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

[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.