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A time variant current through a coil wound around a toroid core will produce a time variant magnetic field within the volume of the toroid, but no field external to that volume. Since a time variant magnetic field propagating in space must be accompanied by a time variant electric field to propagate, there can be no resultant time variant electric field external to the toroid volume either.

Now, make a toroidal transformer by threading a loop of wire through the "donut hole" in the toroid and you will find that an EMF is generated in this secondary loop. If there is no electric or magnetic field in the location of the electrons in the secondary loop, what causes them to move? Distances are too great for the Nuclear strong or weak forces to be in effect and gravitation is too weak; so if there is no electric or magnetic field - what else is there to physically explain the production of the EMF in the secondary loop?

And yes, I understand the mathematics of a time variant field contained within the area bound by the secondary loop - but that is not the issue here - is it!

If a physical field is the mechanism by which a particle at one location (electron in the primary wire) changes the behavior of a second particle at another distant location (electron in the secondary wire), and if there is no field, what is causing the effect? How does the electron "know" it should do anything? What accounts for the motion produced? What caries the information to the secondary wire electrons regarding the movement of the primary wire electrons?

Are we to see physical fields as being merely mathematical constructs with no physical reality behind them? Is there no intuitively understandable physical explanation and reality to "action at a distance"?

To clarify the questions being asked:

1) Is an electromagnetic field a real physical entity or just a mathematical construct - a mere map of action potential vs position without any explanation of cause?

2) Is it not paradoxical to state that an EM field is the means by which one charged particle influences another and to then also state that field theory does not require that the field actually exist at the location of the second particle - ie. no local cause. (Example : the electrons in the secondary wire that are being influenced by the electrons in the primary wire of a toroidal coil? EM theory only requires that there be a changing magnetic field somewhere within the area bounded by the secondary loop, not at the actual location of the secondary loop.)

3) Does modern physics and field theory in particular require the abandonment of local causation?

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closed as unclear what you're asking by CuriousOne, Gert, ACuriousMind, user36790, John Rennie Jan 6 '16 at 6:35

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    $\begingroup$ Why would there be no electric field around a toroid???? $\endgroup$ – CuriousOne Jan 6 '16 at 1:08
  • $\begingroup$ @curious because it's not exactly obvious, how a completely contained magnetic field can influence anything outside the torus. $\endgroup$ – LLlAMnYP Jan 7 '16 at 1:03
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    $\begingroup$ @LLlAMnYP: The field isn't completely contained. You are welcome to take a voltmeter and a wire and do your own measurements. The complete containment is a fictional explanation which, it seems, leads to the wrong conclusions if taken literally. I do acknowledge that the topology of the toroid is non-obvious, but if a measurement says one thing and a hand-waving explanation says another, then the hand-waving explanation is simply wrong. Maxwell's laws do, of course, predict the correct thing. $\endgroup$ – CuriousOne Jan 7 '16 at 3:36
  • $\begingroup$ @CuriousOne Surely you wouldn't claim, that the current/electric field in the secondary is driven by the mere leakage of field outside the volume of the primary torus? Moreover, one can get almost arbitrarily close to complete containment of the primary B field by making, say, two windings with opposite circumferential current. I believe, OP is missing the fact, that dB/dt creates an electric field inside the torus, but demands of continuity inevitably mean, that this field extends also outside of it. As I said, this is not an obvious conclusion to jump to. $\endgroup$ – LLlAMnYP Jan 7 '16 at 13:34
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Something for your intuition:

When you turn on the current in the toroid, magnetic field lines "comes from infinity" to enter the core. These lines will cross other loops, and this relative motion of magnetic fields and the charges in the wire creates the emf.

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  • $\begingroup$ You just put a beautifully intuitive picture into my head with a single sentence! I never looked at it that way... but now I don't even need a movie to "see" it. Where can I donate a hundred up-votes? $\endgroup$ – CuriousOne Jan 6 '16 at 3:16
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    $\begingroup$ @CuriousOne - coming from you that's a real compliment. Worth more than a hundred upvotes, really. Thank you. $\endgroup$ – Floris Jan 6 '16 at 3:18
  • $\begingroup$ Thank you. Moments when it really clicks and one learns something new about an object that one has handled thousands of times are so rare... didn't think I would get one today... and there it is! $\endgroup$ – CuriousOne Jan 6 '16 at 3:20

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