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

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Discussion Overview

The discussion revolves around the application of Faraday's Law to explain electromotive force (EMF) induction in a circuit outside a solenoid when the current through the solenoid is varied. Participants explore the implications of changing magnetic fields and the conditions under which electric fields may be induced, addressing both theoretical and experimental aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants assert that Faraday's Law indicates a time-varying magnetic field induces an electric field, which should account for the observed potential changes in the resistor circuit.
  • Others argue that the magnetic field is only non-zero inside the solenoid, suggesting that outside the solenoid, the rate of change of the magnetic field (dB/dt) would be zero, thus implying no induced electric field.
  • A later reply suggests that while the curl of E is non-zero only where a magnetic field exists, the integral form of Faraday's Law allows for the possibility of a non-zero electric field around a closed path that is not inside the solenoid.
  • Some participants question the assumption that the magnetic field is zero outside the solenoid, noting that in practical scenarios, the field may be small but not negligible.
  • There is a discussion about the implications of having an infinitely long solenoid and how that might affect the results of the experiment.
  • Concerns are raised about the apparent conflict between the integral and differential forms of Faraday's Law, particularly regarding the source of the electric field when the magnetic field appears to be zero outside the solenoid.
  • Participants also discuss the nature of magnetic fields and their behavior at distances from current-carrying wires, suggesting that magnetic fields can exist even when the current is not nearby.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of the magnetic field outside the solenoid and its implications for induced electric fields. The discussion remains unresolved, with multiple competing interpretations of Faraday's Law and its application to the experiment.

Contextual Notes

Participants highlight the importance of distinguishing between local properties of the electric field (curl of E) and the global properties related to induced EMF around closed paths. There is also mention of the limitations of assuming a zero magnetic field outside the solenoid, which may not hold true in practical scenarios.

  • #91
Per Oni said:
Do you in turn agree that this energy is locked up in the toroid? Consider the case where we have a constant dc current in the primary.
Yes of course. Electrical energy expended in setting up the solenoid current I against a back emf -∂∅/∂t appears in the magnetic field having an energy density 1/2B2/(μ0μr) - assuming a linear response μr = const. applies. This neglects any ohmic/hysteresis losses. Now - do you accept everything said in #89?
 
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  • #92
Q-reeus said:
Yes of course.
Suppose the dc source is placed a good deal away from the transformer. Do you agree that at t=0 and I=0, all this energy was still locked up in the dc source?

Now - do you accept everything said in #89?
Nope, but I’ll answer that question later so as not to interrupt the flow of the main discussion.
 
  • #93
Per Oni said:
Suppose the dc source is placed a good deal away from the transformer. Do you agree that at t=0 and I=0, all this energy was still locked up in the dc source?
Obviously. But let me guess. This is an 'how did the energy get from A to B' type leading question, right? If I say 'through the connecting wires' that then begs another question. There are no real paradoxes involved, but at this point will stop second guessing - ball's in your court. Take your time on it - I'm off again.
Nope,...
Darn, raining on my day again. :frown:
 
  • #94
Q-reeus said:
Obviously. But let me guess. This is an 'how did the energy get from A to B' type leading question, right? If I say 'through the connecting wires' that then begs another question. There are no real paradoxes involved, but at this point will stop second guessing - ball's in your court. Take your time on it - I'm off again.

Darn, raining on my day again. :frown:

Here you are finally latching on. Get the energy from A to B. Join the dots. This does not involve some magical rabbit in the hat appearing/disappearing trick. Although that view was quite popular pre Maxwell, some 150 years ago.

I’ve outlined my ideas.

It’s quite sunny today, lots to do. Take care.
 
  • #95
To answer the question: The energy transfer is not through cables but mediated by the electromagnetic field. The most simple example is a coaxial cable, where you can solve the stationary Maxwell equations + boundary conditions analytically. Then calculate the Poynting vector of the field and see, how the energy flows. You find this discussion in

A. Sommerfeld, Lectures on Theoretical Physics, Vol. 3

which I recommend for a careful study of these issues. It's still one of the best books on the subject ever written!
 
  • #96
vanhees71 said:
To answer the question: The energy transfer is not through cables but mediated by the electromagnetic field. The most simple example is a coaxial cable, where you can solve the stationary Maxwell equations + boundary conditions analytically. Then calculate the Poynting vector of the field and see, how the energy flows. You find this discussion in

A. Sommerfeld, Lectures on Theoretical Physics, Vol. 3

which I recommend for a careful study of these issues. It's still one of the best books on the subject ever written!

I know that the em energy flows not just in the cables but also partly outside. The picture I painted is still very limited. It can only be seen as a first step. Hopefully somebody some day writes a good Wikipedia article on transformer emf.

A few weeks ago somebody described a “catapult” magnetic field when talking about electrical motors. I fully describe to that image.

Consider a transformer with 2 separate coils in opposite legs. With this transformer fully loaded, if we could see the magnetic field, catapult like magnetic flux would be seen in the airspace between the coils. If the transformer is mechanically not strong enough the 2 coils would fly apart in opposite directions. Practical use of this effect is the squirrel cage synchronous motor. Here the secondary coil and part of the magnetic circuit are in fact the rotor. Big currents are generated in the cage by the “primary” stator windings. Once the motor runs, the distinction of transformer emf and motional emf disappear.
 
  • #97
Per Oni said:
I know that the em energy flows not just in the cables but also partly outside.
Neglecting ohmic loss in wires, energy flow is completely outside such wires.
The picture I painted is still very limited. It can only be seen as a first step. Hopefully somebody some day writes a good Wikipedia article on transformer emf.
You still argue with current explanation? Again - do you acknowledge your idea demands a large magnetic field exists outside of transformer core? Can you demonstrate it? Shouldn't be hard - grab a good toroidal transformer, run DC through primary, and check with compass needle for this hefty 'external' B field. Which won't be there.
A few weeks ago somebody described a “catapult” magnetic field when talking about electrical motors. I fully describe to that image.
Consider a transformer with 2 separate coils in opposite legs. With this transformer fully loaded, if we could see the magnetic field, catapult like magnetic flux would be seen in the airspace between the coils. If the transformer is mechanically not strong enough the 2 coils would fly apart in opposite directions.
There may be a quite weak attraction or repulsion, owing to an inevitable small amount of 'leakage' flux exterior to core. Will depend on the phase relations between two coils, and if coil acting as secondary is resistively loaded - the usual case, time-averaged forces will be zero because of 90-degree phase relationship of currents. If secondary is shorted, a small repulsion will be present, but very small and should be much less than if magnetic core were absent. There are no 'catapult' effects as you describe. If you insist otherwise - demonstrate it! Set up a test rig with strain gauges or the like. It is you, not the world, that will be surprised at results.
Practical use of this effect is the squirrel cage synchronous motor. Here the secondary coil and part of the magnetic circuit are in fact the rotor. Big currents are generated in the cage by the “primary” stator windings. Once the motor runs, the distinction of transformer emf and motional emf disappear.
Better description is that motional and transformer effects are both present. And of course Lorentz force which does not act on a 'catapult' basis
 
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  • #98
Q-reeus said:
Neglecting ohmic loss in wires, energy flow is completely outside such wires.
Yes you are correct here. That was once one of my conclusions in another thread here at PF. That’s why I want to see a good Wikipedia article showing all fields in a simple transformer. Including flow of energy.
You still argue with current explanation? Again - do you acknowledge your idea demands a large magnetic field exists outside of transformer core?
No it does not demand that. I have indicated from the start that such fields flow with the speed of light for that particular medium. This in turn means that any flow of field is in fact fast but with a low density.
Can you demonstrate it? Shouldn't be hard - grab a good toroidal transformer, run DC through primary, and check with compass needle for this hefty 'external' B field. Which won't be there.
Nope, it will not be there.
There may be a quite weak attraction or repulsion, owing to an inevitable small amount of 'leakage' flux exterior to core. Will depend on the phase relations between two coils, and if coil acting as secondary is resistively loaded - the usual case, time-averaged forces will be zero because of 90-degree phase relationship of currents. If secondary is shorted, a small repulsion will be present, but very small and should be much less than if magnetic core were absent. There are no 'catapult' effects as you describe. If you insist otherwise - demonstrate it! Set up a test rig with strain gauges or the like. It is you, not the world, that will be surprised at results.
With the secondary coil shorted the currents have a 180 degree phase shift. This means that they are running in opposite directions. Opposite directed currents are repulsive, so are the coils.
Better description is that motional and transformer effects are both present.
Ok.
 
  • #99
http://www.youtube.com/watch?v=UvHCQswnjEg&feature=related

This is not a bad demo of what I’m going on about. The magnetic field is expanding from the primary coil. Ofcourse there's much more to it then what is shown here. Remarkable that he says: nobody really knows how this works! I'll have a further look for some more involved, more detailed stuff.

Warning! I was fast asleep within 1 ½ minutes. This man is absolutely priceless for insomniacs.
 
  • #100
Per Oni said:
No it does not demand that. I have indicated from the start that such fields flow with the speed of light for that particular medium. This in turn means that any flow of field is in fact fast but with a low density.
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?

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. And further on what value of line-density is chosen as reference value. Line 'movement' is thus a purely arbitrary and entirely mathematical concept. It's a somewhat strained model but is self-consistent if viewed on that basis and applied to the action of a given current element as per first model shown - two single-turn loops interacting. The next part, purporting to show the same flux-cutting but for many-turn windings with very different orientations, is quite misleading. With a toroid, there is simply no mutual flux-cutting primary-to-secondary, and any secondary-to-primary 'flux-cutting' is small and inconsistent with emf's induced. A better idea is gained in last part of this Video: http://www.youtube.com/watch?v=2-Ijjm7if5g&feature=related

But we are free to believe whatever we wish. Just don't expect to get a job designing transformers!
 
  • #101
Q-reeus said:
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!
 
  • #102
Per Oni said:
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. :-p
 
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  • #103
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).
 
  • #104
Per Oni said:
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!
 

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