How Does Magnetic Flux Density B Relate to E and H in Electromagnetic Waves?

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SUMMARY

The discussion focuses on the relationship between magnetic flux density B and the electric field E and magnetic field H in the context of electromagnetic waves. It establishes that B follows a homogeneous wave equation, specifically expressed as ∇²B - εμ ∂B/∂t = 0, applicable in a homogeneous, linear, uncharged conductor. The participants highlight the orthogonality of E and H and seek clarification on how B is derived from these fields through auxiliary equations that connect E and H to D and B, referencing Maxwell's equations for further understanding.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with wave equations in electromagnetism
  • Knowledge of magnetic flux density (B) and electric displacement field (D)
  • Concept of orthogonality in vector fields
NEXT STEPS
  • Study the derivation of the wave equation for magnetic flux density B
  • Explore the auxiliary equations connecting E, H, D, and B
  • Investigate the implications of electromagnetic wave propagation in uncharged conductors
  • Review the mathematical treatment of Maxwell's equations in different media
USEFUL FOR

This discussion is beneficial for physics students, electrical engineers, and researchers focusing on electromagnetic theory and wave propagation in materials.

faber
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Hi,
We were told to show that the magnetic flux density B obeys a homogenous wave equation. This case applies to electromagnetic waves in a homogenous, linear, uncharged conductor.
Now I know that the wave equation for magnetic flux density is as follows.

[ tex ] \nabla^2-\epsilon\mju \frac {\deltaB} {\deltaT}=0 [ \ tex ]

However I am a little confused on what the solution of the wave equation will be for B. I have the solution for E and H and know they are both orthogonal how is B related to these?
 
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There're two auxiliary equations that relate E and H to D and B via material properties. They have it in Wikipedia http://en.wikipedia.org/wiki/Maxwell's_equations [/URL]
 
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