"Ian White GM3SEK" wrote:
That was not a "shortcut" or approximation.

It really doesn't matter if it is or it isn't. I was quoting another pretty
smart guy who seems to know the history of these models. He said
Maxwell's equations matured first, then the distributed network model
matured as a simplified subset of Maxwell's equations, then the lumped-
circuit model matured as a subset of the distributed network model.
But a chicken/egg argument is meaningless except for historical
accuracy. We are in the present looking at those models.

In that limiting case, the current at the two terminals of a pure
inductance must be the same in both magnitude and phase.

There's that catch word, "pure". Pure inductances do not exist
in the real world. They are a construct of the lumped-circuit
model and are presupposed to have the characteristice that
you mention. One cannot prove the validity of that model by
quoting the presuppositions. A 75m bugcatcher coil is NOT
a pure inductance.

By "current" we
mean the simple, straightforward movement of charge. If you count the
electrons in and out at the two terminals, there can be no difference in
either magnitude or phase because that would require electrons to be
stored or lost from somewhere - which inductance cannot do. Kirchhoff's
current law recognises the logic of this.

Standing wave current with its cos(kz)*cos(wt) equation is not constrained
by those rules since the phase of the standing wave is everywhere zero deg
for a 1/2WL thin-wire dipole.

This is how inductance always works in every type of non-radiating
circuit, both in theory and in real life.

A pure inductance cannot work that way in real life because it doesn't
exist in real life. If the forward current is in phase with the reflected
current at one end of the coil, the current will be a maximum (loop)
at that point. If the forward current is 180 degrees out of phase with
the reflected current at the other end of the coil, the current will be a
minimum (node) at that point. Please take a look at:

http://www.qsl.net/w5dxp/3freq.gif

How does one explain the current reported by EZNEC at two times
the resonant frequency?

When developing a new theory, it is normal, standard required practice
to test it for simplified, limiting cases that we already understand.
The new theory MUST work for all these test cases; it MUST connect
seamlessly with everything we already know.

The distributed network model predates my birth by decades and is not
new. It is known to work in situations where the lumped-circuit model
fails. It has never been known to fail in a situation where the lumped-
circuit model works.

At his point, some heckler pipes up: "Ah, but what about Einstein?"
Thank you, sir - the perfect example to prove my point! If Einstein's
equations of relativity are tested for the limiting case where
velocities are very low, they connect seamlessly into Newton's laws of
motion. If they hadn't, Einstein would have thrown them out and gone
back to think again.

The distributed network model is to relativity as the lumped-circuit model
is to Newtonian physics. Newtonian physics is a subset of relativity.
The lumped-circuit model is a subset of the distributed-network model.

When Cecil's theory is tested for the simple limiting case of pure
inductance, it MUST join up seamlessly with conventional circuit theory.

It's not my theory and it does indeed join up seamlessly. It is the lumped-
circuit model that does not join up seamlessly with Maxwell's equations.
How could it since it assumes faster than light speed of current flow?
The presuppositions of the lumped-circuit model even violate the
theory of relativity.

If it requires anything that "don't fit", such as a phase shift in
current through a pure inductance, or special kinds of "current" that
are different from the simple, straightforward movement of charge
(electrons), then the theory fails.

It doesn't require anything of pure inductances since pure inductances
don't exist in reality. It requires that real world inductances obey the
laws of physics.

If one doesn't understand the implications of the equation for standing
wave current, one needs to crack open that old dusty math book.
--
73, Cecil, W5DXP