Conservative fields in a transverse plane of a transmission line

[maria clara]

Hello,

As far as I understand, a transmission line is simply a wave-guide for TEM modes.
If the waves are propagating in the z direction so Hz=Ez=0. How does this fact leads to the conclusion that in any transverse plane (xy plane) the fields are conservative?
Thanks a lot.

 

[gnurf]

As far as I understand, a transmission line is simply a wave-guide for TEM modes. If the waves are propagating in the z direction so Hz=Ez=0. How does this fact leads to the conclusion that in any transverse plane (xy plane) the fields are conservative?

Since there's no z-component of H (or E), the electric field (magnetic field) distribution in any given transverse plane at any given instant of time is the same as the static electric-field distribution. Question: Why is this true?

With this information at hand, go back to Faraday's Law in integral form and look at the static case (i.e. d/dt=0). Question: What does it mean that the line integral is equal to zero?

EDIT: If you stop at path-independence, I obviously made it too easy for you. To really understand your problem you should look at the http://en.wikipedia.org/wiki/Conservative_vector_field#Definition" and understand how it applies to your scenario.