How Does Faraday's Law Explain EMF Induction Outside a Solenoid?

[Per Oni]

I cannot imagine how it could work - especially for toroidal transformer. Have you actually sat down and figured out a fully consistent picture of where the field lines all go? For 50Hz operation, at light speed, lines must somehow travel outward ~ c/(4*50) ~ 1.5 million meters every quarter cycle, and then somehow know to come on back in next quarter cycle. But then - real interesting part, lines manage to reverse direction before repeating this amazing in-then-out feat. Can you explain this all to yourself - where in space the lines reside 'out there', how they know to return, reverse direction as endless loops, and what happens to them when the current is switched off completely?

This would work exactly the same as it happens in an antenna. It is well known that a wave front of speed C leaves the antenna. Where do those lines go, how far, what when the current is max, what when reversing etc. there’s no difference.

Just in time to catch your #99. I agree that linked YouTube audio is great for relaxation. But the flux-cutting model used there does *not* work on basis of field lines expanding at c speed. The idea there is that 'expansion rate' corresponds to how fast a given value of *line-density* = field strength propagates outward/inward, and that will be relatively sedate. Depends entirely on operating frequency for one.

No. Again, exactly the same as a coil antenna would work. Speed does not depend on frequency.

And further on what value of line-density is chosen as reference value. Line 'movement' is thus a purely arbitrary and entirely mathematical concept.

No. Flux density represents real energy. Flux movement is also real flowing energy.

Just don't expect to get a job designing transformers!

They could do a lot worse then taking me on!

 

[Q-reeus]

This would work exactly the same as it happens in an antenna. It is well known that a wave front of speed C leaves the antenna. Where do those lines go, how far, what when the current is max, what when reversing etc. there’s no difference.

Big difference. Radiation fields keep going; they do not return. The near fields it's true move in and out with phase speed that is roughly c further out. But we are talking about open structures that generate finite field strengths throughout space. This simply does not apply in case of region exterior to a toroidal transformer core. There B field has zero strength* in all exterior space. It is entirely illogical then to try and draw some parallel. And what can't be escaped even in antenna case is that the near-field lines are periodically created and destroyed every half-cycle. This has to be so since line directions reverse. Once that single fact is grasped and accepted, the need for flux-cutting evaporates. Lines simply materialize and vanish periodically 'in-place'. They conveniently represent field strength/direction, nothing more than that. True for antenna, true for transformer. Lines are part of the map - not the territory! We have gone over this all before.
[* Not exactly true in AC case. As there is an exterior E and thus ∂E/∂t, it follows from Maxwell-Ampere in vacuo: ∇×B = 1/c²∂E/∂t, that a finite B exists outside of core. Do the sums though and you will find it's value is exceedingly small in transformer situation. Many orders of magnitude too small to account for any 'flux-line cutting' emf.]

No. Again, exactly the same as a coil antenna would work. Speed does not depend on frequency.

It does in the model used in that video. Radial speed of a front of constant field strength will, for a given relative phase, be directly proportional to frequency. And 'motion' halts every half-cycle - what happens to light speed concept? And arbitrarily depends on units used for field strength. To argue otherwise is without sense.

No. Flux density represents real energy. Flux movement is also real flowing energy.

Here we go again. Did I say anything to suggest otherwise? Check my words - it was in reference to line *movement* - what 'speed' these lines are supposed to move at.

They could do a lot worse then taking me on!

Hehe - I'm sure you could come up with some interesting new designs. Not so sure how well they might work though.

 

[Per Oni]

Ah, I finally found what I was looking for.

http://en.wikipedia.org/wiki/Near_and_far_field#Regions_and_their_cause

Some quotes from that article.

Magnetic induction (for example, in a transformer) can be seen a very simple model of this type of near-field electromagnetic interaction.

Also, in the part of the near-field closest to the antenna (called the "reactive near-field", see below), absorption of electromagnetic power in the region by a second device has effects that feed-back to the transmitter, increasing the load on the transmitter that feeds the antenna by decreasing the antenna impedance that the transmitter "sees". Thus, the transmitter can sense that power has been absorbed from the closest near-field zone, but if this power is not absorbed by another antenna, the transmitter does not supply as much power to the antenna, nor does it draw as much from its own power supply.

Because of this energy storage and return effect, if either of the inductive or electrostatic effects in the reactive near-field transfers any field energy to electrons in a different (nearby) conductor, then this energy is lost to the primary antenna. When this happens, an extra drain is seen on the transmitter, resulting from the reactive near-field energy that is not returned. This effect shows up as a different impedance in the antenna, as seen by the transmitter.

(My bold script)

The near-field is remarkable for reproducing classical electromagnetic induction and electric charge effects on the EM field, which effects "die-out" with increasing distance from the antenna (with magnetic field strength proportional to the inverse-cube of the distance and electric field strength proportional to inverse-square of distance), far more rapidly than do the classical radiated EM far-field (E and B fields proportional simply to inverse-distance). Typically near-field effects are not important farther away than a few wavelengths of the antenna.

This is all very close to how I imagine power transfer takes place in an air core transformer. Note that I’m especially interested in the near field. I hope that doesn’t need explaining. Of course this article deals only with an air core since it's about antennas, but one day hopefully, an article dealing with magnetic cores will be made as well.

Some more sites:

http://en.wikipedia.org/wiki/Near-field_magnetic_induction_communication
http://en.wikipedia.org/wiki/Wireless_energy_transfer

I lot of your question will be answered in those articles.

Yeah, I’ve got this design of an air core transformer, where the secondary coil speeds off close to the speed of light away from the primary coil, at the same time that the power is switched on in the primary. It only needs to travel 1 meter. It would be interesting to see whether transformer emf can catch up. (Answer: no it can’t).

 

[Q-reeus]

I lot of your question will be answered in those articles.

My questions? You mean those in #100? Linked articles agree with #102.

Yeah, I’ve got this design of an air core transformer, where the secondary coil speeds off close to the speed of light away from the primary coil, at the same time that the power is switched on in the primary. It only needs to travel 1 meter. It would be interesting to see whether transformer emf can catch up. (Answer: no it can’t).

Wow! If you can pull off close-to-light-speed motion of secondary, I suggest forget about transformer design. After patenting such break-through propulsion technique, consult a good lawyer. Discuss pros and cons of contacting top brass in the Pentagon. Suppression gags are occasionally slapped on hapless inventors who venture into 'national security related' areas. Still, they will be falling over themselves in rush to secure such a winning-edge technological feat. Best of luck Per Oni!