Momentum of electromagnetic fields

In summary, the speaker is struggling with incorporating the Taylor expansion and cross product into their understanding of the current density vector, J(x). They are seeking some hints to help them get started on the problem, which involves expanding J, integrating by parts, and using dyadics to simplify the process.
  • #1
golfingboy07
17
0
I am having a little trouble with this. To attack this problem (I reckon anyway) is to recognise that the current density vector J(x) can be written it terms of the number density and the velocity. But I'm not sure how to incorporate the Taylor expansion with the cross product. If somebody could give me a few hints just to get me started again that would be great!

Cheers

GM
 

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  • #2
You have to:
1. Expand J in a 3D Taylor expansion.
2. Integrate by parts to get from phi to E.
3. Go from \int xj to m by writing xj as a sum of sym and asym parts.
This is easiest using dyadics.
 

1. What is the definition of momentum of electromagnetic fields?

The momentum of electromagnetic fields refers to the measure of the amount of motion or inertia of an electromagnetic wave. It is a vector quantity that is dependent on the electric and magnetic field strengths and their direction of propagation.

2. How is the momentum of electromagnetic fields calculated?

The momentum of electromagnetic fields can be calculated using the equation p = ε0E x B, where p is the momentum, ε0 is the permittivity of free space, E is the electric field strength, and B is the magnetic field strength.

3. What is the relationship between momentum and energy of electromagnetic fields?

Momentum and energy are related through the equation E = pc, where E is the energy, p is the momentum, and c is the speed of light. This means that as the momentum of electromagnetic fields increases, so does its energy.

4. How does the momentum of electromagnetic fields affect matter?

The momentum of electromagnetic fields can transfer to matter through the process of radiation pressure. This can result in the movement or displacement of matter, as well as the absorption or emission of energy.

5. Can the momentum of electromagnetic fields be manipulated?

Yes, the momentum of electromagnetic fields can be manipulated through the use of devices such as mirrors, lenses, and diffraction gratings. These devices can change the direction and intensity of electromagnetic waves, thus altering their momentum.

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