Faraday's Law: False Claim & Feynman's Critique

[cabraham]

Claude,

Where do you get the idea that FL requires the cutting of magnetic flux lines? It only addresses the time rate of change of flux linkage. In the case we are discussing, the flux linkage starts out as the number of turns of the secondary winding times the flux in the core. It ends up as zero when that winding is fully unwound, so there is certainly a flux change, and therefore FL specifies an EMF. By the way, there is no frequency involved here. If the secondary is unwound at a constant rate, the time rate of flux change will be constant.

Mike

Where did you get the idea that FL does NOT require the cutting of flux lines. The cutting is spelled out in the vector equation "u X B". The cross product of velocity U and magnetic flux density B is 0 when the velocity is along a flux line. Since the angle is 0 along a flux line, the cross product is also 0. Cutting means 90 degrees, hence the cross product is maximized.

This is so well known, I'm amazed you even bring it up. An experiment in the basement will affirm this.

When the winding is undone, there is a velocity, and you must consider the magnitude and direction of the flux. I've given the computations above that v is in nanovolts. Depending on dimensions, it could even approach microvolts. You'd need good equipment to measure, but it's there.

When you and I are long gone, FL wil be standing like Gibraltar.

Claude

 

[MS La Moreaux]

Claude,

The "u x B" expression is part of the equation for the Lorentz force, gives the motional EMF, and has nothing to do with Faraday's Law, which is EMF = dPhi/dt and involves the change of flux linkage only. The wire of the circuit does not even have to be in the magnetic field as long as it is linked by it.

Mike

 

[cabraham]

Claude,

The "u x B" expression is part of the equation for the Lorentz force, gives the motional EMF, and has nothing to do with Faraday's Law, which is EMF = dPhi/dt and involves the change of flux linkage only. The wire of the circuit does not even have to be in the magnetic field as long as it is linked by it.

Mike

Sorry, but it has everything to do with FL. The "dphi/dt" quantity is related to "u X B". In order to obtain non-zero emf/mmf, the flux must be time-changing with respect to the conductor.

When the conductor moves through a static field, the time rate of change seen by said conductor is u X B. Along a flux line gives 0, since the cross product goes to 0 for 0 angle. Across the flux line gives maximum induction. For an oblique angle, the component of motion in the direction normal to B is used for computation of emf.

As far as your statement "The wire of the circuit does not even have to be in the magnetic field as long as it is linked by it." goes, I don't even know where to begin. How can the conductor not be in the field, yet be linked by it? Would you please draw an illustrative diagram? Please clarify your counter-examples to FL. A picture would help immensely. So far you're shooting blanks. Nothing you've stated has a remote chance of invalidating FL.

Just curious, how much e/m field theory have you taken? To challenge an established axiom is quite ambitious for just about anyone. Do you have the academic knowledge sufficient for such an ambitious undertaking? Based on what you've stated thus far, I believe that with your current e/m fields skill set, challenging axioms is too ambitious for you.

Claude

 

[chrisphd]

When one asks what is the physical principle behind a law, one must determine whether mathematical consequences of the law are most fundamental or if the law itself is most fundamental. For example, Maxwell's equations lead to Einstein's postulate of relativity that the speed of light (laws of physics) is (are) the same for all inertial observers. One might then make the claim that Einstein's postulate is in fact more fundamental than Maxwell's Equations.

When one takes this view, assuming only the postulates of relativity and assuming Electric fields exists due to charged sources, one can easily deduce the appearance of the presence of a force in certain reference frames with properties that exactly match that of the so called "magnetic field". That is, the magnetic force in this view can be regarded as pseudo force directly derivable from more fundamental postulates. (ie, relativity and electric field)

In other words, this means that the behavior of charged particles can be exactly predicted merely by assuming Einstein's postulates in relativity and that charged particles produce an electric field thus removing the necessity of the magnetic field (whereas without Einstein's postulates, the behavior of charges couldn't be explained without the presence of magnetic field).

In order to get back Maxwell's equations, you examine how the equations from the above analysis transform if one were to neglect the postulate of relativity. By doing this it is then possible to derive Maxwell's equations including Faraday's Law.

In this sense, one may then say the physical basis for Faraday's Law is the postulates of relativity.

(Note: Faraday's law did come first, but was purely empirical. It was then able to be used to drive Einstein to think of more fundamental postulates. These fundamental postulates are then the physics behind our empirically observed Faraday's Law)

 

[cabraham]

When one asks what is the physical principle behind a law, one must determine whether mathematical consequences of the law are most fundamental or if the law itself is most fundamental. For example, Maxwell's equations lead to Einstein's postulate of relativity that the speed of light (laws of physics) is (are) the same for all inertial observers. One might then make the claim that Einstein's postulate is in fact more fundamental than Maxwell's Equations.

When one takes this view, assuming only the postulates of relativity and assuming Electric fields exists due to charged sources, one can easily deduce the appearance of the presence of a force in certain reference frames with properties that exactly match that of the so called "magnetic field". That is, the magnetic force in this view can be regarded as pseudo force directly derivable from more fundamental postulates. (ie, relativity and electric field)

In other words, this means that the behavior of charged particles can be exactly predicted merely by assuming Einstein's postulates in relativity and that charged particles produce an electric field thus removing the necessity of the magnetic field (whereas without Einstein's postulates, the behavior of charges couldn't be explained without the presence of magnetic field).

In order to get back Maxwell's equations, you examine how the equations from the above analysis transform if one were to neglect the postulate of relativity. By doing this it is then possible to derive Maxwell's equations including Faraday's Law.

In this sense, one may then say the physical basis for Faraday's Law is the postulates of relativity.

(Note: Faraday's law did come first, but was purely empirical. It was then able to be used to drive Einstein to think of more fundamental postulates. These fundamental postulates are then the physics behind our empirically observed Faraday's Law)

You treat magnetic fields as fictituous, pseudo, & derived. Yet Einstein emphasized in his 1905 paper, that elec & mag forces are equally important, and that neither is the "seat". Nobody has successfully refuted this viewpoint.

So in a nutshell, the OP claimed that FL is false. What are you saying? Is FL true or false? Please answer. You gave your treatise but never answered the original question explicitly. Thanks in advance.

Claude

 

[WiFO215]

The version of Faraday's Law which purports to include both motional EMF and transformer EMF for circuits is false. There is no theoretical basis for it. Richard Feynman, in his "Lectures on Physics," pointed out the fact that this so-called law, what he called the "flux rule," does not always work and gave two examples. Every textbook and encyclopedia that I know of treats it as a true law. There is a lot of confusion and nonsense related to it. I believe that it is an indictment of the status quo and a scandal.

I am going to reply only to post #1 quoted above. I understand your question MSLM as it is a question that comes up often. Here is the problem:

Maxwell's equations themselves don't define EMF. EMF is defined as the line integral of the force per unit charge, the line integral done along the line you wish to calculate the EMF across.

EMF = \epsilon = \int_{a}^{b} (E + [v \times B]).dl

In certain cases, it so happens that the above equation simplifies to
\epsilon = - \frac{d \phi}{dt}.

In such cases, you will have to revert to the above definition.

Faraday's law is

\nabla x E = - \frac{\partial B}{\partial t}

or in integral form can be written as

\int E.dl = - \frac{d \phi}{dt} (This is only for stationary integral paths)

and is not to be confused with

\epsilon = - \frac{d \phi}{dt}

which does not work all the time. For instance, in your example above, the whole equation is ill-suited.

 

[chrisphd]

To Claude:
Just as magnetic fields can be derived from Einstein's postulates and the Electric field, one can also use gravitational fields and Einstein's postulates to derive a psuedo gravitational field that is analogous to the magnetic field in electromagnetism. However this pseudo gravitational force is always regarded as fictitious. One may ask, why is the pseudo gravitational force fictitious but magnetism isn't?
The answer is that magnetism was empirically observed first, and those who observed it thus believed it was real as they had no grounds to claim it was fictitious at the time. Had humans been the size of planets, we would have noticed the pseudo gravitational fields first and called these real and magnetic fields fictitious. Basically you can see that neither the pseudo gravitational force or the pseudo electric force should have any fundamental physical priority over the other.

However, in saying that, these ideas of what forces are derived and what are real is purely a matter of "interpretation", analogous to the various interpretations of quantum mechanics. They are different ways of thinking about theories that lead to the same physical conclusions. For example, one could claim only magnetic forces are real and use Einstein's postulates to derive the electric force. This is what Einstein means when he says that neither can take the "seat".

Physically my intuition prefers to accept that electric forces are real because magnetic forces have no monopoles, where as electric forces do. It is thus easier to think of these monopoles as the sources of the charge, and the magnetic force being pseudo. This is the same situation for gravitational fields.

With regards to the openers question:
The opener believed there was no theoretical/intuitive basis for the existence of Faraday's law. I disagree and a valid physical basis is Einstein's postulates and the electric field. From this basis, Faraday's law can be derived.
This means that since Faraday's law is not itself fundamental (ie, based on the fundamental postulates listed), deviations observed from Faraday's law can be attributed to slight errors in the underlying fundamental postulates. For example, if only general relativity applies to a particular problem, then a new version of Faraday's law may be derivable using Einstein's principle of general relativity as opposed to the special theory. The point being however, is that one may know when Faraday's law is applicable, by seeing if its fundamental basis is also applicable to the situation you wish to model.

 

[cabraham]

To Claude:
Just as magnetic fields can be derived from Einstein's postulates and the Electric field, one can also use gravitational fields and Einstein's postulates to derive a psuedo gravitational field that is analogous to the magnetic field in electromagnetism. However this pseudo gravitational force is always regarded as fictitious. One may ask, why is the pseudo gravitational force fictitious but magnetism isn't?
The answer is that magnetism was empirically observed first, and those who observed it thus believed it was real as they had no grounds to claim it was fictitious at the time. Had humans been the size of planets, we would have noticed the pseudo gravitational fields first and called these real and magnetic fields fictitious. Basically you can see that neither the pseudo gravitational force or the pseudo electric force should have any fundamental physical priority over the other.

However, in saying that, these ideas of what forces are derived and what are real is purely a matter of "interpretation", analogous to the various interpretations of quantum mechanics. They are different ways of thinking about theories that lead to the same physical conclusions. For example, one could claim only magnetic forces are real and use Einstein's postulates to derive the electric force. This is what Einstein means when he says that neither can take the "seat".

Physically my intuition prefers to accept that electric forces are real because magnetic forces have no monopoles, where as electric forces do. It is thus easier to think of these monopoles as the sources of the charge, and the magnetic force being pseudo. This is the same situation for gravitational fields.

With regards to the openers question:
The opener believed there was no theoretical/intuitive basis for the existence of Faraday's law. I disagree and a valid physical basis is Einstein's postulates and the electric field. From this basis, Faraday's law can be derived.
This means that since Faraday's law is not itself fundamental (ie, based on the fundamental postulates listed), deviations observed from Faraday's law can be attributed to slight errors in the underlying fundamental postulates. For example, if only general relativity applies to a particular problem, then a new version of Faraday's law may be derivable using Einstein's principle of general relativity as opposed to the special theory. The point being however, is that one may know when Faraday's law is applicable, by seeing if its fundamental basis is also applicable to the situation you wish to model.

Wll then, it looks like we agree after all. My understanding of relativity has been that just as an H field can be regarded as a relativistic view of an E field, so can an E field be viewed as a relativistic view of an H field. We do agree. Einstein emphasized this and regarded neither as the "seat".

Regarding monopoles, many prefer to start with E, and then view H as a relativistic manifestation of E. Their reasoning is along your lines, that monopoles exist for E, but not for H. Although you have the correct viewpoint that either can be the relativistic view of the other, some firmly, and wrongly, insist that E is the seat since H has no monopoles, while E does.

But if we examine FL, the OP original question, there is a marked difference between E fields due to discrete charged particles, i.e. monopoles, vs. E fields due to induction/Faraday. With monopoles, the E lines have a source and a sink (start and end), whereas H fields do not since H is di-polar, not monopolar. H lines are closed loops, or "solenoidal" in nature. Solenoidal flux lines indicates di-pole and NOT monopole since monopoles have a start and an end. Also, discrete charge E fields are conservative, whereas induction/solenoidal E fields are non-conservative.

But the E fields induced per FL are solenoidal in nature. They have no start or end. They look like H loops. Although E monopoles do exist, that is not what happens when E fields are induced due to time-varying H fields. These E lines do not have a monopolar like appearance.

Correct me if I'm wrong, but E lines with start and end points, DO NOT relativistically transform into solenoidal closed loops in a moving reference frame. What is happening here does not involve monopoles. Thus I cannot accept the existence of E monopoles and the non-existance of H monopoles as a basis for treating E as more basic than H. Also, conservative E fields do not transform to non-conservative under relativistic transformations.

We agree that neither is the seat, and we also agree with Einstein, so I think we hold a safe position. Thanks for your input.

Claude

 

[Archosaur]

Nowhere in his lectures does Feynman question the validity of Faraday's Law.
He merely adressed the issue of scale, which puts limits on the applications of every law.

General Relativity breaks down on a small scale, and quantum mechanics takes over, but neither is more or less "valid". Since we haven't discovered the infamous "Theory of Everything", we have to break physics into separate models with particular jurisdictions.

 

[MS La Moreaux]

Claude,

FL is not related to u x B and says nothing about time-changing flux with respect to a conductor. EMF = - d\Phi/dt is the whole of FL with the only restriction being that it only applies to circuits.

A simple case of a flux linkage without the conductor being in the magnetic field is a magnetic flux confined to a tube threading a circuit without touching the wire of the circuit. Transformer EMF does not even require a circuit, just a closed path. An intrinsically time-varying magnetic field produces an electric field. Any closed path within this electric field which has a magnetic flux linkage will have an EMF.

I do not know at this point how to get a drawing into my reply. I will try to find out later. The homopolar generator is clearly a case of steady state operation. There is no flux change. To a first approximation, the magnetic flux lines are parallel to the plane of the circuit, so there is no flux linkage. FL gives an EMF of zero because of the zero flux change, which is completely wrong.

In the case of the modified toroidal transformer, there is a constant flux in the core. The secondary winding is gradually unwound, obviously eventually eliminating its flux linkage to the core flux. The slip ring and brush combination is just to allow the winding to be unwound without breaking the circuit. There is obviously a change in the flux linkage, and so FL predicts an EMF, which could be substantial if the core flux is big and the unwinding is fast. There is no intrinsic change of flux, so Maxwell's Law for transformer EMF does not apply. For a theoretical example I see no reason not to assume no magnetic field leakage from the core. Therefore there is no motional EMF. Since between them transformer EMF and motional EMF cover all cases, there is no EMF

I have a bachelor of science in engineering degree in electrical engineering from the University of Michigan. It seems that, unlike others, I actually understand Faraday's Law, and was able to spot the inconsistencies and pure nonsense surrounding it in the textbooks. It seems from your comments that your understanding of the subject is between minimal and nonexistent.


chrisphd,

The version of FL we have been discussing cannot be derived.


anirudh215,

You are confusing the FL we have been discussing with one of Maxwell's Laws. The version of relevance utilizes the ordinary derivative, not the partial derivative.


Archosaur,

When you say that nowhere in his lectures does Feynman question the validity of FL, you are wrong. See these previous posts in this thread: Phrak Oct 11-09, 11:53 PM and my post of Oct 15-09, 08:14 PM.

Mike

 

[WiFO215]

anirudh215,

You are confusing the FL we have been discussing with one of Maxwell's Laws. The version of relevance utilizes the ordinary derivative, not the partial derivative.

You can convert the partial derivative to the ordinary derivative using Stokes' theorem.

http://en.wikipedia.org/wiki/Stokes'_theorem

What I stated above was Faraday's law in differential form; below that I also stated it in integral form.

 

[cabraham]

Claude,

FL is not related to u x B and says nothing about time-changing flux with respect to a conductor. EMF = - d\Phi/dt is the whole of FL with the only restriction being that it only applies to circuits.

A simple case of a flux linkage without the conductor being in the magnetic field is a magnetic flux confined to a tube threading a circuit without touching the wire of the circuit. Transformer EMF does not even require a circuit, just a closed path. An intrinsically time-varying magnetic field produces an electric field. Any closed path within this electric field which has a magnetic flux linkage will have an EMF.

I do not know at this point how to get a drawing into my reply. I will try to find out later. The homopolar generator is clearly a case of steady state operation. There is no flux change. To a first approximation, the magnetic flux lines are parallel to the plane of the circuit, so there is no flux linkage. FL gives an EMF of zero because of the zero flux change, which is completely wrong.

In the case of the modified toroidal transformer, there is a constant flux in the core. The secondary winding is gradually unwound, obviously eventually eliminating its flux linkage to the core flux. The slip ring and brush combination is just to allow the winding to be unwound without breaking the circuit. There is obviously a change in the flux linkage, and so FL predicts an EMF, which could be substantial if the core flux is big and the unwinding is fast. There is no intrinsic change of flux, so Maxwell's Law for transformer EMF does not apply. For a theoretical example I see no reason not to assume no magnetic field leakage from the core. Therefore there is no motional EMF. Since between them transformer EMF and motional EMF cover all cases, there is no EMF

I have a bachelor of science in engineering degree in electrical engineering from the University of Michigan. It seems that, unlike others, I actually understand Faraday's Law, and was able to spot the inconsistencies and pure nonsense surrounding it in the textbooks. It seems from your comments that your understanding of the subject is between minimal and nonexistent.
chrisphd,

The version of FL we have been discussing cannot be derived.


anirudh215,

You are confusing the FL we have been discussing with one of Maxwell's Laws. The version of relevance utilizes the ordinary derivative, not the partial derivative.


Archosaur,

When you say that nowhere in his lectures does Feynman question the validity of FL, you are wrong. See these previous posts in this thread: Phrak Oct 11-09, 11:53 PM and my post of Oct 15-09, 08:14 PM.

Mike

I already explained that u X B is related to -N*dphi/dt, if you consider the relative motion between the conductor and static magnetic field. With a stationary conductor, the field must change in order to obtain induction. FL covers this. But if the field is static with the conductor moving, consider the scenario from the conductor's moving reference frame. The conductor "sees" a time-varying magnetic field. When I have time, I'll compute the math based on relative motion, and the u X B in the moving frame should map into -N*dphi/dt in the rest frame. They are equivalent.

As far as my understanding of FL being "between minimal and nonexistent", here is my reply. That is a pretty bold statement from someone with a mere BS. I have about a year or less left on the Ph.D. (EE). I worked in the magnetic components design group for 4 years in the 1980's for a fortune 50 company famous for transformers. I used FL on a daily basis. Since then, I've designed some custom transformers for switching power converters.

You don't know as much as you think. At the BS level, one can only accept e/m field teachings on faith. It takes post graduate study and/or working in the field to really digest it. If you "saw its inconsistencies" in undergrad, you are super-human, which I don't believe you are.

My understanding agrees with the peer-reviewed texts and publications. Who are you to say otherwise? I'll try to make time this weekend to compute the equivalence between "N*dphi/dt" & "u X B".

Claude

 

[WiFO215]

@Claude http://xkcd.com/386

 

[MS La Moreaux]

anirudh215,

In your reference it states, under "In electromagnetism," "Caution must be taken to avoid cases with moving boundaries: the partial time derivatives are intended to exclude such cases."

Mike

 

[MS La Moreaux]

Claude,

If u x B were included in FL, FL would not fail in the case of the homopolar generator. Your work with transformers is irrelevant because the applicable law was Maxwell's Law for transformer EMF, which is included in FL. That is not the problem with FL. FL both includes too much and not enough, but it does include every case where that one of Maxwell's Laws applies. So one does not have to take post graduate teachings on faith, eh? It seems to me that all of science is based upon faith in natural laws, which cannot be proved. You are not the first post graduate that I have run across that did not know what he was talking about. In regard to FL, the writings of Richard Feynman agree with me. He certainly had more than a mere BS. And he disagreed with the peer-reviewed texts and publications.

Mike

 

[cabraham]

Claude,

If u x B were included in FL, FL would not fail in the case of the homopolar generator. Your work with transformers is irrelevant because the applicable law was Maxwell's Law for transformer EMF, which is included in FL. That is not the problem with FL. FL both includes too much and not enough, but it does include every case where that one of Maxwell's Laws applies. So one does not have to take post graduate teachings on faith, eh? It seems to me that all of science is based upon faith in natural laws, which cannot be proved. You are not the first post graduate that I have run across that did not know what he was talking about. In regard to FL, the writings of Richard Feynman agree with me. He certainly had more than a mere BS. And he disagreed with the peer-reviewed texts and publications.

Mike

But u X B[/b} IS included in FL. I've stated this repeatedly, but you won't listen. One more time.

The eqns. "v = -N*dphi/dt", and " v integral E*dl, where E = u X B", are stating the exact same thing. If a conductor moves within a static mag field, it encounters a spatial flux distribution that varies with position in space, and thus it varies in time. If the conductor is stationary and the magnet moves, then the field encountered by the conductor is time-varying.

The conductor in both cases, encounters a flux, phi, that is varying wrt time. The emf is "-N*dphi/dt", in the reference frame of the conductor. If, however, an observer in the rest frame is viewing the conductor moving relative to the magnet, and wishes to compute the resultant emf, they use E = u X B, then v = integral E*dl, around the path of the loop encircling the flux.

So FL, which states that v = -N*dphi/dt, is complete. As long as it is understood what frame of reference we are using. Motors and generators illustrate my point. Take an ac synchronous motor/generator. One can place the dc field on the stator. The rotor spins through said field, and the rotor emf can be computed. In the rotor's frame of reference, the rotor is at rest, and the stator is spinning the opposite direction. The rotor winding encounters a spatial flux pattern that changes with time. Hence v = N*dphi/dt. The stator's field is static wrt to an observer at rest, but time-changing from the rotor reference frame.

But a stationary observer, or the stator, are both at rest and see the rotor spinning. The emf on the rotor is given by the u X B relation. The stationary observer only sees a static mag field on the stator, and sees the rotor spinning through this static field. The reason for u X B is to compensate for reference frames. Since we seek to know the rotor emf, we must transform from our static frame to that of the spinning rotor. Hence the motional action and the transformer action are essentially one and the same action viewed from 2 different reference frames.

You're making this much harder than it really is. Please show this treatise of mine to your trusted gurus, colleagues, profs, or whomever you deem credible. If I've erred, let them point it out.

We could also place the dc field on the rotor instead, and measure the induced emf on the stator as well. The same principles apply. It's all about relative motion between the 2 reference frames.

Seriously, that's all there is to it. You can make it harder if you wish, but I've given you exactly what peer-reviewed texts, and experts in the field have empirically verified for over a century.

I know that my xfmr design skill is not directly applicable to motional action, but I design, past and present, dc motor drives for actuators, missile guidance, pumps, compressors, etc. Included is regenerative braking (motional emf/mmf). I have substantial experience with motional action as well as static.

Oh yeah, you said "You are not the first post graduate that I have run across that did not know what he was talking about". Well, how much experience/skill do YOU have with motors, xfmrs, generators, induction heating, etc.? Is there any transducer work in your past such as microphones, speakers, etc.? What have you done to be the expert on motional emf? I'm not attacking you, but I'm just curious what makes you think you are head and shoulders above qualified experts. You have a BS, a good achievement. A BS qualifies you to do some good work in science to produce products that benefit mankind.

But to topple established axioms requires much much much much more. A PhD in phy or EE is still not enough. You'd need a huge lab, budget, and staff with accelerators, scanning microscopes, etc. to advance Maxwell's equations to a new level. Your BS is a useful degree which empowers you to a limited degree.

Even should I get my PhD, and with my 32 yrs. of engr background, I am still NOT qualified to topple Faraday. Here's what you and I have in common - we both have limited knowledge.

Here is where we differ - I am well aware that my knowledge is too limited to go challenging Faraday. Nothing personal, thanks for the interesting chat. Good day.

Claude

 

[WiFO215]

anirudh215,

In your reference it states, under "In electromagnetism," "Caution must be taken to avoid cases with moving boundaries: the partial time derivatives are intended to exclude such cases."

Mike

Please look up how

\epsilon = -\frac{d \phi}{dt}

is derived from Maxwell's equations. I too have the read the Feynman lectures and I strongly feel that was not what Feynman tried to convey. Feynman disagrees that

\epsilon = -\frac{d \phi}{dt}

includes all cases. That is true. It does not include all cases. The most popular example to show that it does not include all cases is the example that you yourself have stated. In such a case, the path of the current is itself not clear and applying the above law does not hold good. The above law is NOT Faraday's law. I have already stated Faraday's law above. When using the law that I have stated, indeed, the integral IS done around a stationary path.

Why don't you take up some standard text like Griffiths' Introduction to Electromagnetism or Schwartz's Principles of Electrodynamics and look this up? It is quite lucidly explained. The vxB part is definitely included in the flux rule which you have stated above.

 

[MS La Moreaux]

anirudh215,

I do not believe that we really have much of a disagreement. You agree that the flux rule does not work in all cases. Therefore it is not a law. You claim that it is not Faraday's Law. Some texts give it as FL and others give one of Maxwell's Law as FL. That Maxwell's Law is true. This entire thread treats the version of FL which is identical to the flux rule. If you insist that FL is not the flux rule, that is a completely separate argument and does not belong in this thread. Personally, I do not see why one law should have two different names.

Mike

 

[MS La Moreaux]

Claude,

If a conductor moves within a uniform magnetic field, it will not encounter a spatial flux distribution that varies with space or time. This is the case with a homopolar generator with a uniform magnetic field penetrating the entire disk. This is a case of pure motional EMF with no time-varying magnetic flux and thus separates the two for analysis. It demonstrates that FL is false.

Do you have any experience with homopolar generators? I imagine that it would be difficult to design one using FL since it does not apply, although it claims to.

It seems to me that FL is very simple. People bring in all sorts of extraneous and incorrect nonsense that might seem to relate to it, but does not really. I am just using logic to analyze FL. I have addressed points which I have never seen addressed by anyone else. I have proved my case.

Mike

 

[sokrates]

You have never had a case (Just look at the title of this thread).

ZapperZ put the period to this. Your point is unsustainable due to many reasons none of us have time to belabor on.

Why don't you think of publishing your results as a groundbreaking discovery?

Every law has its limits, Feynman NEVER intended to convey what you wish here. I read the relevant chapters more than once. That's not the message. I'd advise you to go back and read it more carefully. He himself would have been furious by the idea of using his name for a baseless claim.

You probably did not even do any of these experiments yourself, and the VERY relevant experimental point (due to Per Oni) of eddy currents are "cleverly" ignored with a comment by you saying: "No, I don't think so". Edit: (Post#51)Theory by itself only goes this far. You start reinventing your own laws.

 

[WiFO215]

anirudh215,

I do not believe that we really have much of a disagreement. You agree that the flux rule does not work in all cases. Therefore it is not a law. You claim that it is not Faraday's Law. Some texts give it as FL and others give one of Maxwell's Law as FL. That Maxwell's Law is true. This entire thread treats the version of FL which is identical to the flux rule. If you insist that FL is not the flux rule, that is a completely separate argument and does not belong in this thread. Personally, I do not see why one law should have two different names.

Mike

Well, why SHOULD it be true; simply because it has the tag name law? For instance, Ohm's LAW is not a law in the sense it is ALWAYS true and it is fairly easy to spot cases where it does not work. As already stated, LAWs have limitations. Their purpose is only suited for certain things. That doesn't exactly make them wrong.

As to the question of why there ought to be two different names, the FL that I stated was for stationary integral paths.

The flux rule, on the other hand, also deals with moving circuits. A popular example for this would be the "rod on rail track" wherein a rod is placed on a rail track perpendicular to which a magnetic field passes through. Given a velocity 'v', the EMF in the loop can be calculated using the flux rule. I am sure you would have seen this example often.

 

[cabraham]

Claude,

If u x B were included in FL, FL would not fail in the case of the homopolar generator. Your work with transformers is irrelevant because the applicable law was Maxwell's Law for transformer EMF, which is included in FL. That is not the problem with FL. FL both includes too much and not enough, but it does include every case where that one of Maxwell's Laws applies. So one does not have to take post graduate teachings on faith, eh? It seems to me that all of science is based upon faith in natural laws, which cannot be proved. You are not the first post graduate that I have run across that did not know what he was talking about. In regard to FL, the writings of Richard Feynman agree with me. He certainly had more than a mere BS. And he disagreed with the peer-reviewed texts and publications.

Mike

In the homopolar generator case, HG, it is Hall effect & Lorentz force acting on the free electrons resulting in "induced current". It is not Faraday.

One thing that seems to have escaped all of us, and I'm just as embarassed, is that the induced current in an HG is dc! As in zero frequency. Surely this cannot be per Faraday. Something else is happening outside of FL (Faraday's law).

I design power electronics including switching power supplies & motor drivers. I always need to sense current. I've used low-valued resistors, transformers, & Hall effect sensors to do so. One of the limitations with current xfmrs is the inability to operate to dc (0 freq). A Hall device, OTOH, does not have this limitation.

The output terminals of a Hall device present a voltage which is galvanically isolated from the input terminals, and is a facsimile of the input current. Hence a current through the input terminals induces a voltage at the output terminals galvanically isolated. According to FL, this happens only under ac conditions, never with dc! This does not invalidate FL, it just shows that there is another separate means by which induction takes place.

The HG is such an example. The flux through the disk is dc, as is the induced current. The free electrons incur a Lorentz force since the electrons have a velocity as the disk is spinning, oriented normal to the B field. The force is directed radially outward for positive current, inward for electrons for example, ref magnet polarity & rotational direction. Clearly a dc flux inducing a dc current cannot be per FL.

Faraday published his findings well before Hall discovered the effect in 1879. Lorentz published his force relation just after 1890, I believe. Maxwell finalized his equations, publishing them in 1873, including FL. Hall-Lorentz force acting on free electrons requires no time rate of change, operating down to zero freq.

FL, including motional emf, is still valid, but does not encompass all induction. The HG does not disprove Faraday, but simply demonstrates that Hall-Lorentz force is present as well.

As long as I can remember, "Hall effect devices", and "transformers" are NOT the same thing, although both involve induction, where galvanic isolation occurs. Likewise, motional emf as in generators and motors, per FL, are not the same as Hall induced action.

I don't see any "paradox" whatsoever. The HG operates with dc flux & dc induced current, on the Hall-Lorentz principle. Other generators operate per FL, which only works with ac.

Any comments/feedback are welcome. Cheers.

Claude

 

[MS La Moreaux]

Claude,

It is good to hear from you, again. I am afraid that we still disagree. The operation of the HG has nothing to do with the Hall effect. It is an example of pure motional EMF, which is synonymous with the magnetic part of the Lorentz force. Both motional EMF and the Hall effect are direct applications of the definition of the magnetic field. The Hall effect does not involve motion (excepting the current electrons.) FL supposedly includes motional EMF, something with which you agree. The HG, being an instance of motional EMF, and having no flux change, should, according to FL, produce no EMF, but does, thus showing the failure of FL. FL does not specifically address either ac or dc. It simply purports to explain induction in a circuit solely by means of time rate of magnetic flux change, caused either by an intrinsic change in the magnetic field, or by motion. If the rate of flux change is constant, it predicts dc.

Mike

 

[cabraham]

But FL does not say that no flux change produces no induction. It says that a flux change produces induction. FL is stated as a positive, and does not mention the negative.

In addition to Lorentz, a current can be "induced" in a galvanically isolated circuit by optical coupling. Have you used optocouplers? The flux due to current in the input LED is static. There is a current in the output transistor due to optical coupling. Optical transfer is yet another way to couple energy.

FL states 2 ways for energy to be transferred between isolated networks, xfmr & motional. Lorentz covers another case extending to dc, whereas FL does not. Optical transfer is another way. I use xfmrs, Hall devices, & optocouplers, all in order to transfer energy and/or info across isolation boundaries.

The flux is static in an HG and yet there is a current (dc). FL says a time changing flux induces a current. FL does not state that a static flux results in no current. That is just a hangup. Obviously there is something besides FL at work, namely Lorentz. Tonight I'll post a treatise on the HG based on special relativity.

Claude

 

[MS La Moreaux]

Claude,

FL is purported to cover both transformer and motional EMF. Motional EMF is mistakenly supposed to be the result solely of flux change. Either it is or it is not. If FL is supposed to cover motional EMF, it would have to do so in every case, including those where the flux change is zero. You see that motional EMF is independent of flux change. It should never be associated with flux change. They are two completely different phenomena. Again, motional EMF and what you are referring to as Lorentz are identical.

There is no magnetic flux involved in optocouplers. They act as switches. They do not really transfer energy between systems so much as transfer a signal. They have nothing to do with electromagnetic induction.

Mike

 

[cabraham]

Claude,

FL is purported to cover both transformer and motional EMF. Motional EMF is mistakenly supposed to be the result solely of flux change. Either it is or it is not. If FL is supposed to cover motional EMF, it would have to do so in every case, including those where the flux change is zero. You see that motional EMF is independent of flux change. It should never be associated with flux change. They are two completely different phenomena. Again, motional EMF and what you are referring to as Lorentz are identical.

There is no magnetic flux involved in optocouplers. They act as switches. They do not really transfer energy between systems so much as transfer a signal. They have nothing to do with electromagnetic induction.

Mike

Please review the attached, as it explains the HG using SR. In a nutshell, the Lorentz force moves electrons towards the center of the disk and holes (+ve charge) towards the rim. This charge separation results in a static E field and potential. Separation of charges explains the static nature of the E field. The current density J is related per J=sigma*E, which is Ohm's law.

Regarding FL, you firmly state that FL is valid for xfmr induction, i.e. time-varying flux. You state that it must be true always, and that with static flux, no inducton can take place. Yet a Hall effect current sensor produces induction with static flux. A xfmr cannot do this. So there is something else going on here. In a HG, the flux & induced current/voltage are static. FL relates the induced I/V to the change rate of the flux. Motional emf/mmf is due to the flux spatially varying so that the actual flux encountered by the circuit is time changing. Moving through a spatial flux change results in a time varying flux in the circuit reference frame.

Thus if phi varies with spatial position r, and velocity u is dr/dt, then d(phi)/dr * dr/dt = d(phi)/dt, by the chain rule. So FL covers this aspect of induction. Moving through a flux that is static wrt time, but varying wrt position, is equivalent to sitting still with the flux time-varying.

The HG is best explained by Lorentz force & relativity. Remember in a HG, we set the electrons in motion by expending energy in rotating the disk. Then the magnetic field acts upon the moving electrons per Lorentz. Charges are separated and a static E field is formed, with a dc voltage & current.

E fields induced per FL are solenoidal. No sources or sinks exist, they have rotation, & are non-conservative. E = -dA/dt, where A = magnetic vector potential, B = curl A.

E fields in the HG have sources and sinks due to charge separation, have no rotation, are conservative, and E = -grad V, where V is scalar electric potential.

Clearly the E fields in the HG are markedly different than those in FL type generators. This is a different mechanism, likely related via relativity.

Optical is energy. Have you seen what happens when sunlight is focused through a magnifying glass into a point and focused on a piece of paper? No energy?! Indeed!

That's all for now. Let's review the paper and discuss further later. BR.

Claude

 

[cabraham]

One more thing should be mentioned. According to Maxwell's published law of Faraday (1873):

curl E = -dB/dt.

What is he saying here? If the flux time derivative is zero, is E zero? Of course not. He's saying that the curl of E is zero. In the HG case, that is exactly what is measured. The Lorentz force due to electron motion relative to the static field acts radially so that plus & minus charges are separated, center & periphery, resulting in an E field radially. But this E field is due to charged particles. It has no curl.

Maxwell/Faraday predicts just that. A non-rotational E field. The HG perfectly affirms and vindicates FL per Maxwell. Transformers & motors/generators OTOH, per Faraday induction, exhibit E fields with curl. So there is no paradox after all. Maxwell & Faraday got it right all along.

I'm glad that's settled. Good day to all and feedback is welcome.

Claude

 

[diagopod]

I'm not sure if this is helps or not, but for what it's worth, in Daniel Fleish's "A student's guide to Maxwell's Equations" he distinguishes b/w the convenient Flux Rule, which is a handy formula, and a modified version of Faraday's Law, which is more subtle and rigorous, and, he believes, correct. I'll post the quote and formula if I can find it.

Regarding Feynmann's quote, I found the likely source in the Wikedia article http://en.wikipedia.org/wiki/Faraday_paradox"

The "flux rule" does not work in this case. It must be applied to circuits in which the material of the circuit remains the same. When the material of the circuit is changing, we must return to the basic laws. The correct physics is always given by the two basic laws

• 
  
  http://upload.wikimedia.org/math/1/8/f/18ff316d4977d68c2cd17db2fd64ec0b.png

-- – Richard Feynman  The Feynman Lectures on Physics

Just after the Feynman quote, the argument is made that once SR is taken into account, Faraday's law holds true. I don't know enough to pass any judgment, but at first pass it seems Feynman is arguing more against the universality of the handy flux rule, but not necessary the fully expressed Faraday's law w/ perhaps SR taken into account.

 

[MS La Moreaux]

Claude,

I did not say that with static flux, no induction could take place; I said that that is what FL implies. That is one reason why FL is false. Flux change due to motion is not physically (in the sense of physics) the same as time-varying flux without motion. That is the whole crux of the matter. The two have completely different physical results. The former leads to motional EMF and the latter results in transformer EMF in accordance with one of Maxwell's four classic laws. When you say that E fields induced per FL are solenoidal, you are mistaken. That is only true when there is an intrinsic change in the flux. It is not true when there is motional EMF. FL does not distinguish between the two, which is why it is false.

Light is certainly energy. But energy transfer in an optocoupler, though necessary, is incidental to the transfer of a signal, which is the purpose of an optocoupler.

Mike

 

[MS La Moreaux]

diagopod,

The flux rule discussed by Feynman is exactly the same as what we are referring to as Faraday's Law in this thread. Relativity is really irrelevant, as it came along long after FL. FL is very simple and simply false, as I have demonstrated earlier in this thread.

Mike