What is physical meaning of the EM force density?

In summary, the continuous version of the Lorentz force, represented by the equation \mathbf{f}=\rho\mathbf{E}+\mathbf{j}\times\mathbf{B}, is the density of the electromagnetic force per unit volume. This is related to the equation of motion of a charged particle, which can be described by the discrete version F=q\mathbf{E}+q\frac{d \mathbf{x}}{dt}\times\mathbf{B}. The equation of motion for a continuous charge density can be found in Sections 3.5 and 4.7 of the source provided.
  • #1
pellman
684
5
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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  • #2
Electromagnetic force density is the density of the electromagnetic force per unit volume.
 
  • #3
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.
 

Related to What is physical meaning of the EM force density?

1. What is the definition of EM force density?

The EM force density, also known as the electromagnetic force density, is a measure of the amount of force exerted per unit volume by electric and magnetic fields on charged particles. It is a vector quantity, meaning it has both magnitude and direction, and is typically denoted by the symbol Fem.

2. How is EM force density related to electric and magnetic fields?

EM force density is directly related to the electric and magnetic fields in a given region. The force density is given by the cross product of the electric and magnetic field vectors, as shown in the equation Fem = E x B. This means that the direction of the force density is perpendicular to both the electric and magnetic fields.

3. What is the physical meaning of EM force density?

The physical meaning of EM force density is that it represents the amount of force per unit volume that is exerted on charged particles by the electric and magnetic fields. This can help us understand the forces acting on charged particles in a given region, and can be used to calculate the motion of these particles.

4. How is EM force density used in practical applications?

EM force density is used in many practical applications, including in the design of electrical circuits and devices, electromagnetic motors, and in the study of plasma physics. It is also an important concept in understanding the behavior of particles in particle accelerators and in the field of high energy physics.

5. Can EM force density be negative?

Yes, EM force density can be negative. This occurs when the electric and magnetic fields are in opposite directions, resulting in a negative cross product. In this case, the force density points in the opposite direction of the electric and magnetic fields, indicating a net force acting in the opposite direction on charged particles in that region.

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