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

[harrylin]

The assumption that the B-field outside the coil is zero leads directly to the erroneous conclusion that the curl of the E field is 0 outside the coil.

Sorry, once more: the local curl of the E-field is irrelevant for the topic (see also post#22). That's where the OP went wrong, as most people explained starting with post #4.

 

[harrylin]

[..] the only place where the B-field is non zero is inside the solenoid itself. The circuit of the resistor was not a part of the inside of the solenoid. So -dB/dt would have to be zero for all points in space except inside the it. And that means no electric field can possibly have been induced from the varying magnetic field in the solenoid into the circuit of the resistor.
So how is the above experiment explained?

What perhaps was not clear, is that it can be misleading to say that the electric field is induced into the circuit.
In fact, the B-field induces an E-field everywhere around the field lines - not just where the circuit is. The induced E-field spreads out all around the solenoid.

Does that help?

 

[Q-reeus]

Yes it does.
If properly done it will give the correct direction of E-field in the same way as a traveling B field does. Maybe one day it will be thought at college/uni who knows? 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.

For sure there are situations where flux-linkage and flux-cutting can be used interchangeably, like that illustrated towards the bottom of the page here: http://www.thestudentroom.co.uk/showthread.php?t=1296165
On the other hand, take that toroidal (or any 'iron core') transformer case. No appreciable magnetic field ever 'cuts' the conductor windings wrapping around the magnetic core. I think historically there were many proponents of the idea that flux lines could in some way expand and shrink in and out of such magnetic cores. Just where those lines went to or came from was never quite explained. But it fell out of favor as giving physical reality to 'indestructible' lines, rather than viewing them as merely convenient visualizations of strength and direction for a continuous field that in the AC case, simply grows and diminishes in strength 'in place' - i.e. in the core. One situation where flux-cutting still seems to be in vogue is in explaining Faraday disk operation, although special relativity is nowadays seen as the underlying explanation.

 

[Dale]

Sorry, once more: the local curl of the E-field is irrelevant for the topic (see also post#22). That's where the OP went wrong, as most people explained starting with post #4.

Agreed.

 

[Per Oni]

On the other hand, take that toroidal (or any 'iron core') transformer case. No appreciable magnetic field ever 'cuts' the conductor windings wrapping around the magnetic core.

Thanks for your interesting reply. Good to know that in the past people were thinking up similar ideas then I do now.

I’m not sure why you single out iron core transformers. The same rules should apply for any type of transformer. Once one accepts the picture (visual aid) of a magnetic field spreading out from a single conductor it follows for all coils.

Of course the question is, is that a valid picture? Perhaps I could ask: is the picture of field lines valid? How many lines are there around a current carrying conductor? Why did Gauss need field lines but Coulomb did not?
Without Gauss we would perhaps still be in the stone age as far as em theory is concerned because his theory gives an action at a more precise location in space. But all could be explained and viewed as action at a distance.

 

[Q-reeus]

Thanks for your interesting reply.

Happy to provide.

I’m not sure why you single out iron core transformers. The same rules should apply for any type of transformer.

It's just that ferromagnetic core transformers are ubiquitous owing to the huge advantage of using that arrangement - enormous amplification of the relatively tiny magnetic field generated by the conducting windings. Anywhere from 100's up to ~ 1,000,000 times amplification. Also, by being confined to a closed magnetic circuit, the core field does not add unwanted appreciable EM interference to surrounding environment.

Once one accepts the picture (visual aid) of a magnetic field spreading out from a single conductor it follows for all coils.

Not necessarily. It does not follow that what applies to a straight wire carries over to all coil geometries. You get cancellation of magnetic field outside of an 'infinitely long' solenoid, or more practically, a toroidal geometry (analogy - electrostatic field of a charged infinitely long cylinder or torus appears only on the outside, none inside). So, if the primary windings are inside the secondary windings, none or very little field owing to the primary ever intersects the secondary windings. Taking advantage of the huge ferromagnetic core amplifications mentioned above, the kind of 'inverted toroid' geometries mentioned in #39 allow that very little of the net threading flux intersects either primary or secondary windings.

Of course the question is, is that a valid picture? Perhaps I could ask: is the picture of field lines valid? How many lines are there around a current carrying conductor? Why did Gauss need field lines but Coulomb did not?

The advantage of thinking in terms of field lines is that it allows a geometrically and visually neat way of explaining certain relationships. Simply by positing that electrostatic E field lines must begin and end on charge, we arrive at Gauss's law. But Coulomb's mathematical expression for field strength as a function of distance yields the same thing. There is never a need to use the concept of lines, but it can help. In the magnetic case it helps to know that expressed in terms of lines of B, they always form closed loops, given the absence of monopoles. But Biot-Savart expression just gives field strength and direction as a function of source current - no need for lines to enter the picture. And that's really where it's at. The source of both E and B field is always source currents - although, and this point I emphasize, in the case of ferromagnetic media as source, those currents, treated as a collection of Amperian loop currents, are formal and not real. It's a mistake then to think that time-changing B 'causes' an emf in a coil. There is an association between B and E, not a cause-effect relationship. Source of both is always currents - both actual moving charge, and formal as static or time-changing magnetization.

Without Gauss we would perhaps still be in the stone age as far as em theory is concerned because his theory gives an action at a more precise location in space. But all could be explained and viewed as action at a distance.

That last point is questionable when it comes to explaining EM waves. Field concept is there really indispensable, at least according to the overwhelming majority.

 

[andrien]

outside the solenoid,if one want to calculate induced electric field then considering a circular path whose radius R>r,where r is the radius of solenoid.we will have according to faraday law,

E.2∏R=-∂∅/∂t, where ∅=B.∏r²
clearly there is an induced electric field outside when B is varied because of faraday law.
however the region must include changing magnetic field location( the big circle must contain the changing B region).

 

[harrylin]

[..] I see a moving B field whenever dB/dt occurs).

That should give the same answer, but it's a different picture from that of the OP. Faraday's law works for two different cases (and the second is even a whole class, related to relative motion!).
- What the OP refers to is the picture of constant magnetic flux lines, but of varying intensity.
- You seem to picture moving flux lines, such as when a magnet is moved towards a conductor.

- http://en.wikipedia.org/wiki/Faraday's_law_of_induction

 

[Per Oni]

It's just that ferromagnetic core transformers are ubiquitous owing to the huge advantage of using that arrangement - enormous amplification of the relatively tiny magnetic field generated by the conducting windings. Anywhere from 100's up to ~ 1,000,000 times amplification. Also, by being confined to a closed magnetic circuit, the core field does not add unwanted appreciable EM interference to surrounding environment

The way I see the contribution of say a ferromagnetic core is that magnetic randomly aligned domains will be starting to line up. The only way their flux can go around the toroid is by traveling across the air gap (the inner ring) of the toroid. In doing so they will cut all windings.

You get cancellation of magnetic field outside of an 'infinitely long' solenoid, or more practically, a toroidal geometry (analogy - electrostatic field of a charged infinitely long cylinder or torus appears only on the outside, none inside). So, if the primary windings are inside the secondary windings, none or very little field owing to the primary ever intersects the secondary windings. Taking advantage of the huge ferromagnetic core amplifications mentioned above, the kind of 'inverted toroid' geometries mentioned in #39 allow that very little of the net threading flux intersects either primary or secondary windings

.
All the same cancellations will apply in my picture. The vast majority of field lines end up inside the toroid.

I can very well understand the objections to my non scientific approach, however, this model works for me.

That last point is questionable when it comes to explaining EM waves. Field concept is there really indispensable, at least according to the overwhelming majority

OK no problem accepting that.

 

[Q-reeus]

The way I see the contribution of say a ferromagnetic core is that magnetic randomly aligned domains will be starting to line up. The only way their flux can go around the toroid is by traveling across the air gap (the inner ring) of the toroid. In doing so they will cut all windings.

Yes it's proper to think in terms of individual domains aligning with the applied H field. But even without taking into account the mutual effect of adding all such domain fields - which leads to net cancellation exterior to the core, only some typically small fraction of any given domain's field lines intersect the windings. True regardless of domain orientation initially or finally. That becomes evident by studying the field of a dipole - e.g. http://en.wikipedia.org/wiki/Magnetic_dipole In terms of the domain's magnetic contribution to the -d∅/dt emf, all of it's field lines contribute [strictly true only if the core is driven to saturation]. So on that basis alone there is for your model a deficit to explain - no? [STRIKE]Another not so small factor is that, while some lines of a given domain may cut the windings, it's always overall a double-cut, that cancels - i.e. out+in = 0![/STRIKE] [Edit: Actually, thinking about it in terms of individual fictitious monopoles at each end of a magnetic dipole, there can be validity to the notion of line cutting. But given the overall exterior field cancellation, it's not one I'd use. But I do in hindsight concede it can have a certain use even in transformer core case]

OK no problem accepting that.

Glad we have some agreement.

 

[Per Oni]

That should give the same answer, but it's a different picture from that of the OP. Faraday's law works for two different cases (and the second is even a whole class, related to relative motion!).
- What the OP refers to is the picture of constant magnetic flux lines, but of varying intensity.
- You seem to picture moving flux lines, such as when a magnet is moved towards a conductor.

- http://en.wikipedia.org/wiki/Faraday's_law_of_induction

Yeah I realize very well what the op is asking:

BUT! As my friend correctly stated, the only place where the B-field is non zero is inside the solenoid itself. …-dB/dt would have to be zero for all points in space except inside the it. And that means no electric field can possibly have been induced from the varying magnetic field in the solenoid …

Many years ago I was pondering exactly the same question, which is: how can there be an E field in a conductor when there’s no dB/dt in the conductor? I was familiar with the concept that when magnetic field lines cut a conductor an electric field is set up in that conductor. But in case of a transformer (apparently) no lines ever cut the conductor. I therefore developed my own visualisation of a traveling B field. Of course I realized very well that to apply Faradays law for transformers no such picture was required.

At Q-eerus, I’m not sure what the content of your last post is saying.

 

[Q-reeus]

At Q-eerus, I’m not sure what the content of your last post is saying.

And I was guessing to some extent in answering your #59. Any particular part(s) of #60 not clear?

 

[harrylin]

Yeah I realize very well what the op is asking:
Many years ago I was pondering exactly the same question, which is: how can there be an E field in a conductor when there’s no dB/dt in the conductor? I was familiar with the concept that when magnetic field lines cut a conductor an electric field is set up in that conductor. But in case of a transformer (apparently) no lines ever cut the conductor. [..]

Yes, and same for me. I thought to have now answered that most clearly in post #52...
So I'll repeat: The induced E-field spreads out all around the solenoid.
(and sorry for the shouting )

 

[Per Oni]

And I was guessing to some extent in answering your #59. Any particular part(s) of #60 not clear?

In terms of the domain's magnetic contribution to the -d∅/dt emf, all of it's field lines contribute [strictly true only if the core is driven to saturation]. So on that basis alone there is for your model a deficit to explain - no?

I don’t get this question .

@ harrylin: Yeah ok I do hear you. I know what you are saying, no problem. Faradays law says so. I knew that years ago.

 

[harrylin]

[..]
@ harrylin: Yeah ok I do hear you. I know what you are saying, no problem. Faradays law says so. I knew that years ago.

If you knew that Faradays law (although I think in fact Maxwell's) says that a varying B-field induces an E-field all-around (and not just at a distance), then why did you ask how can there be an E field in a conductor at that place?

 

[Per Oni]

If you knew that Faradays law (although I think in fact Maxwell's) says that a varying B-field induces an E-field all-around (and not just at a distance), then why did you ask how can there be an E field in a conductor at that place?

Because at that time I wasn’t happy just to cram that law in my head without any visualisation.
My dilemma was: when considering motional emf we insist on the conductor cutting magnetic flux (or visa versa). No flux cutting = no emf.
Next step was: forget all such considerations when dealing with transformer emf. No flux cutting needed. No flux cutting = lots of emf.

 

[harrylin]

Because at that time I wasn’t happy just to cram that law in my head without any visualisation.
My dilemma was: when considering motional emf we insist on the conductor cutting magnetic flux (or visa versa). No flux cutting = no emf.
Next step was: forget all such considerations when dealing with transformer emf. No flux cutting needed. No flux cutting = lots of emf.

I'm afraid that I can't follow that, and perhaps suggest a personal theory, so let's not got there!

The first 6 min. of the following video going into details about applying Faraday's law may be useful:
http://www.youtube.com/watch?v=EYYNRubHIno&NR=1&feature=endscreen

 

[Q-reeus]

Q-reeus: "In terms of the domain's magnetic contribution to the -d∅/dt emf, all of it's field lines contribute [strictly true only if the core is driven to saturation]. So on that basis alone there is for your model a deficit to explain - no?"
I don’t get this question .

Well I took it you basically stated in #59 that the field lines of an aligning domain, in cutting the windings surrounding the transformer core, fully explain the induced emf. Obviously that's after summing over all domains. My point on that in #60 was this could not be so as typically only a tiny fraction of a domain's field lines exit the core region - depending on just where a domain is situated in the core of course. Vast majority of lines simply loop back on themselves 'internally' - within the core region. Nevertheless when domains are fully or near fully aligned, there is a strong *internal* reinforcement of domain flux lines to give a large net field strength B, and it's this reinforced internal value - confined to the core, that governs the driving emf = -AdB/dt (A the X-sectional core area) seen in the windings. This net core B is considerably greater in fact than that typically existing inside a randomly oriented domain. So do you now get why I said your idea had a big deficit problem?

[I take this back - it wasn't ringing quite true and now I see why. Hadn't taken into account the 'velocity leverage factor' that would apply to flux-cutting owing to a rotating domain. Few lines compensated by large relative motion of those lines. Kind of dovetails as per #60 with the notion of changing core flux being seen as a magnetic monopole displacement current - if one substitutes 'true magnetic dipoles' for Amperian loop currents. It's clearer then how motion of monopoles could achieve the flux-cutting needed to explain emf - particularly evident in long straight solenoid case. All such being fictitious entities but equally able to give consistent results re observed emf. Still, best to stick with that actual source of emf is overwhelmingly owing to -dM/dt, M owing to intrinsic moments.]

 

[Per Oni]

I'm afraid that I can't follow that, and perhaps suggest a personal theory, so let's not got there!

When considering motional emf we insist on the conductor cutting magnetic flux (or visa versa). No flux cutting = no emf.

When dealing with transformer emf, no flux cutting is needed. No flux cutting = lots of emf.

Which of these 2 sentences can you not follow (perhaps both)? Those sentences have nothing to do with a personal theory!

@ Q-eerus: I think it will be better for us to start a new thread about magnets. This is getting a bit too far removed from the OP.

 

[Q-reeus]

@ Q-eerus: I think it will be better for us to start a new thread about magnets. This is getting a bit too far removed from the OP.

Maybe. But anyway I have erred - see edit in #68

 

[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.

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.

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! :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.

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!