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

[Per Oni]

I want to give example of the strangeness of having 2 different flux cutting laws.

Imagine a horse shoe electromagnet (no permanent magnet) and switch on the current supply. Now approach this magnet with a search coil. During the approach you will be able to see the voltage output of the coil on an oscilloscope. This voltage and its magnitude can be explained using the flux cutting law. No problem here, I’m absolutely fine with that.

Next, keep the coil in place and switch of the current. Depending on the time constant of the electromagnet circuit there will again be a voltage displayed on the scope. But now we not only have to accept that there’s no flux cutting involved but we also have to accept that this field somehow mysteriously disappears. I’m not fine with that at all. (Never was).

@ Q-eerus. I’m sure you can teach me a lot about magnets but again I’d like to talk in a different thread.

 

[harrylin]

Which of these 2 sentences can you not follow (perhaps both)? [..]

I did not understand what you meant with "No flux cutting = lots of emf."
If you simply meant that there is lots of E around dB/dt, then that corresponds to Maxwell's explanation of Faraday's law (if I have the history right!).

 

[Q-reeus]

Imagine a horse shoe electromagnet (no permanent magnet) and switch on the current supply. Now approach this magnet with a search coil. During the approach you will be able to see the voltage output of the coil on an oscilloscope. This voltage and its magnitude can be explained using the flux cutting law. No problem here, I’m absolutely fine with that.

Next, keep the coil in place and switch of the current. Depending on the time constant of the electromagnet circuit there will again be a voltage displayed on the scope. But now we not only have to accept that there’s no flux cutting involved but we also have to accept that this field somehow mysteriously disappears. I’m not fine with that at all. (Never was).

If that horseshoe electromagnet is purely air-core, then agree flux-cutting approach fails in 2nd instance. If it is iron-core, then as per my revised position in #68, it is actually possible to apply flux-cutting method to the core contribution by summing for each elemental dipole's rotating field lines. A cumbersome methodology though and not in accord with the modern approach of simply applying Faraday's integral law in either case. In the first instance, it pays to remember that emf = -d∅/dt (total derivative), not merely the -∂∅/∂t (partial derivative) applying in the purely time-changing flux case of 2nd instance.

@ Q-eerus. I’m sure you can teach me a lot about magnets but again I’d like to talk in a different thread.

Something we haven't covered in the past? OK but I'm nearing exhaustion on this topic. Well there is one very interesting and sure to be controversial aspect I'd like to cover down the track, but not any time soon.

 

[Per Oni]

If it is iron-core, then as per my revised position in #68, it is actually possible to apply flux-cutting method to the core contribution by summing for each elemental dipole's rotating field lines. A cumbersome methodology though and not in accord with the modern approach of simply applying Faraday's integral law in either case.

Ah, I do understand your point of view a bit better after reading this. Anyway, (at least for us 2) the mystery remains for an air core. And yeah I’m also done on this subject.

@ harrylin Yes that is indeed what I meant.

 

[Per Oni]

Saying on Sunday I was done with this subject, but as often happens some thoughts keep on lingering.
So, today I started Googling a bit and this is what I found:

http://en.wikipedia.org/wiki/Faraday's_law_of_induction#Proof_of_Faraday.27s_law

Halfway down the page:

This step implicitly uses Gauss's law for magnetism: Since the flux lines have no beginning or end, they can only get into the loop by getting cut through by the wire.

Gauss’s law is a general law and must therefore apply to transformers. So this law completely vindicates what I was arguing all along, namely that magnetic flux cannot just appear/disappear without cutting the coils.

Everyone, thanks for all the help I got reaching this result. You were ace!

 

[Q-reeus]

"This step implicitly uses Gauss's law for magnetism: Since the flux lines have no beginning or end, they can only get into the loop by getting cut through by the wire."
Gauss’s law is a general law and must therefore apply to transformers. So this law completely vindicates what I was arguing all along, namely that magnetic flux cannot just appear/disappear without cutting the coils.

Don't want to spoil your day Per Oni, but if you check the context of that wording carefully (in the drop-down 'show' part), it will be seen to apply only to the 2nd term on the RHS - the motional d∅/dt emf part, not the 'transformer' ∂∅/∂t part, in agreement with my comments in #73. As I wrote then, you can use a flux cutting approach even for transformer part, but not on the basis of 'aggregate flux line motion', because the aggregate is clearly zero in transformer cores. Only field intensity varies with time - there is no net 'motion' at all. Thinking about it some more, even in the air core case, by summing over individual conduction charge motions, flux cutting can work there also, but again, not on any aggregate flux motion basis. The simplest and preferred approach is to always apply emf = -d∅/dt; the total derivative of threading flux in a given frame.

 

[Per Oni]

Q-reeus. You are one of only a handful around here I’ve got respect for.

But can you explain to me when a circle, no beginning no end, can enter another such circle without cutting a circumference? But no, so far you have not spoilt my day. In fact I’m looking forward to be proven wrong, it can only improve my understanding. But please just answer the above question.

 

[Q-reeus]

Q-reeus. You are one of only a handful around here I’ve got respect for.

Shucks Per Oni - I feel chuffed!

But can you explain to me when a circle, no beginning no end, can enter another such circle without cutting a circumference?

I will take it the first mentioned circle here represents a line of flux circulating within a transformer core. And the second circle represents a conducting winding wrapped around that core, right? Correct me if wrong, but I will assume so. Well this is where 'aggregate' comes into force. Suppose we have an air-core toroidal transformer here, with inner primary winding generating that core flux, the outer secondary windings (one of which is the 'second circle') having a small radial gap separating them from the primary windings. It is simply a consequence of applying the Biot-Savart expression for flux owing to a current element, then integrating over all such elements comprising the solenoidal current circulating in the primary windings, that all flux lines are confined to a region encompassed by the primary windings. In principle none intersect the secondary - although owing to inevitable manufacturing limitations, a small amount of leakage is inevitable - but small is the word. That can easily be checked physically using e.g. a magnetometer.

So with AC currents flowing, all that can happen is for flux lines to appear and disappear periodically in the core, without ever moving in and out of the core. The lines aren't real and, according to vector summation over contributing moving source charges, simply 'come into being' within the core, as mere indicators of the ever changing continuum field strength. Field lines are an artifice - they represent strength and direction of a continuous field that owes it's existence to flowing source charges or magnetized media.

What's considered fundamental is not 'flux line cutting' or even 'changing threading flux' - these are associations, not ultimate causes of transformer action. The true cause is always motion of charge, plus that of magnetized media (intrinsic electron magnetic moments + atomic orbital moments) if present. Work fundamentally from the field definitions:

E = -∇V - ∂A/∂t, B = ∇×A, and in turn the definitions for scalar potential V and vector potential A given by the Lienard-Wiechert expression http://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential#Definition_of_Li.C3.A9nard-Wiechert_potentials
They always work, even in ultra-relativistic situations. Must go :zzz:
[Edit: Customarily we add Lorentz force expression F = q(E+u×B) to above. That allows the motional emf part to be calculated without resort to 'flux-cutting' as such.]

 

[Per Oni]

I will take it the first mentioned circle here represents a line of flux circulating within a transformer core. And the second circle represents a conducting winding wrapped around that core, right? Correct me if wrong, but I will assume so.

Yes correct.

You have avoided answering this question (asked 2x):

“Can you explain to me when a circle, no beginning no end, can enter another such circle without cutting a circumference?”

OK we both know that the real answer to my simple question is: no, it is not possible.

Well this is where 'aggregate' comes into force. Suppose we have an air-core toroidal transformer here, with inner primary winding generating that core flux, the outer secondary windings (one of which is the 'second circle') having a small radial gap separating them from the primary windings. It is simply a consequence of applying the Biot-Savart expression for flux owing to a current element, then integrating over all such elements comprising the solenoidal current circulating in the primary windings, that all flux lines are confined to a region encompassed by the primary windings.

The Biot-Savart law doesn’t deal with changing currents. And it is only when the current changes that we have a dB/dt in the coils. So this part of your answer is not valid.

In principle none intersect the secondary - although owing to inevitable manufacturing limitations, a small amount of leakage is inevitable - but small is the word. That can easily be checked physically using e.g. a magnetometer. So with AC currents flowing, all that can happen is for flux lines to appear and disappear periodically in the core, without ever moving in and out of the core.

Same answer as my last one.

The lines aren't real and, according to vector summation over contributing moving source charges, simply 'come into being' within the core, as mere indicators of the ever changing continuum field strength. Field lines are an artifice - they represent strength and direction of a continuous field that owes it's existence to flowing source charges or magnetized media.

This is another answer I was expecting: “field lines are not real!”
Except when we need them to explain energy, force, momentum of moving magnetic fields they are real enough. We can’t have it both ways.

Furthermore I really wonder why Maxwell went through the trouble of including magnetic fields in his equations. If you can show me that we can do away with all the Maxwell equations dealing with magnetism and we can fully replace them with purely electrical static and moving fields then you will have made inroads to me believing you. Note that these alternative equations need to have all the proper vectors, dots, crosses etc.

Have fun!

 

[Q-reeus]

You have avoided answering this question (asked 2x):
“Can you explain to me when a circle, no beginning no end, can enter another such circle without cutting a circumference?”
OK we both know that the real answer to my simple question is: no, it is not possible.

It's not possible provided the first circle is a real entity that must somehow be conserved - i.e. not allowed to materialize/vanish. But I'm saying that's in fact how one needs to treat magnetic field lines generated by a time-changing current. Because the field itself changes sign in keeping with an AC source current! Hence must appear and disappear cyclically. How else do you imagine it all works? Very different to the case for say lines of E owing to a static charge, where a conservation law - Gauss's law, forbids any appearing/disappearing trick. That does not apply to B field whose source - *moving* charge, can be turned on or off, one-way then that, at will.

The Biot-Savart law doesn’t deal with changing currents. And it is only when the current changes that we have a dB/dt in the coils. So this part of your answer is not valid.

Biot-Savart is typically applied for steady currents, but nothing prevents it's application to time-varying situation. Only when very high frequencies are involved need we take extra care to allow for phase delay. Transformers are typically nowhere near that regime. It's just a mathematical fact that cancellation of field occurs everywhere except inside solenoidal core region. You can check out any of the many sites that will derive field for a long straight solenoid. And toroid is similar.

This is another answer I was expecting: “field lines are not real!”
Except when we need them to explain energy, force, momentum of moving magnetic fields they are real enough. We can’t have it both ways.

Fields are real. Field lines are not, but they are very handy to use for many situations. But there are limitations. If you really believe those lines of B have to cut through the secondary windings of say a toroidal transformer, explain why a compass needle for instance undergoes no deflection when a steady or slowly-varying current runs through the primary. Don't believe me? Ask around - contact some transformer manufacturers/sellers. They make it their living to know the business of how these things work.

Furthermore I really wonder why Maxwell went through the trouble of including magnetic fields in his equations. If you can show me that we can do away with all the Maxwell equations dealing with magnetism and we can fully replace them with purely electrical static and moving fields then you will have made inroads to me believing you. Note that these alternative equations need to have all the proper vectors, dots, crosses etc.

Not getting your drift here. Maxwell gave us an extremely important set of relationships between fields, and between fields and sources of those fields. Check out the Ampere-Maxwell eq'n here. Notice how those moving charges enter the picture?

Have fun!

After all this? You've rained on my day bud.

 

[harrylin]

[..] “Can you explain to me when a circle, no beginning no end, can enter another such circle without cutting a circumference?”
OK we both know that the real answer to my simple question is: no, it is not possible. [..]

I know a magician trick like that. :tongue2:

But seriously, In the OP I don't see two circles cutting each other.
Instead, I "see" for this case how very weak magnetic fields (see post #1) form right through the circle. If you visualise "field lines" by adding iron powder, then you will see the field lines take more shape inside the wire loop without laterally cutting through the wire loop.

And more importantly (and I stressed this before in #36), those weak changing magnetic fields have the opposite effect of the induced electric field which is according to Maxwell responsible for the EMF in this case. If you don't believe this, please make a drawing and you will see for yourself.

 

[Per Oni]

How else do you imagine it all works?

As you can see I'm working on it . Halfway there.

That does not apply to B field whose source - *moving* charge, can be turned on or off, one-way then that, at will.

Nope not thru. B fields need energy to come in existence. B fields are just as real as all other stuff containing energy, such as E fields, atoms, your shirt etc. If B fields are not real nothing is real. Anyway how are you going to stop a charge from moving? Impossible!

Fields are real. Field lines are not, but they are very handy to use for many situations. But there are limitations. If you really believe those lines of B have to cut through the secondary windings of say a toroidal transformer...

In that case do you believe they cut through a coil in case of motional emf?

 

[Per Oni]

I know a magician trick like that. :tongue2:

When I wrote that question that picture appeared also in my mind. Once upon a time they were quite popular but now they are seen as boring in comparison with what’s around now. (Walking on the Thames etc.)

 

[Q-reeus]

Q-reeus: "That does not apply to B field whose source - *moving* charge, can be turned on or off, one-way then that, at will."
Nope not thru. B fields need energy to come in existence. B fields are just as real as all other stuff containing energy, such as E fields, atoms, your shirt etc. If B fields are not real nothing is real.

Not making sense here. When did I even suggest B fields aren't real, or don't have energy? Arguing against a phantom. I said *lines* aren't real - big difference!

Anyway how are you going to stop a charge from moving? Impossible!

Perhaps you should explain what your notion of alternating current entails. You can arrange to avoid that twice every cycle, current = moving charges has zero net speed!?

Q-reeus: "Fields are real. Field lines are not, but they are very handy to use for many situations. But there are limitations. If you really believe those lines of B have to cut through the secondary windings of say a toroidal transformer..."

In that case do you believe they cut through a coil in case of motional emf?

Already covered in #53 - you know the answer.
Now, please do contact transformer designer/manufacturers, and see if any agree with your idea of how a transformer works. Evidently clear by now; flux lines expanding in and out of the core, and cutting the secondary (or even primary) windings of a toroidal (or any 'iron-core') transformer. Be prepared for some laughter! :tongue: :zzz:

 

[harrylin]

When I wrote that question that picture appeared also in my mind. Once upon a time they were quite popular but now they are seen as boring in comparison with what’s around now. (Walking on the Thames etc.)

Hehe yeah. But what about the serious content of my reply??

 

[Per Oni]

Perhaps you should explain what your notion of alternating current entails. You can arrange to avoid that twice every cycle, current = moving charges has zero net speed!?

What I was thinking was that electrons still have the Fermi speed. But forget that and yes you are correct here.

This is my point of view as per #50:

Note that when dI/dt exist there will be a wave front spreading out from a conductor having the same speed as the speed of light for the medium in which the conductor is located (think antenna). Perhaps you can see therefore that my picture is not that far fetched.

To add to this from Wikipedia #75:

Since the flux lines have no beginning or end, they can only get into the loop by getting cut through by the wire.

Let’s look at your points of view #78:

So with AC currents flowing, all that can happen is for flux lines to appear and disappear periodically in the core, without ever moving in and out of the core. The lines aren't real and, according to vector summation over contributing moving source charges, simply 'come into being' within the core, as mere indicators of the ever changing continuum field strength. Field lines are an artifice - they represent strength and direction of a continuous field that owes it's existence to flowing source charges or magnetized media.

And #80:

…Gauss's law, forbids any appearing/disappearing trick. That does not apply to B field whose source - *moving* charge, can be turned on or off, one-way then that, at will.

You admit that a magnetic field is real and contains energy (#84), but also according to you, the field just appears in the core. Also according to you: Gauss’s law does not forbid any appearance trick in the case of magnetic fields. Can you tell me how that energy got there? Just at will? Chemical energy? Time to wake up!

 

[Per Oni]

Hehe yeah. But what about the serious content of my reply??

Thanks for your reply but I just don’t want to run 2 virtually identical discussions.

 

[harrylin]

Thanks for your reply but I just don’t want to run 2 virtually identical discussions.

There is only one discussion.

 

[Q-reeus]

This is my point of view as per #50:
Note that when dI/dt exist there will be a wave front spreading out from a conductor having the same speed as the speed of light for the medium in which the conductor is located (think antenna). Perhaps you can see therefore that my picture is not that far fetched.
To add to this from Wikipedia #75:
Since the flux lines have no beginning or end, they can only get into the loop by getting cut through by the wire.

That last bit I covered back in #76 - applies to motional not time-changing component. (And btw, it really is no service to the other readers when there is no mention the above quoted bit from Wikipedia article is 'buried' inside a drop down box one has to click on, and is not part of a normal read of that page.)
Your first bit from #50 is fine if restricted to considering just the contribution from a single current element, as I have acknowledged earlier and you should remember such things. Far from being an essential perspective though, it leads to a faulty notion of needing to have real flux lines cutting things. Just aint so. Transformers.

Let’s look at your points of view #78:
So with AC currents flowing, all that can happen is for flux lines to appear and disappear periodically in the core, without ever moving in and out of the core. The lines aren't real and, according to vector summation over contributing moving source charges, simply 'come into being' within the core, as mere indicators of the ever changing continuum field strength. Field lines are an artifice - they represent strength and direction of a continuous field that owes it's existence to flowing source charges or magnetized media.
And #80:
…Gauss's law, forbids any appearing/disappearing trick. That does not apply to B field whose source - *moving* charge, can be turned on or off, one-way then that, at will.

You admit that a magnetic field is real and contains energy (#84), but also according to you, the field just appears in the core. Also according to you: Gauss’s law does not forbid any appearance trick in the case of magnetic fields. Can you tell me how that energy got there? Just at will? Chemical energy? Time to wake up!

There is no conflict at all: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indeng.html Energy is supplied by the currents which are the field's source.

Now I have to pull you up on a serious matter - misrepresenting my actual position a number of times now. Above is just the latest example. I preceded 'appear and disappear' with 'So with AC currents flowing'. Having previously emphasized a number of times that currents and/or magnetized media are the real source of both E and B fields, there is no excuse to slant things as you have done here. I will not accuse you of being deliberate in this - in your mind there may be a faulty interpretation process going on. Inadvertent or not, stop and think carefully before putting into print claims of what I have said or believe, which keep turning out to be false. :grumpy:

Getting back to what I consider your fixation with the absolute need to explain Faraday's law entirely in terms of flux-line cutting. Please, take on-board the fact that, for an infinitely long solenoid, or quite finite toroid, there is zero magnetic flux-line density except within the core region. The resolution to the apparent paradox of closed flux-lines in infinite solenoid case is that the equivalent fictitious 'poles' at each end are infinitely removed, therefore the return flux lines exterior to the solenoid core are infinitely diluted. And the problem does not exist at all for toroid geometry. So again, to put paid to your notion of flux lines expanding in and out of the core region, acknowledge this necessarily implies a quite strong and detectable B field must exist exterior to the core. Well just put it to the test. I guarantee you will be disappointed. Again, I urge you to contact those whose livelihood depends on knowing just how transformers actually behave.

 

[Per Oni]

Energy is supplied by the currents which are the field's source.

Totally agree.
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.

 

[Q-reeus]

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/(μ₀μ_r) - assuming a linear response μ_r = const. applies. This neglects any ohmic/hysteresis losses. Now - do you accept everything said in #89?

 

[Per Oni]

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.

 

[Q-reeus]

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.

 

[Per Oni]

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.

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.

 

[vanhees71]

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!

 

[Per Oni]

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.

 

[Q-reeus]

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

 

[Per Oni]

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.

 

[Per Oni]

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.

 

[Q-reeus]

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!

 

[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. :tongue2:

 

[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!