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