What is physical meaning of the EM force density?

AI Thread Summary
The discussion centers on the physical meaning of electromagnetic force density, defined by the continuous version of the Lorentz force equation. It questions how this force density relates to the equation of motion for charge density, particularly in a continuous context. The conversation highlights the need for clarity on the equation of motion for continuous charge density, with references provided for further reading. Participants express a desire for more comprehensive explanations and sources related to this topic. The thread emphasizes the importance of understanding the relationship between force density and motion in electromagnetic contexts.
pellman
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The continuous version of the Lorentz force is

\mathbf{f}=\rho\mathbf{E}+\mathbf{j}\times\mathbf{B}

but what does f mean?

In the discrete version F is the force on the charged particle appearing on the RHS. So if x is the position of the charged particle we have that its equation of motion is

m\frac{d^2\mathbf{x}}{dt^2}=\mathbf{F}=q\mathbf{E}+q\frac{d \mathbf{x}}{dt}\times\mathbf{B}

So I guess what I am asking is how does f relate to the equation of motion for the charge density? (for that matter, what is the equation of motion of a continuous charge density?)
 
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Electromagnetic force density is the density of the electromagnetic force per unit volume.
 
I just now got an email notice about the reply above. I guess the forum email program is a year off? Anyway, I'd still be interested in replies to this thread. Greg's reply doesn't really help. What happens to a continuous charge density? A reference to a source that covers the equation of motion of a continuous charge density will do.
 
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