No, I will make one more comment. After a bit of reflection, I think
this might be at the core of some people's problem in envisioning a
lumped inductor.

When a current flows into an inductor, it doesn't go round and round and
round the turns, taking its time to get to the other end. An inductor
wound with 100 feet of wire behaves nothing like a 100 foot wire. Why?
It's because when the current begins flowing, it creates a magnetic
field. This field couples to, or links with, the other turns. The
portion of the field from one turn that links with the others is the
measurable quantity called the coefficient of coupling. For a good HF
toroid, it's commonly 99% or better; solenoids are lower, and vary with
aspect ratio. The field from the input turn creates a voltage all along
the wire in the other turns which, in turn, produce an output current
(presuming there's a load to sustain current flow). Consequently, the
current at the input appears nearly instantaneously at the output. Those
who are physics oriented can have lots of fun, I'm sure, debating just
how long it takes. The field travels at near the speed of light, but the
ability of the current to change rapidly is limited by other factors.

So please flush your minds of the image of current whirling around the
coil, turn by turn, wending its way from one end to the other. It
doesn't work at all like that. The coupling of fields from turn to turn
or region to region is what brings about the property of inductance in
the first place.

Radiation is another issue, and provides a path for current, via
displacement current, to free space. (I can see it now in Weekly World
News: WORLD FILLING WITH COULOMBS! DISASTER LOOMS!) For a component to
fit the lumped element model, radiation has to be negligible. And, for
the same reason, it can't be allowed to interact with external fields as
a receiver, either.

This is very fundamental stuff. You can find a lot more about the topic
in any elementary circuit analysis or physics text. If you don't believe
what you read there, just killfile my postings -- you won't believe me,
either, and reading what I post will be a waste of time for both of us.

Real inductors, of course, are neither zero length nor do they have a
perfect coefficient of coupling. And they do radiate. The essence of
engineering is to understand the principles well enough to realize which
imperfections are important enough to affect the outcome in a particular
situation. We simplify the problem by putting aside the inconsequential
effects, but don't oversimplify by ignoring factors that are important
for the job at hand. Those who insist on using only the simplest model
for all applications will often get invalid results. And those who use
only the most complex model for all applications (as is often done in
computer circuit modeling), often lose track of what's really going on
-- they become good analysts but poor designers. I've seen people
capable of only those approaches struggle, and fail, to become competent
design engineers.

And with that, I'm outta here. Hope my postings have been helpful.

Roy Lewallen wrote:

Sigh.

I give up. It's time for me to get back to work. Have fun, folks.

Roy Lewallen, W7EL

Jim Kelley wrote:

Roy Lewallen wrote:


Gee whiz, golly, yes, representing an antenna as a two terminal black
box with zero size presents a problem. And no, you can't put a box
around anything having any length and expect the current in to equal the
current out. And why should this be surprising to anyone?



The wire comprising an inductor has length. The inductor radiates.
The inductor has two terminals with different currents at each. What
was it you said about Coulombs again?

73, Jim AC6XG