It sure looks like the electric and magnetic fields, which are in-phase in your traveling wave, do periodically go to zero as they reverse direction.
I've lost count of the straw men that you have attempted to set up for torture.
I was not talking about instantaneous values of E and H. I was talking about the ExH Poynting vector for plane waves which has a constant term indicating that the wave carries an average power.
Bull. You never said anything about averages. You keep trying to get yourself out of this mess of your own creation.
You said, "For real world EM waves, the electric and/or magnetic energy cannot fall to zero while the wave exists."
I'm not going to work out another example because 1) I don't want to take the time to do it, 2) I don't think you'll understand it anyway, and 3) you'll just come up with another lame excuse.
So I'll again refer to the document I found today when I was looking for a picture of a traveling wave, http://www.people.fas.harvard.edu/~djmorin/waves/electromagnetic.pdf
Page 15, equation 52.
The energy density of a plane wave in free space isE
(kz - wt)
and the Poynting vector isS
= c eps0
(kz - wt)k
There is no constant term. For a traveling wave in free space, the energy density E
and energy flux S
do go to zero whenever E
are zero. The energy travels in bunches.
You're wrong, again.
So let me upgrade my sentence:
"For real world EM waves, the average ExH value cannot fall to zero while the wave exists."
That's a statement entirely of your own making, based on your distinction between "real-world EM waves" (whatever that means) and something else.
Question: What is the value of the Poynting vector for a pure standing wave?
This one I did work out for you (post #30). The energy density is
U = 0.5 eps0
(wt) + cos2
and the Poynting vector isS
/ w mu0
) sin(kx) cos(kx) sin(wt) cos(wt)
/ 4 Z0
) sin(2kx) sin(2wt).
The behavior of the lowest mode, where the cavity walls are 1/2 wavelength apart, is the easiest to picture. During one cycle of the field (0 < wt < 2 pi), the energy density (given by the function U) starts at the walls (none in the middle), then flows to the middle (none at the walls), then back to the walls, two times. The energy oscillates twice as fast (frequency 2w) as the fields themselves.
The Poynting vector S
describes the flow of the energy. It vanishes at the times of maximum energy density (all at the walls or all in the middle) since there is momentarily no flow at these peak times (like waves coming onto a beach, stopping, and then retreating). The energy flux reaches its peak values at the times between the energy peaks, as the energy moves back and forth. S
is a vector quantity so its sign indicates its direction, positive means right, negative means left. S
is positive between the left wall and the center as the energy there flows to the right, from the wall to the center, and, at the same time, negative between the right wall and the center as the energy there flows to the left, from that wall to the center. A quarter of a cycle later the sign of S
reverses, as the energy flows back out to the walls.
As I also said before, the average value of S
is zero and there is no net
energy flow. That does not mean S
is always zero.
Section 8.4.3 of the same document, also starting on page 15, describes the energy in standing waves, and gives essentially the same expressions that I derived. You can see that he switches freely between the two representations of a standing wave, namely as a single expression or as two opposing traveling waves (also in 8.3.3 where he deals with E
). As I have always said, there is no physical or mathematical difference between the two viewpoints. Note the last paragraph of that section, at the top of page 16, where he says the energy flow in a standing wave is only zero on average, not identically zero.
Strange that this fellow also fails to mention "real-world EM waves." He just merrily switches back and forth between the two representations. Poor devil, he just doesn't realize the error of his ways.
BTW, you never thanked me for setting you straight about your phasors in my last post, when I was responding to your statement"Please note that, unlike the standing wave current phasor, the magnitude of the traveling wave current phasor is constant and never zero. For real world EM waves, the electric and/or magnetic energy cannot fall to zero while the wave exists."
I clearly showed that the fields (and energy) do go to zero, and your assumption that a constant-magnitude phasor somehow prevented this was completely wrong. You're welcome. I'm sure the fact that you failed to mention this was just an oversight.
This is absolutely my last post on this thread. You can follow this with any crazy ideas about "real-world EM waves" or anything else that you like. I will never respond to another of your posts. To the other readers of this forum I will only say buyer beware.