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

[elect_eng]

If needed, tomorrow I can quote two other EM books I have at work, and later 50 more if I go to the library. At some point this will become very silly, but I'll do it if I think it may prevent even one student from taking the wrong message from this confusing discussion.

I'll now quote my final remaining textbook. I'll hold off on going to the library to see if 100% of books define FL properly. Hopefully, the 4 books I've quoted provide ample evidience that there is a well established definition of Faraday's Law.

From "Electromagnetics", 3rd edition by John D. Kraus (an excellent undergraduate text) we find the following.

Section 8.2, titled Faraday's Law says the following"

"The emf induced in the loop is equal to the emf-producing field E (associated with the induced current) integrated all the way around the loop, the gap separation being considered negligible. Thus,

$$V=\ointop_{\partial S} E \cdot dl$$

He then quotes the general integral form of Faraday's Law as follows:

$$V=\ointop_{\partial S} E \cdot dl=-{{d}\over{dt}}\Biggl(\int_S B \cdot ds\Biggr)$$

Then he states, "When the loop or closed circuit is stationary or fixed, this reduces to,

$$V=\ointop_{\partial S} E \cdot dl=-\Biggl(\int_S {{\partial B}\over{\partial t}} \cdot ds\Biggr)$$

Note that he is very careful in the definitions and the statements of which law is general and which is specific. The general law is always valid and there exists no experimental evidence of any case in classical physics where the general law does not hold.

Hence, Faraday's Law is True!

The discussion then goes on to talk about moving conductors in a magnetic field (section 8-3) and the general case of induction (section 8.4). It is here that people are becoming confused. But this discussion is basically the same type of thing that I quoted above in Jackson. We can separate the motional induction and the transformer induction and express (not define!) the EMF as follows.

$$V=\ointop_{\partial S} (v\times B) \cdot dl-\int_S {{\partial B}\over{\partial t}} \cdot ds$$

Kraus does not talk about the limitations of this formula, but we know from Jackson's description that this is an approximate (non-relativistic) expression.

If one takes the clear definitions quoted from the 4 well-respected and generally used texts, and combine this with the very lucid explanations from the paper by Frank Munley, it is clear that there are no issues with Faraday's Law. I would encourage anyone who is still confused on this issue to study all of this carefully. The truth will be clear. The most important lesson here is that a firmly established scientific law can not just be dismissed without clear evidence, and a careful study will reveal that there is no basis in fact to indicate that Faraday's law is not true. It is indeed true.

 

[Prologue]

This paper explains Feynman's error in analyzing the rocking plates. It also discusses the other "paradoxes" you've mentioned:

www.hep.princeton.edu/~mcdonald/examples/EM/munley_ajp_72_1478_04.pdf[/URL]

...[/QUOTE]

Ben to the rescue. I am glad that this paper agrees on the decomposition to what I called 'orthogonal effects' (transformer stuff and motional stuff). They may not actually be 'orthogonal' in the sense that they have no relation to each other, but still, this is the right path I believe. I haven't read the whole thing but I think this guy knows what he is talking about and will come to the correct conclusion, give me a day or so and I'll comment.

 

[bjacoby]

I'm sorry, this is a nonsense assertion. First off, your proposed rods are exactly the system Munley analyzes, and he shows that the flux change is small. Second, if there is any flux change at all, then there is EMF and therefore meter movement (provided the meter is sensitive enough to detect it).

Yes, you are correct that they make the same assumptions I do about the rods and they come to the same conclusions too! Namely that there is a SMALL (but non-zero) induction due to the rocking plates. This is NOT what I"m asserting! I'm saying that if the rocking plates are working as a proper "switching" circuit there is ZERO induction not just a "small" small one. This goes to Ben's assertion that by shorting across a wire loop with a magnet in it you see induction because the area and hence the flux is changing with time. I suggest that experiment easily shows this is not the case.

The paper is interesting and like most here I have not gone through it in detail yet. I have seen their methodology before, however. Which is to say their arguments about "sweeping out areas". I have seen that work and give correct answers, but I don't think it "proves" Faraday's law always works. Nobody here is arguing that Faraday's law doesn't work SOME of the time!

 

[elect_eng]

Nobody here is arguing that Faraday's law doesn't work SOME of the time!

The title of this thread is "Faraday's Law is False". Doesn't this imply that someone is arguing that Faraday's law doesn't work SOME of the time.

I most certainly am arguing that Faraday's law is valid always.

 

[Ben Niehoff]

Yes, you are correct that they make the same assumptions I do about the rods and they come to the same conclusions too! Namely that there is a SMALL (but non-zero) induction due to the rocking plates. This is NOT what I"m asserting! I'm saying that if the rocking plates are working as a proper "switching" circuit there is ZERO induction not just a "small" small one. This goes to Ben's assertion that by shorting across a wire loop with a magnet in it you see induction because the area and hence the flux is changing with time. I suggest that experiment easily shows this is not the case.

I repeat:

If you have actually done this experiment and found such a gross violation of Faraday's law, then you should publish in a peer reviewed journal immediately. Such a find would be revolutionary! But I hope you carefully accounted for all sources of experimental error.

 

[amyfrog]

Faraday's induction law is used to derive Maxwell's electric curl equation but light is not emitted by Faraday's wire loop that describes Faraday's law. Does Faraday's law include the emission of light, somewhere?

 

[bjacoby]

I repeat:

If you have actually done this experiment and found such a gross violation of Faraday's law, then you should publish in a peer reviewed journal immediately. Such a find would be revolutionary! But I hope you carefully accounted for all sources of experimental error.

You are being totally silly! Of course I've done the experiment. Many people have! I doubt it's considered a "gross" violation of Faraday's law. Nor is it "revolutionary" and any reviewer would laugh the suggestion out of his office in into the wastebasket which is where your "repeated" statement belongs. Obviously YOU have never tried any of your great theories! No need to try to publish them. Just educate yourself. Just take ANY loop of wire and attach it to a sensitive galvanometer. Take another piece of wire and attach it one side of the loop. Run it across the loop and try shorting it to the other side. Does the meter move? (The Earth supplies the magnetic field). According to you by dividing the loop you have doubled (or halved) the total flux. Try it. We'll wait.

PS. And just for fun try SLIDING the shorting bar across the loop. Oh MY! Somehow that is different! So which one is Faraday's law?

 

[elect_eng]

elect_eng,

You asked for correct equations. Maxwell's Law for transformer EMF is E = - $$\partial$$$$\Phi$$/$$\partial$$t, which is correct. The equation for motional EMF is E = (v x B) . l, which is correct.
The Lorentz equation is EMF = $$\int$$ (e + v x B) . dl, which is correct. (Sorry, I do not have a complete handle on printing equatiions.) The first two, between them, cover every case of the two types of electromagnetic induction. The Lorentz equation covers both the above and is correct. Notice that the Maxwell law uses the partial derivative and not the ordinary. This eliminates the effect of motion.

One can see a few issues here.

1. You did not write out one complete equation which would allow us to be exactly sure what you are saying. It's not clear to me which version of EMF should go into the flux law. Why not write out exactly what you mean, including writing out the integral? It would be nice to know what exact equation you are talking about. Note, you can double click on some of the previous equations and cut/paste the latex code.

2. You say that this equation is correct E = - $$\partial$$$$\Phi$$/$$\partial$$t. However, aside from the fact that it is unclear what you mean by EMF, you should either put the partial derivative inside the integral (for the no-motion case), or keep a total derivative outside the integral (to include the effects of motion).

3. Your equation for Lorentz EMF should not be used in Faraday's Law, although there is no indication that you are saying that it should be. Actually, it's not even clear to me what the physical signifcance is for that Lorentz EMF. In the case of motional induction we have the relation that the integral of E equals the integral of vxB, which seems to indicate that the Loretz EMF is twice the voltage? Anyway the correct relations for non-relativistic and general cases are as follows.

$$EMF\approx \ointop_{\partial S} (v\times B) \cdot dl-\int_S {{\partial B}\over{\partial t}} \cdot ds, \;\;\;\;{\rm (non-relativistic \;\;case)}$$

$$EMF=-{{d}\over{dt}}\Biggl(\int_S B \cdot ds\Biggr)=\ointop_{\partial S} E \cdot dl$$

I really think you can clear a lot up if you write out the equation you mean. We can then judge if the equation is an exact version of FL. If it is not, then we are talking about a minor debate about an incorrect formula that is naturally limited. If the equation is FL, then we are talking about a major debate on whether a fundamental law of physics is valid. There is a big difference between the two, obviously.

 

[bjacoby]

The title of this thread is "Faraday's Law is False". Doesn't this imply that someone is arguing that Faraday's law doesn't work SOME of the time.

I most certainly am arguing that Faraday's law is valid always.

Then I guess you must be smarter than Feynman! According to him with regard to his "rocking plates" :

"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 basic laws."

"F = q(E + v x B),

Curl E = -dB/dt"

We need to be a bit more careful here because Feynman call the second equation above "Faraday's Law" even though he notes it was first written by Maxwell. Most people call the "flux rule" Faraday's Law which is to say EMF = - dB/dt. Resnick and Halliday so define it as well and say:"The electrical effect of a changing magnetic field" which is a statement of causality which is plain wrong.

Furthermore, when using mathematical models such as these I suggest it is important to make sure at all mathematical requirements have been met. One cannot say that Faraday's Law "always" works when it's possible to have mathematical expressions that are not defined in the operations. I refer here to functions being continuous and differentiable. That should provide a hint why "switching" circuits do not obey Faraday's Law.

But the main point here is that you have hauled out a stack of textbooks and I have just hauled out Feynman. All that remains is to determine who is the greater authority! Right?

 

[elect_eng]

Then I guess you must be smarter than Feynman! According to him with regard to his "rocking plates" :

"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 basic laws."

"F = q(E + v x B),

Curl E = -dB/dt"

We need to be a bit more careful here because Feynman call the second equation above "Faraday's Law" even though he notes it was first written by Maxwell. Most people call the "flux rule" Faraday's Law which is to say EMF = - dB/dt. Resnick and Halliday so define it as well and say:"The electrical effect of a changing magnetic field" which is a statement of causality which is plain wrong.

Furthermore, when using mathematical models such as these I suggest it is important to make sure at all mathematical requirements have been met. One cannot say that Faraday's Law "always" works when it's possible to have mathematical expressions that are not defined in the operations. I refer here to functions being continuous and differentiable. That should provide a hint why "switching" circuits do not obey Faraday's Law.

But the main point here is that you have hauled out a stack of textbooks and I have just hauled out Feynman. All that remains is to determine who is the greater authority! Right?

First, no I'm not anywhere near as smart as Feynman, but that is not relevant.

You say Feynman called the second rule Faraday's Law. Well that is exactly what I've been trying to say. That is Faraday's Law and it is always valid. That equation can be transformed into an integral version, which is the relation I quoted from 4 textbooks.

The thing I'm trying to figure out here is whether there is a difference between what you call the flux rule and what Feynman and I call Faraday's Law, as stated by Maxwell.

Perhaps if I were as smart as Feynman, it would be obvious to me from reading this thread, but my limited mind is very confused by many of the descriptions here. Do you have any idea how vague your quoted flux rule looks? (EMF = - dB/dt ) First of all you use the letter B, so I don't know if you mean field or flux. Then you write it in plain text, so I can't be sure if you mean partial or total derivative. And, it's not clear what the definition of EMF is. If I look back in this thread, I see several formulas quoted for EMF, and the definition is critical because the concept of voltage gets confusing when dealing with non-conservative fields.

I'd like to be clear that I have not yet looked at this "rocking plates" problem, and I intend to do so shortly. The thing is that very often we find paradoxical questions and problems that seem to challange fundamental laws. Generally, the paradox is eventually resolved and the law ends up holding up. My first impulse is to hold this view until there is clear evidence to the contrary. Don't forget, even Feynman is not infallible, nor is any other genius. What is amazing is that Faraday seems to have gotten it right so long ago. So the question is not whether I'm smarter than Feynman, but whether Feynman is smarter than Faraday.

 

[cabraham]

The Munley paper is really good, and settles the issue. Earlier I made a concession that the simplified scalar version of FL does not cover the HG. But after reading Munley, I am convinced that no concession should be made. The scalar form of FL is also valid as is the full vector form.

In the HG, we've been assuming that the "flux" is static wrt time as well as space. i.e. no spatial variation. But that is true only with the flux density. The flux linkage is the flux density times the area Ac of the loop. The meter attached to the HG has its leads at the axis and periphery. The area of the loop determines the flux. As the disk spins, the Lorentz force acts radially on free electrons. The fixed B field times the enclosed area is the flux phi.

So the area is a sector, pie shaped since the periphery is moving. Although the B is spatially static, angle theta is varying, hence the area is dynamic. So the flux phi, is varying with time! The area enclosed, Ac, is simply the rotational speed omega, times the radius^2, times 0.5, times time (t). This is logical. Then,

phi = 0.5*B*omega*r^2*t

We know that the induced current/voltage is dc, or static. Since v = -N*d(phi)/dt = constant, what does that tell us? Phi has a time derivative of constant value (dc) meaning that phi is a constant multiplied by time to the 1st power. Only a constant times time plus an offset has a time derivative equal to a constant.

Then, d(phi)/dt = 0.5*B*omega*r^2.

So it appears that the fixed B links a changing area Ac, producing a varying phi. The variation with time is linear, so that the 1st time derivative of phi is a constant. This agrees with the observed nature of the induced current/voltage, as it is dc.

Wow, I love it! An exciting problem to say the least! It taught me one thing. I took long enough to get it, and I needed help to do so. I'm not as great as I'd like to believe. But that isn't so bad. Even the great RF didn't get it all right either! BR to all.

Claude

 

[bjacoby]

The Munley paper is really good, and settles the issue. Earlier I made a concession that the simplified scalar version of FL does not cover the HG. But after reading Munley, I am convinced that no concession should be made. The scalar form of FL is also valid as is the full vector form.

In the HG, we've been assuming that the "flux" is static wrt time as well as space. i.e. no spatial variation. But that is true only with the flux density. The flux linkage is the flux density times the area Ac of the loop. The meter attached to the HG has its leads at the axis and periphery. The area of the loop determines the flux. As the disk spins, the Lorentz force acts radially on free electrons. The fixed B field times the enclosed area is the flux phi.

Wow, I love it! An exciting problem to say the least! It taught me one thing. I took long enough to get it, and I needed help to do so. I'm not as great as I'd like to believe. But that isn't so bad. Even the great RF didn't get it all right either! BR to all.

Claude

I"m sorry, but the Munley paper is not "really good". It's nothing but a bunch of slight of hand and imagination. They start out OK with the "flux rule" namely: emf=-d(flux)/dt. That IS the flux rule. It is NOT the Lorentz relation (F=-qvxB) which is usually considered to be the definition of a magnetic field. Hence the flux rule can be derived from Lorentz but not the other way round.

It has been pointed out that the flux in the flux rule can change two ways. One is that strength of the magnetic field changes and nothing moves. That is called "transformer action". The other is when the area used to define the flux (the conductive wire giving the emf) changes with time. That is called "flux cutting" or "generator action".

Consider the following: A U shaped piece of wire with a sliding cross bar submersed in a uniform unchanging magnetic field.

. _____________|_
. | |
. |____________|_
. |
Sorry I can't seem to get this ascii diagram to work so you may have to imagine it!

We note that the flux area is defined by the slider and the U and the area enclosed by both. If we slide the slider the flux area changes with time. If we calculate that change (see any Freshman text) we see it gives an EMF developed. The flux rule WORKS! One can also use the Lorentz relation to find the EMF developed in the moving slider and it is the same value. CONFIRMATION!

But wait. Now let us start as above. But this time lay a second shorting bar across the U dividing it in two. Is there a quick "jump" of the meter since we divided the flux area in two? No. The Earth is not flat and so long as we do not move the shorting link sideways (giving a lorentz emf) there is NO jump. Now remove the outside link. FLux area has CLEARLY changed from the full U to half the U. But no induced emf has been observed. Flux rule fails!

So now let's get with the Munley solution. They (and this is all I'll talk about now) start with the Faraday generator. We look at the Faraday generator and first we note that the strength of the magnetic field is not changing with time! Ok. One down. Next we want to know if the "flux" is changing with time. Well what defines the Flux? It is the magnetic field integrated over the area of the circuit. Question: Is the area of the circuit changing with time? Answer: no it is NOT! At this point most people (see Munley references) throw up their hands and pull out the Lorentz relation and TRY to calculate an answer that way. The problem is you CAN'T even though you DO get the "right answer"! People just "assume" the current flows from a straight line from the axle to the perimeter of the disk. And then apply Lorentz to that line. Again "correct" answer (meaning agrees with observations).

But there is nothing to make one assume current (and charges in the disk) are in such a line. The disk is a metallic conductor. The positive charges (nuclei) are fixed. Yes, they do indeed move with the disk as it rotates, but also cannot move sideways to create an E field that creates the emf! Electrons in the metal are free. So they can move sideways to create an E field. But being free they can also move backward as the disk rotates. Do they? Who knows. For one thing if they do it surely changes the assumed straight-line path of our current! Truth is the actual current path is unknown and has just been "assumed" like the current path Feynman "assumed" in his rocking plates. Hence the whole operation is speculative and has no basis in the reality of the physics of the apparatus!

Munley carry this one step further with slight of hand. They make the bold assumption that the rotating disk somehow "sweeps out" an area that is called the "flux". This swept area as well as the line defining is are PURELY imaginary! There is NO physical basis for doing this!. Yes, indeed the disk is rotating. And yes if one were to DRAW a line on it it would indeed "sweep" out an area. But that has nothing to do with the material inside the conductive disk. Basically they have used the same (false) assumptions people use when using Lorentz forces to "solve" the disk but disguised as a "flux". It is NOT a "flux". They are basically using slight of hand to redo the Lorentz calculations calling them "flux".

They do however, make a point relevant to the Lorentz solution. Namely that with a uniform magnetic field the path of the current in the disk does not matter. Which probably explains why just assuming a straight line for ether Lorentz or Munley solutions gives a "correct" value. But then Munley go on to the case where magnet does NOT cover the disk. In that case they note that the actual path becomes important! That is correct.

So what happens when the magnet only covers a small part of the disk? Does the field change? No. Does the area defined by the magnetic field on the disk change? No. So what is "sweeping" out a flux area? The current path inside the disk? Probably. Is that path known? No. Does anybody know how to calculate it? I doubt it. Sorry Flux Law fails.

Lastly let me be clear here about what we are talking. Maxwell's equations do not "fail". Feynman makes that clear in his lecture. Thus to apply Maxwell's equations to a problem such as this and use the fact you can get a correct answer simply begs the question. The question is NOT Maxwell even though the flux law can be derived from Maxwell. The question is does the flux law always "work". The answer is clearly No. To derive "backward" from the flux law to Maxwell and then note that Maxwell works and point to that saying that therefore the flux law works is fraud pure and simple!

It seems what Munley has done is to cobble together some "alternate explanation" which can't be justified by the apparatus characteristics and point to the correct answer they got and conclude that therefore the "flux law" ALWAYS works... if you are clever enough! Well yeah if I came up with a formula that included my shoestring length and also gave a correct answer I could point to it and say that the shoestring theory always works too. But in truth I'd have proved nothing at all but an over-worked imagination.

 

[bjacoby]

First, no I'm not anywhere near as smart as Feynman, but that is not relevant.

You say Feynman called the second rule Faraday's Law. Well that is exactly what I've been trying to say. That is Faraday's Law and it is always valid. That equation can be transformed into an integral version, which is the relation I quoted from 4 textbooks.

The thing I'm trying to figure out here is whether there is a difference between what you call the flux rule and what Feynman and I call Faraday's Law, as stated by Maxwell.

Perhaps if I were as smart as Feynman, it would be obvious to me from reading this thread, but my limited mind is very confused by many of the descriptions here. Do you have any idea how vague your quoted flux rule looks? (EMF = - dB/dt ) First of all you use the letter B, so I don't know if you mean field or flux. Then you write it in plain text, so I can't be sure if you mean partial or total derivative. And, it's not clear what the definition of EMF is. If I look back in this thread, I see several formulas quoted for EMF, and the definition is critical because the concept of voltage gets confusing when dealing with non-conservative fields.

I'd like to be clear that I have not yet looked at this "rocking plates" problem, and I intend to do so shortly. The thing is that very often we find paradoxical questions and problems that seem to challange fundamental laws. Generally, the paradox is eventually resolved and the law ends up holding up. My first impulse is to hold this view until there is clear evidence to the contrary. Don't forget, even Feynman is not infallible, nor is any other genius. What is amazing is that Faraday seems to have gotten it right so long ago. So the question is not whether I'm smarter than Feynman, but whether Feynman is smarter than Faraday.

You are right there is some confusion here due to failure to carefully define what we are talking about. Just call the equation emf = -d(flux)/dt the "flux rule". (I hope I've typed it right this time. I'm sure you are smart enough to have seen it before so a typo-flame isn't necessary. And let's call Curl E = -dB/dt ("d" stands for partial derivative, OK?) Maxwell.

Feynman asserts (and so do I) that the flux rule does not always work. Feyman (and I) assert that Maxwell always works. Now you have shown that the flux rule is derivable from Maxwell, but that doesn't prove it always works, does it? One must ask what are the conditions required by the derivation? I suggest that some of those conditions are functions be continuous and differentiable. Therefore when we have "switched" circuits those conditions fail and the flux rule fails as a result.

As to whether challenges to long-established rules usually fail is irrelevant. If there were not such challenges that occasionally succeeded in proving the long-established laws invalid (at least in some range of values) then there would be no progress in science at all would there?

 

[elect_eng]

I"m sorry, but the Munley paper is not "really good". It's nothing but a bunch of slight of hand and imagination.

You are clearly not qualified to make this judgement. Your explanations reveal a general lack of understanding. I've never seen a better example of how a little bit of knowledge can be a dangerous thing.

I've lost a lot of respect for this forum in allowing this thread to continue. I'll be bowing out of this discussion since it is clearly pointless to continue. Additionally, I'll need to make a decision on whether to continure to visit Physics Forums from now on. That decision will be based on just how long this nonsense is allowed to continue.

Free energy scammers will be pointing to this thread as evidence that scientist and engineers can not reach a consensus on the validity of Faraday's Law. I'm really disappointed.

 

[elect_eng]

Just call the equation emf = -d(flux)/dt the "flux rule". (I hope I've typed it right this time. I'm sure you are smart enough to have seen it before so a typo-flame isn't necessary.

This is perfect example of why it is pointless to try to have a discussion with you. You call my request for clarification a typo-flame and then refuse to provide the definition of EMF which was the most critical part of the request. Yes, I was reasonably sure that you meant total derivative of flux, but if you then go on to define EMF properly as the line integral of electic field, your flux rule will become identical to the integral form of Maxwell's Equation that expresses Faraday's Law. There would then be no difference between the Curl E = -dB/dt and the flux rule because they would just be different versions of the same law. Then, your argument that one is a universal law and the other is not, would fall apart. So it's clear why you did not answer, but instead tried to portray my request as unnecessary.

Anyway, I'm done now.

 

[Per Oni]

You are trying too hard to bring practical details into this "thought experiment". Just wire the apparatus a different way! make the center "switch" a simple copper bar that bolts across the other larger rectangle. Make the magnet a compact pole that has little fringing. Now once the link is removed I can slide the magnet to the other end with virtually no induced voltages. The fact that there may be some teeny-tiny voltage induced somewhere is not important in the light of our primary conclusion which is that there has been a HUGE flux change in our first loop with NO (or very little) change on the meter. The Flux rule on the other hand predicts a LARGE change (which is seen in most cases).

Sorry for not replying earlier, I had a couple of busy days (and will have some more).

Lets exam your 2nd (or 3rd ) circuit. In this one there is apparently no material being cut by a magnetic field. It’s a bit like a person walking through a long corridor with many automatic sliding doors. At no time does s/he need to go through a glass pane but still reaches the end ot the corridor. (we hope). At least I think this is what you are now describing.

Compare that with the real situation. In reality: 1 magnetic field lines enter the front surface and leave the rear surface of the paddles and 2, there is relative movement between paddles and field lines.

Time for a new circuit?

Btw my last question of post #121 is still unanswered.