How to Tackle the Momentum of Electromagnetic Fields Problem?

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SUMMARY

The discussion focuses on tackling the Momentum of Electromagnetic Fields problem by utilizing the current density vector J(x). Key steps include expanding J in a 3D Taylor expansion, integrating by parts to transition from the potential function phi to the electric field E, and expressing the integral of xj as a sum of symmetric and asymmetric parts. The use of dyadics is emphasized as the most effective method for these transformations.

PREREQUISITES
  • Understanding of current density vector J(x)
  • Familiarity with 3D Taylor expansion techniques
  • Knowledge of integration by parts in vector calculus
  • Proficiency in dyadic notation and operations
NEXT STEPS
  • Study the application of 3D Taylor expansions in physics problems
  • Learn about integration by parts in the context of vector fields
  • Research the use of dyadics in electromagnetic theory
  • Explore the relationship between potential functions and electric fields
USEFUL FOR

Physicists, electrical engineers, and students studying electromagnetic theory who are looking to deepen their understanding of momentum in electromagnetic fields.

golfingboy07
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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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Physics news on Phys.org
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.
 

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