John Popelish wrote:

If we assume the coil is an idealized lumped inductance with no stray
capacitance at all (not a real inductor) then it would have the same
instantaneous current at each end and that current would be zero, since
it has zero size. In other words it would fit entirely in the point
that holds the node.

Real inductors with stray capacitance and imperfect magnetic coupling
for all parts of its internal current path, would have a phase shift in
the current at opposite ends, so they would have current at their ends
that was 180 degrees out of phase, if they were centered on the node
points. For half of each cycle, current would be entering each end, and
for the other half of each cycle, current would be leaving each end.
Both those currents would detour out the sides f the inductor into
displacement current through the stray capacitance of the surface of the
inductor to its surroundings.

I think (with very little actual knowledge of the software) this
conceptual model is how EZNEC handles current through a modeled inductor
and how it can have different currents at the inductor ends, without
being aware of whether those currents are driven by traveling or
standing waves. It is all based on current through inductor segments
and voltage across capacitive segments. If the segments are small
enough, it is a good approximation of a distributed solution.

There are two ways of modeling an inductor in EZNEC. One is by using an
inductive "load". This is a pure lumped inductance, which takes up zero
physical space and whose currents are equal at its two terminals. It
does not couple or react at all to its surroundings other than via its
terminals, and its voltage-current characteristics are dictated by that
of a pure inductance, v = L di/dt. For a number of reasons discussed
many times here, this isn't a good model for many or most typical
loading coils.

The other way of modeling an inductor in EZNEC is by making it from
conductors -- "wires" -- arranged in a polygonal helix. (EZNEC v. 4.0
provides an automated way to generate this structure.) These wires are
treated exactly the same as all other wires in the model. As long as the
turns aren't too close together (conservatively, closer than several
wire diameters, but in practice good results are usually obtained with
spacing as close as one diameter air space between wires), it does a
very good job of calculating the inductor currents and radiation. (It's
a little generous about loss if the turns are close because it doesn't
account for proximity effect.)

EZNEC calculates the total current by first calculating the self and
mutual impedances of every segment in the model from a fundamental
equation, then using Ohm's law to find the total current in each segment
from those impedances and the voltages from the user specified
sources.(*) It's not aware of traveling or standing waves. The presence
or absence of standing waves -- that is, a changing magnitude of current
with position -- can be seen by viewing its output. Displacement current
is a consequence of mutual coupling between segments -- in a dipole, the
dominant coupling is to the other half of the dipole, and in a grounded
monopole, to ground. However, each segment couples to every other, even
on its own wire, and it's this coupling which brings about the current
distribution that ultimately occurs.

EZNEC deals only with total currents and makes no effort to detect, use,
or break up total current into individual traveling waves. It isn't
aware of whether currents are "driven by traveling or standing waves" if
for no other reason that no currents are ever "driven by" traveling or
standing waves. Voltage differences cause currents which can be
described as traveling waves. When multiple traveling waves are summed
to find a total current, the amplitude of the sinusoidal current varies
with position along the line, and this envelope is called a "standing
wave". A standing wave is simply a description of the magnitude
distribution of the total current along a wire or transmission line. It
doesn't drive or cause anything -- it's a description of an effect, not
a cause. All the fuss about standing waves is a diversion which confuses
the issue and deflects attention from the salient issues involved in
understanding the topic under discussion.

(*) This is a simplified explanation. For details, see Part I of the
NEC-2 manual.

Roy Lewallen, W7EL