What is physical meaning of the EM force density?

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SUMMARY

The discussion focuses on the physical meaning of electromagnetic (EM) force density, defined by the continuous Lorentz force equation: f = ρE + j × B. The relationship between this force density and the motion of charged particles is explored, particularly how it relates to the equation of motion for continuous charge density. The user seeks clarification on the equation of motion for continuous charge density, referencing specific sections (3.5 and 4.7) of a source document for further understanding.

PREREQUISITES
  • Understanding of the Lorentz force equation
  • Familiarity with electromagnetic theory
  • Knowledge of charge density concepts
  • Basic principles of classical mechanics
NEXT STEPS
  • Study the sections 3.5 and 4.7 of the provided source on continuous charge density
  • Research the derivation of the continuous Lorentz force equation
  • Explore the relationship between force density and motion in electromagnetism
  • Learn about Maxwell's equations and their implications for charge density
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Physicists, electrical engineers, and students studying electromagnetism who seek to deepen their understanding of force density and its implications on charged particle motion.

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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