Why is del(E_t) zero in TEM mode of transmission lines?

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SUMMARY

The divergence of the transverse electric field (E_t) is zero in transmission line mode due to the absence of free charge in the region between the conductors, as established in equations 7.1.37 and 7.1.38 from the MIT OpenCourseWare. While surface charge density exists on the transmission line, it does not contribute to the divergence in the space between conductors, which is considered source-free. This mathematical treatment is essential for applying boundary conditions when solving for electric fields in transmission lines.

PREREQUISITES
  • Understanding of Maxwell's equations, particularly Gauss's law.
  • Familiarity with electromagnetic field theory concepts.
  • Knowledge of boundary conditions in electromagnetic problems.
  • Experience with transmission line theory and its applications.
NEXT STEPS
  • Study the implications of Gauss's law in electromagnetic fields.
  • Explore boundary condition applications in electromagnetic field solutions.
  • Learn about surface charge density effects in transmission lines.
  • Investigate the mathematical derivation of divergence in electromagnetic theory.
USEFUL FOR

Electrical engineers, physics students, and professionals involved in electromagnetic field analysis and transmission line design will benefit from this discussion.

Adit112
I was going through MIT opencourseware https://ocw.mit.edu/courses/electri...s-spring-2009/readings/MIT6_013S09_chap07.pdf and I didnt understand exactly why in equation 7.1.37 and 7.1.38 in page 192 the divergence of transverse electric field is taken as zero ? The only reason this would be true is if the region is source free but we clearly see that this field does setup a surface charge density on the surface of the transmission line so intuitively and mathematically why would the divergence of Et be zero? I can always construct a surface in the transverse plane to include the transmission line which has charge and so the del.Et should be equal to the surface charge density isn't?
 
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The divergence of E is zero in between the conductors because there is no charge in that space. The surface charge density is only used for boundary conditions when solving for the fields.
 

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