a point charges governed by maxwell's equations and I try to solve/simulate the movement of this charge what is the free current density I have to put into the equation?

I think it is something like

[tex]J_f(x) = q*v'*delta(x-x')[/tex]

(where x' and v' is the position and velocity of the particle)

But I can't find a explicit equation for J in any textbook. So I'm somewhat confused.

thx

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# Ampère's circuital law and the free current density

Can you offer guidance or do you also need help?

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