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Old January 21st 08, 04:14 PM posted to rec.radio.amateur.antenna
Cecil Moore[_2_] Cecil Moore[_2_] is offline
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First recorded activity by RadioBanter: Mar 2007
Posts: 3,521
Default Poynting Vector in Standing Waves

Gene Fuller wrote:
"Figure 8.3.2 Propagation of a circularly polarized pure direct (in the
+z direction) travelling wave with phase velocity vf = c."

Whether Cecil did not see this caption, did not understand it, or was
again trying to pull a fast one remains unknown. It matters not in any
case.


If I was trying to pull a fast one, I wouldn't have
posted the reference along with the graphic.

The phasors associated with a traveling wave rotate in
opposite directions for forward and reflected traveling
waves, i.e. in their exponential notations, they are
indeed polarized. If the forward and reflected waves
didn't rotate in opposite directions, the standing
waves wouldn't stand. That graph is a reasonable graph
of a uniform plane wave in exponential notation.

My graph of the superposition of forward wave phasors
and reflected wave phasors still stands at:

http://www.w5dxp.com/EHSuper.JPG

The Re part of those phasors (the fields) are 180 degrees
out of phase.

Quoting "Optics" by Hecht, concerning a traveling wave:
"... a phasor rotating counterclockwise at a rate omega
is equivalent to a wave traveling to the left (decreasing x),
and similarly, one rotating clockwise corresponds to a wave
traveling to the right (increasing x)."

The graphic I posted is a reasonable representation of
a traveling wave illustrated in exponential form. The
fields of a circularly polarized waves are virtually
identical to the phasors of a uniform plane traveling
wave. You can observe the rotation of a traveling wave
by downloading http://www.w5dxp.com/rhombicT.EZ and
turning on the current phase option.

What is immediately observed is that the Poynting vector for an ordinary
standing wave is zero only for specific locations or for specific times.
At other locations and times the Poynting vector is non-zero. Only the
time or space *average* is zero.


Which is exactly what I have been saying. The instantaneous
Poynting vector is of limited usefulness. The time-averaged
Poynting vector is the one that is useful and the one I have
been talking about, as I stated a couple of times previously.
Every time I have used the words, "Poynting vector", I have
been referring to the average Poynting vector. As you know,
I have been using the word "net" as in, "there is no net energy
flow in a standing wave".

We both agree that in a traveling wave the voltage and
current are in phase for forward waves and 180 degrees
out of phase for reflected waves. The E-field and H-field
are 90 degrees apart in both traveling wave cases. A
traveling wave is an example of a uniform plane wave.

The technical fact that the voltage and current in a pure
standing wave are 90 degrees out of phase proves that the
standing wave is NOT a uniform plane wave. In fact, in an
earlier posting, a standing wave failed all 7 properties
of a uniform plane wave.

V*I*cos(A) = average Poynting vector = 0 for a standing wave.
--
73, Cecil http://www.w5dxp.com