Cecil Moore wrote:
Gene Fuller wrote:
The graph is complete nonsense. There is no rotation of the fields
when they undergo reflection. Any ordinary text on E&M or optics will
show you the equations and the correct sketches.

Good grief, Gene. There is a 360 degree rotation in the fields
every wavelength. The direction of rotation is associated with
the direction of travel of the wave and is displayed by EZNEC
when the current phase option is turned on. All you have to
do to see the rotation of the traveling wave is to download
http://www.w5dxp.com/rhombicT.EZ

Those simplified sketches are making you simple-minded.
Assuming you are a member of the IEEE, look up this paper:
"Rotation in electromagnetic field equations". Or Google
"Rotation and the Electromagnetic Field".

"Optics", by Hecht, is one of your ordinary texts. That is
where the material for that graph comes from. The IEEE Dictionary
says: "E and H are the electric and magnetic field vectors in
phasor notation". If that graph is nonsense to you, it is your
fault, not mine.

Hecht says "Optics", 4th edition, page 289, about standing waves:

"The composite disturbance is then:

E = Eo[sin(kx+wt) + sin(kx-wt)]

Applying the identity:

sin A + sin B = 2 sin 1/2(A+B)*cos 1/2(A-B)

yields:

E(x,t) = 2*Eo*sin(kx)*cos(wt)"

"This is the equation for a STANDING or STATIONARY WAVE, as opposed
to a traveling wave. Its profile does not move through space; it is
clearly not of the form Func(x +/- vt)."

"... 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)."

Hecht uses phasors to represent EM waves all through his book.
He explains the standing wave E-field based on the two traveling
waves, E1-field and E2-field, thusly:

"The resultant phasor is E1 + E2 = E ... Keeping the two [traveling
wave] phasors tip-to-tail and having E1 rotate counterclockwise as
E2 rotates (at the same rate) clockwise, generates E [total] as a
function of 't'."

[Standing wave phase] "doesn't rotate at all, and the resultant
wave it represents doesn't progress through space - its a standing
wave."

Traveling wave phase rotates. Standing wave phase doesn't.

Speaking of "... net transfer of energy, for the pure standing
wave there is none."

The forward wave and reflected wave E-field and H-field vectors
are represented by phasors just as indicated in the IEEE Dictionary.
One is rotating clockwise and the other is rotating counterclockwise.
The Poynting vector for a pure standing wave is equal to zero just
as illustrated in my graph at: http://www.w5dxp.com/EHSuper.JPG
Given those boundary conditions and solving for the angle between
the standing wave E-field and H-field yields 0 or 180 degrees.

Are you really more interested in presenting false information
and saving face than you are in valid technical facts?


Cecil,

This is truly sad. I thought you had finally begun to understand this
stuff, but you have regressed back into the same old nonsense. You are
still totally confusing phasors with field vectors. They are utterly,
totally, and absolutely unrelated.

Get help.

Call me what you like. Bye.

73,
Gene
W4SZ