What is physical meaning of the EM force density?

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Discussion Overview

The discussion revolves around the physical meaning of electromagnetic (EM) force density, particularly in relation to the continuous version of the Lorentz force and its implications for the motion of continuous charge densities. Participants explore the connection between force density and the equations of motion for charged particles and charge distributions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how the continuous version of the Lorentz force relates to the equation of motion for charge density, seeking clarification on the meaning of force density.
  • Another participant defines electromagnetic force density as the density of the electromagnetic force per unit volume, but does not elaborate further.
  • A participant expresses dissatisfaction with the previous reply, indicating a need for more information on the behavior of continuous charge densities and requests references for further reading.
  • Several participants share links to external resources that may provide additional context or information regarding the equations of motion for continuous charge densities.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the implications of electromagnetic force density for continuous charge densities, and multiple viewpoints regarding the need for further clarification and resources remain evident.

Contextual Notes

The discussion highlights a lack of clarity regarding the relationship between force density and the motion of continuous charge distributions, with participants expressing varying levels of understanding and seeking additional references.

pellman
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The continuous version of the Lorentz force is

[tex]\mathbf{f}=\rho\mathbf{E}+\mathbf{j}\times\mathbf{B}[/tex]

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

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

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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