On 4 jun, 14:26, K1TTT wrote:
On Jun 4, 2:12*pm, Cecil Moore wrote:





On Jun 4, 6:35*am, K1TTT wrote:

The easiest explanation though is still the intuitive one, the
solution of the wave equation derived from maxwell's equations results
in the proportionality constant of 1/c^2 which requires the speed of
the wave to be c in the medium where it is evaluated, there is no way
to get that from the standing wave equation since it is obviously
stationary wrt space.

Thanks David, that's good news. It apparently means that the arguments
based on energy not crossing a current node boundary in a standing
wave are invalid - since that singular condition violates the boundary
conditions for Maxwell's equations. So does the "standing wave energy
standing still" argument. Not only does the photonic nature of EM
waves require them to travel at the speed of light in the medium, but
so does Maxwell's equations.

definately. *another simple condition shows this can't be correct
since current nodes correspond with voltage peaks in the standing wave
pattern, so while energy in the magnetic field is a minimum the energy
in the electric field is a maximum.



Such knowledge also has ramifications for the technique of using the
current on a standing wave antenna to try to predict the delay through
a loading coil. If a Maxwell equation analysis of such a condition
yields bogus results, how can simple current phase measurements be
trusted? If the component traveling waves associated with a loading
coil were used in order to obtain a valid Maxwell equation analysis, I
wonder what would be the predicted delay through the coil?
--
73, Cecil, w5dxp.com

this becomes MUCH harder to analyze. *the transmission line case is
easy because the equations collapse to a single linear dimension, so
you can write your simple standing wave equation with a single sin(kx)
term. *in a solenoid, especially a finite length solenoid, and double
especially because the length may be an appreciable fraction of a
wavelength, there is no such simple representation for the fields.
i'm not even sure what software would provide an adequate model of
something like that... the turns are too close for me to trust nec
based programs with out lots more research, and i'm pretty sure finite
element programs like ansoft/maxwell would not be able to handle the
change in current due to length and radiation. *measurement of the
currents in coils like that would also be hard because of the radiated
fields and the shielding needed to prevent measurement errors from
probe lengths in the field... i would only trust fiber optic sensed
probes that were small and self contained, at least that way you would
not be distorting the field with probes or trying to cancel out pickup
from probe cables coupling to the antenna.- Ocultar texto de la cita -

- Mostrar texto de la cita -

Hello and good day all:

I believe perhaps I am not translating/understanding well your posts,
Cecil and David, I post some comments to your consideration.

As I learnt, basic electromagnetic energy propagation Maxwell
equations are satisfied by a traveling wave moving in one direction.
Also I learnt standing waves in a TL results of two of them traveling
in opposite directions (as I understand this is not a questioned point
in this newsgroup), but SW equation it is not a Maxwell eq. solution
but a mathematical result of interference among them. For that reason
directly replacing this one in electroamagnetic energy propagation
Maxwell diff. eqs to satisfy it, do not work, because SW do not travel
anywhere!.
Energy not flowing beyond nodes it is a true, but only for ending
nodes!
Could this be what confuses those who think energy do not cross
INTERNAL TL nodes?

Electromagnetic waves are energy transport phenomenom, SWs not. We can
interpret last ones as a "result of the transport
phenomenom" (interference) = Energy is "trapped" in a resonant ideal
line, as is "trapped" in a resonant ideal cavity, as light ii is
"trapped" in a optical ideal cavity.

Do we see a simple case: If we think in a half wave resonant line we
can interpret/describe its internal state as two traveling waves
(inside system transport) or with a standing wave dynamic interchange
of energy between E and H field without radiation (not transport). In
longer line it is the same: we can describe its internal state a two
waves traveling between end boundaries (transport) or a sistem (line)
located [but not f(x)] energy interchange among magnetic and electric
field. (I said not f(x), because nodes and antinodes are "FIELDS (E
and H) nodes and antinodes", but not "ENERGY nodes or antinodes" (as
we know, where H is 0, E is maximun...)
Seems to me this does not violate any quantum or clasic laws :)

73

Miguel Ghezzi - LU6ETJ