Limitations of Using E to Find B in TEM Waves

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SUMMARY

The discussion focuses on the limitations of using the equation \(\vec H(\vec r, t) = \frac{1}{v} \nabla \times \vec E(\vec r, t)\) for finding the magnetic field \(\vec H\) from the electric field \(\vec E\) in Transverse Electromagnetic (TEM) waves. Key limitations include the requirement for a charge-free medium and the necessity for \(\vec E\) to represent a time-harmonic wave, specifically a sine wave of frequency \(\omega\). Additionally, the applicability of this formula varies in different media, such as lossless, lossy, or practical good conductors. The discussion also clarifies that while TEM waves have perpendicular electric and magnetic fields, they do not inherently define plane waves.

PREREQUISITES
  • Understanding of Maxwell's equations
  • Familiarity with electromagnetic wave propagation
  • Knowledge of time-harmonic wave concepts
  • Basic principles of wave polarization
NEXT STEPS
  • Study the implications of charge-free media on electromagnetic wave behavior
  • Research the characteristics of time-harmonic waves in different media
  • Explore the differences between lossless and lossy media in wave propagation
  • Investigate the relationship between TEM waves and plane waves
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Electromagnetic theorists, electrical engineers, and physics students interested in the behavior of TEM waves and their applications in various media.

yungman
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I have questions:
1) What is the limitation of using:

\vec H ( \vec r, t) =\frac 1 v \nabla \times \vec E(\vec r, t)\;\hbox { where }\; v= \frac 1 {\mu \epsilon}

I know for this formula to work, the medium has to be charge free. I want to know in what other cases I cannot use E to find B. I think the E has to be time harmonic wave which mean it is a sine wave of certain frequency \omega. Any other limitation?2) What is the limitation of using the formula in finding H of TEM wave in a medium ( lossless, lossy or practical good conductor )?

3) TEM wave only say E and B are perpendicular to each other and both perpendicular to direction of travel. Is plane wave part of the TEM wave?

Thanks

Alan
 
Last edited:
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I totally updated my original question in the first post.
 

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