Poynting Vector in Standing Waves
 

I typically do not like to "Xerox" material to support my arguments, but
I will make an exception in this case.

Very recently RRAA's very own "John Smith" included the following
comment in a message.

"I think Cecil has done an excellent job, if you have followed him (and,
I cannot claim I have COMPLETELY done so), however, he has shown there
ARE holes in what we 'believe.' And, some things don't quite 'mate-up'
and what we have taken for granted looks differently when under the
'microscope.' 'Standing Waves' is but the shining example."

Considering the source of that comment, I am not surprised. But for any
others who might have been hoodwinked by the nonsense, I will try to add
a bit of color. As some may recall BG, there has been a bit of an
ongoing discussion about the nature of energy flow, or lack thereof, in
standing waves.

In order to support his point about using phasors interchangeably with
field vectors, Cecil copied and posted a figure on his website under the
page name of "EHWave.jpg". This figure was referenced as an extract from
a book by Haznadar and Stih entitled "Electronic Fields, Waves, and
Numerical Methods."

The figure itself completely misses the point, since it is simply a
representation of an ordinary circularly polarized wave. The topic of
polarization is not particularly relevant here. It merely complicates
the arithmetic, and it adds nothing to the science of Poynting vectors
or standing waves. It is, however, interesting to note that the figure
caption in the original source is given quite clearly. On page 241, the
page containing Cecil's copied jpeg, it says,

"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.

I must give great credit to Cecil's hidden research team for finding
this reference. It seems quite obscure. However, Cecil's groupies appear
to have neglected to turn a few pages to arrive at page 244. On this
page there is a discussion of the Poynting vector for standing waves. An
exact quote, or at least as close as possible in ASCII, is,

***********

"In a real domain, the instantaneous value of Poynting's vector for a
pure standing wave is, according to (8.3.26a,b),

NRe = (ax ExRe x ay HyRe) = -az 1/4 (Eo^2)/Z' sin^2 (2 pi
z/lambda) sin (2wt) (8.3.28b)

Using this expression, we see that the time-averaged value of Poynting's
vector in a real domain is equal to zero since the time-averaged value
of the function sin (2wt) is always equal to zero."

***********


The equation is slightly cleaner when the "Re" subscripts are removed.

N = (ax Ex X ay Hy) = -az 1/4 (Eo^2)/Z' sin^2 (2 pi z/lambda)
sin (2wt) (8.3.28b)

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. This is of course exactly what I and
some others have been saying. This is exactly what the traditional
science says. The colloquial expression is that the energy sloshes back
and forth.

This equation is easily derived from the standard representation of a
standing wave, but it is *so* much more authoritative when Xeroxed from
Cecil's own reference book.

The iconoclasts never give up. The 200 mpg carburetor lives on.

73,
Gene
W4SZ

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

Poynting Vector in Standing Waves
 

On Mon, 21 Jan 2008 15:11:09 GMT, Gene Fuller
wrote:

it is *so* much more authoritative when Xeroxed from
Cecil's own reference book.

Indeed, Gene,

Simply drilling into Cecil's corrupted Xerography always finds the
decay of his logic.

73's
Richard Clark, KB7QHC

Poynting Vector in Standing Waves
 

Richard Clark wrote:
Simply drilling into Cecil's corrupted Xerography always finds the
decay of his logic.

Richard, I admit that I am not perfect nor omniscient.
Will you admit that about yourself?
--
73, Cecil http://www.w5dxp.com

Poynting Vector in Standing Waves
 

Gene Fuller wrote:

...
The iconoclasts never give up. The 200 mpg carburetor lives on.

73,
Gene
W4SZ


Actually, you are quite correct ...

As a boy, I had a moped, it did get mighty close to 200mpg. Depending
on how you "drove" it (peddled it?), it could be pushed to better
performance than that!

Absolute proof the 200 mpg carburetor does exist! ROFLOL

Regards,
JS

Poynting Vector in Standing Waves
 

On Mon, 21 Jan 2008 18:12:00 -0600, Cecil Moore
wrote:

Richard Clark wrote:
Simply drilling into Cecil's corrupted Xerography always finds the
decay of his logic.

Richard, I admit that I am not perfect nor omniscient.
Will you admit that about yourself?

Hmm, I've been called a gay-wad, liar, a sailor, stupid, a cheat, a
vile lover of Shakespeare by any number of correspondents here
(including you) - your fawning need for sentimental admissions that
celebrities love to gush would be a pale shade of mauve in comparison.

Feel free to spit on me again at your convenience. ;-)

Wearing my Nor'wester in this wet climate since 1995,

73's
Richard Clark, KB7QHC

Poynting Vector in Standing Waves
 

Richard Clark wrote:
Hmm, I've been called a gay-wad, liar, a sailor, stupid, a cheat, a
vile lover of Shakespeare by any number of correspondents here
(including you)

Sorry, that's a false statement. I have never called you a
gay-wad, a sailor, or a vile lover of Shakespeare. :-)

- your fawning need for sentimental admissions that celebrities
love to gush would be a pale shade of mauve in comparison.

So the answer to my question is "no", you are unwilling
to admit that you are not perfect nor omniscient. :-)
--
73, Cecil http://www.w5dxp.com

Poynting Vector in Standing Waves
 

Gene Fuller wrote:
In order to support his point about using phasors interchangeably with
field vectors, Cecil copied and posted a figure on his website under the
page name of "EHWave.jpg".

For the record, I have not used field vectors at all
during this discussion. Everything I have ever posted
have used phasors. From the IEEE Dictionary, "E and H
are the electric and magnetic field vectors in phasor
notation". That is what I have been doing all along.

From "Optics" by Hecht: "Therefore, its instantaneous
value [for the Poynting vector] would be an impractical
quantity to measure directly. This suggests that we
employ an averaging procedure." Virtually every time
I have used the term, "Poynting vector", I have been
talking about the average value, not the instantaneous
value.

EHWave.JPG is a good representation of an EM traveling
wave in phasor notation. If we project the fields onto
the real axis, we obtain the conventional representation.
--
73, Cecil http://www.w5dxp.com

Poynting Vector in Standing Waves
 

Cecil Moore wrote:
Gene Fuller wrote:
In order to support his point about using phasors interchangeably with
field vectors, Cecil copied and posted a figure on his website under
the page name of "EHWave.jpg".

For the record, I have not used field vectors at all
during this discussion. Everything I have ever posted
have used phasors. From the IEEE Dictionary, "E and H
are the electric and magnetic field vectors in phasor
notation". That is what I have been doing all along.

The "notation" is not the most important part. "Phasor notation" is
simply a means expressing the phase in terms of complex numbers. The
vector *direction* is all-important. That is the essential "vector" part
of the Poynting analysis. The vector *direction* is not addressed at all
by the phase or by phasor notation. Depending on the exact notation, the
vector "magnitude" may be described by phasor notation. If one is going
to correctly perform Poynting analysis, it is necessary to consider
field vectors. There is no alternative.


From "Optics" by Hecht: "Therefore, its instantaneous
value [for the Poynting vector] would be an impractical
quantity to measure directly. This suggests that we
employ an averaging procedure." Virtually every time
I have used the term, "Poynting vector", I have been
talking about the average value, not the instantaneous
value.

Most of this discussion has been based upon a disagreement between your
insistence that the instantaneous Poynting vector for a standing wave is
always zero at all times and places, compared to my insistence that it
is not zero at all times and places. I have no disagreement with Hecht.


EHWave.JPG is a good representation of an EM traveling
wave in phasor notation. If we project the fields onto
the real axis, we obtain the conventional representation.

The representation in EHWave.jpg is already shown in real axes. There is
no projection needed. The whole point of that figure is to show a
circularly polarized wave. The vector direction does indeed rotate
around the propagation axis exactly as shown. The observed rotation
angles around the propagation axis have nothing to do with phasors; they
are real physical angles of the E-field and H-field.

73,
Gene
W4SZ

Poynting Vector in Standing Waves
 

Gene Fuller wrote:
Cecil Moore wrote:
For the record, I have not used field vectors at all
during this discussion. Everything I have ever posted
have used phasors. From the IEEE Dictionary, "E and H
are the electric and magnetic field vectors in phasor
notation". That is what I have been doing all along.

The "notation" is not the most important part. "Phasor notation" is
simply a means expressing the phase in terms of complex numbers. The
vector *direction* is all-important. That is the essential "vector" part
of the Poynting analysis. The vector *direction* is not addressed at all
by the phase or by phasor notation. Depending on the exact notation, the
vector "magnitude" may be described by phasor notation. If one is going
to correctly perform Poynting analysis, it is necessary to consider
field vectors. There is no alternative.

You apparently did not bother to read the IEEE Dictionary
definition above. Please do it and while you are at it,
would you please explain what the "complex conjugate"
means when one is not dealing with phasors? Exactly what
is the complex conjugate of a vector in free x,y,z space?
For instance, what is the complex conjugate of a vector
running from 0,0,0 to 1,2,3?

From "Optics" by Hecht: "Therefore, its instantaneous
value [for the Poynting vector] would be an impractical
quantity to measure directly. This suggests that we
employ an averaging procedure." Virtually every time
I have used the term, "Poynting vector", I have been
talking about the average value, not the instantaneous
value.

Most of this discussion has been based upon a disagreement between your
insistence that the instantaneous Poynting vector for a standing wave is
always zero at all times and places, compared to my insistence that it
is not zero at all times and places.

Either I misspoke or else you misunderstood. Phasor
magnitudes are usually RMS values, i.e. average
values.

If I ever said anything about the instantaneous Poynting
vector, it was a mistake. Every time I said "Poynting
vector", I was referring to the average Poynting vector.
I tend to agree with Hecht - the instantaneous Poynting
vector is impractical to work with.

I always deal with phasors and averages. When I realized
that Keith was talking about instantaneous values, I
backed out of the discussion. I do not agree or disagree
with anyone about instantaneous values. I just think they
are of very limited usefulness in this discussion. It is
the average values that are important here.

So I repeat: The average energy flow in a standing wave
is zero so the average Poynting vector for a standing
wave is zero. That was the only point I was trying to make.
V*I*cos(A) are RMS phasors.
--
73, Cecil http://www.w5dxp.com

Poynting Vector in Standing Waves
 

Cecil Moore wrote:
Gene Fuller wrote:
Cecil Moore wrote:
For the record, I have not used field vectors at all
during this discussion. Everything I have ever posted
have used phasors. From the IEEE Dictionary, "E and H
are the electric and magnetic field vectors in phasor
notation". That is what I have been doing all along.

The "notation" is not the most important part. "Phasor notation" is
simply a means expressing the phase in terms of complex numbers. The
vector *direction* is all-important. That is the essential "vector"
part of the Poynting analysis. The vector *direction* is not addressed
at all by the phase or by phasor notation. Depending on the exact
notation, the vector "magnitude" may be described by phasor notation.
If one is going to correctly perform Poynting analysis, it is
necessary to consider field vectors. There is no alternative.

You apparently did not bother to read the IEEE Dictionary
definition above. Please do it and while you are at it,
would you please explain what the "complex conjugate"
means when one is not dealing with phasors? Exactly what
is the complex conjugate of a vector in free x,y,z space?
For instance, what is the complex conjugate of a vector
running from 0,0,0 to 1,2,3?


A suggestion. Read the IEEE Dictionary definition of "phasor" and report
back to us if you think it is used to specify a direction in real space
rather than phase space in the complex plane.

Yes, the complex conjugate adjusts the phase portion of the wave
description. However, it does not impact the real-space vector direction.

73,
Gene
W4SZ

Poynting Vector in Standing Waves
 

Gene Fuller wrote:
A suggestion. Read the IEEE Dictionary definition of "phasor" and report
back to us if you think it is used to specify a direction in real space
rather than phase space in the complex plane.

I know the difference between phasors and vectors, Gene.
Most of my textbooks represent the E and H fields as
phasors, rather than vectors, by applying some logical
boundary conditions to the vectors. The IEEE Dictionary
says the E and H fields are represented as phasors.
You seem to stand completely alone in your insistence
that E and H fields cannot be represented as phasors.
Would you mind providing one iota of proof for that
assertion?

Yes, the complex conjugate adjusts the phase portion of the wave
description. However, it does not impact the real-space vector direction.

Contrary to *all* of my references, you said the Poynting
vector equals E x H* which apparently implies phasors rather
than vectors. Would you care to explain your H* notation
as it applies to real-space vectors? This is my question
which you didn't answer - asked in different words.

Exactly what is the complex conjugate of the vector that
extends from 0,0,0 to 1,2,3?
--
73, Cecil http://www.w5dxp.com

Poynting Vector in Standing Waves
 

Cecil Moore wrote:


I know the difference between phasors and vectors


So, is that the reason you created a web page showing 0 and 180 degree
phase shifts resulting from the reflection leading to standing waves and
then tried to use the resulting entities to calculate the Poynting
vector? An instantaneous Poynting vector, no less. (Now denied of course.)


8-)

73,
Gene
W4SZ

Poynting Vector in Standing Waves
 

Gene Fuller wrote:
Cecil Moore wrote:
I know the difference between phasors and vectors

So, is that the reason you created a web page showing 0 and 180 degree
phase shifts resulting from the reflection leading to standing waves and
then tried to use the resulting entities to calculate the Poynting
vector?

I'll get back to you on that one when I figure it out.
--
73, Cecil http://www.w5dxp.com