# What is physical meaning of the EM force density?

1. Apr 25, 2012

### pellman

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?)