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The Toroidal Coil: Discussion of Fields

Discussion in 'Electronic Basics' started by Timothy Golden BandTechnology.com, Apr 29, 2008.

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  1. 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
     

  2. 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
     
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