Cecil Moore wrote:
Gene Fuller wrote:
quoting Born & Wolf:
"However, when the definition has been applied cautiously, in
particular for averages of small but finite regions of space or time,
no contradictions with experiments have been found. We shall therefore
accept the above definition in terms of the Poynting vector of the
density of the energy flow."

There's the meat of the quote as far as transmission lines
are concerned. Given that transmission lines are "small but
finite regions of space or time", and since there are only
two possible directions in a transmission line, Born and
Wolf seem to give us permission to do exactly what you
are complaining about. Your concerns about light waves
in three dimensional free space just don't exist for the
primarily single dimensional "space" in a transmission line.
Ideally, the power density exists only between the inner and
outer conductors of the coax.

It does not make any sense to simply add and subtract Poynting vectors
in elementary fashion and expect to get correct results.

Born & Wolf's own words in the quote above provided by you
contradict that assertion.


Cecil,

You conveniently chopped out the part of the B&W quote that matters. You
continue to claim that energy associated with each of the myriad of wave
components that exist at the point of interest must be reconciled. The
correct application of the Poynting theorem, as noted in the full B&W
quote, says that your requirement is not correct. Only the net energy
flow into that small integration volume has any physical reality.

Unless there is a source or sink at the point of interest, the net
energy flow will be exactly zero. Further analysis is futile.
Conservation of energy, specifically the Poynting theorem, does not
support you or anyone else who tries to atomize the waves in an attempt
to balance energy contribution from individual wave components. You are
on your own.

By the way, a very similar statement about the application of Poynting
vectors appears in Classical Electrodynamics by Jackson. This is not
some strange interpretation by a single author.

73,
Gene
W4SZ