The Toroidal Coil: Discussion of Fields

[Timothy Golden BandTechnology.com]

"Timothy Golden BandTechnology.com">




I'm german and i'm not a writer. I gues style has to be changed.
What I did: I took all my postings here, selected the best, put them each on
one slide. They I shuffled them around, corrected them, add something in,
wrote a lot, sorted things out.

That was roughly the method. Its quick and dirty. So it would need some
cleaning.






I didn't distroy coordinates, and that was not intended. I wanted to arrange
the tools appropropriate to QM and wick-rotate the whole thing into
relations of GR. The pivou point of this is the observer or Nil-point.
The shocking result is, that its really true and you CAN describe our world
by dimensionless numbers.

Thomas Heger

Yeah, but how many numbers? By the time we get to three dimensionless
numbers then we have regenerated dimension. This fits our ordinary
sense of geometry. Then along come the tensor or quaternion and
reencapsulate those dimensions with some satisfaction, but only part
way. Still, OK, we can view the system from those forms as more
integrated and if there are some beneficial side effects in one
particular representation then we can claim one form to be superior
and maybe even claim it to be the native form. If we focus on time as
unidirectional should we anticipate its representation within one of
these formats? It happens that the polysign progression contains a
unidirectional and zero dimensional entity that matches time, that
being P1; the one-signed numbers:
http://bandtechnology.com/PolySigned/OneSigned.html
but that is tangential to any discussion of fields.

Getting back to fields to what degree are we really only discussing a
mathematical entity? The strictly mathematical field behaviors(eg real
numbers, complex numbers) are not at all what we mean though the
physical field's behaviors are mathematically pure.

That brings me to the puzzle of the self shielding toroidal coil. How
is it that the external magnetic field is negligible? Doesn't this
behavior contradict standard electromagnetics? In effect we are
sucking all of the flux into the core when traditionally half of it
had to pass along the outside of each wire. I have yet to see any
treatment that takes this discrepancy head-on. I would appreciate a
link that considers this puzzle directly. I suppose that this puzzle
has been around with ordinary transformers as well, it's just that
visualizing all of that flux whirring around in the toroid is far
prettier.

If the flux did travel through air for even a portion of its trip then
the remarkable permeabilities of any core xformer would be corrupted.
If that flux that would have travelled through air went into the core
then it would cancel out any induced magnetic field. The
interpretation can no longer be of a loop of flux traveling about the
conducting wire. I don't see any way around this and it goes against
traditional EM interpretation. Trying to visualize a double ended
strand of flux feels alright, but nobody uses this as a model do they?

Am I missing something?
Are we all a bunch of morons?

- Tim

 

[Timothy Golden BandTechnology.com]

The idea is that the magnetic field produced (strictly) by the current flowing
in the conductors that completely enclose the toroid produce zero external
field. Certainly in the real world there are wires running up to that toroid
and those wires will contain a field around them. This is probably not
specifically mentioned in the text because (1) it detracts from the problem at
hand (determining the fields inside and outside of the toroid), (2) actually
computing the fields at the junction between, say, some twisted pair of wires
that then diverge and encircle the toroid is a highly non-trivial problem that
probably can't be solved analytically (look up the papers on calculating the
fields in something as "simple" as a step change in the width of a microstrip
transmission line and you'll get a field for what you're up against), (3) the
field from the wires leading up to the toroid will generally be quite small in
comparison to those inside of it and hence can be neglected, and (4) some
authors probably figure this would all be self-evident.

(Note that authors usually do explicitly mention "feed" concerns when they're
dealing with devices intended to create significant external fields, such as
antennas. Pretty much every discussion of dipole antennas, for instance,
contains at least a little bit about how you need to be careful in arranging
the feed...)


The other thing is that, by design, transformers are controlling where almost
all of the flux goes (the bit that "gets away" is leakage, and there's plenty
of discussion on designing transformers to minimize it), whereas with "random
wiring" there's no such control and it's difficult to make accurate
predictions. There are common middle grounds, though, such as microstrip
lines and twisted-pair wiring where -- while the field does extend off to
infinity -- you can still draw reasonably accurate pictures of what's going on
in regions close to the conductors.


Um, no, it just creates leakage inductance, which primarily serves to limit
frequency response and decrease the transformer's efficiency.


Not in the general case... fields are vector quantities, so unless you can get
the magnitudes and directions to line up exactly the right way (like a
reversed secondary coil on a transformer does), the fields don't cancel.

---Joel

Thanks Joel for the detailed response. But I don't feel that my
concern has been sufficiently quashed. Still, I really like the
details that you've gone into. Magnetism does seem to get complicated
quickly when real world materials are used.

But lets just focus on a current carrying wire and the circular loop
of flux that supposedly exists around that wire. Vector, yes, but also
with this loop concept supposedly unbreakable. Now when we bring a
little dl of wire up against a toroidal core we should still see half
of its magnetic loop passing through the air. This has nothing to do
with effects of the leads. If we allow all of the flux to enter the
core then we have broken the basic model of the wire and loop of
flux.

Is there actually leakage around a toroidal coil neglecting the leads?
We see a beautiful clean inner circular path and tend to visualize all
of the flux travelling that inner path, but it had to get there from
the wire so for every line of flux inside doesn't there have to be as
much travelling outside?

Another way of getting to a theoretical conflict is to consider that
when a gap is introduced into a core (which I've read is done to keep
a flat frequency response for low frequency inductors) then that gap
becomes the controlling factor. Don't we really see an air gap for
every line of flux when we come back to studying a differential piece
of the winding? Even for the non-gapped toroidal core I do see that
this is true. Worst of all half of the flux path is through air so we
observe this conflict unless the winding is completely immersed as
with a 'pot' core.

How can we be comfortable with the closed flux path in the toroid? It
goes against theory more than it goes against the toroidal coil. I
must be oversimplifying something. To stay with theory it should
probably be that the flux within the core itself is induced flux and
so those lines of flux should not be confused with the lines of flux
of the wire. This then sets up an extremely high impedance to the
wire's own flux which I guess causes the radius of that flux to be
extremely small. So then we would admit that there is leakage but that
it is small. Is this a clean analysis? I think if it is then alot of
sources may be oversimplifying.

Even the air core coil is inducing those lines of flux of its solenoid
form. It may be that even the loops of flux around the differential
piece of current carrying wire are merely induced. Could this
reasoning take us all the way down to the electron? Perhaps.

- Tim