Faraday's Law Is False!

elect_eng

OK, before I try to comment on this, can you please express what you believe to be the correct formulas. I've read through many of the previous posts, but it is hard to absorb everything, and explanations in words can be misinterpreted.

If you write the equations I'll be able to clearly understand what you are saying.

At the same time, I'll double check the one I posted. It's a version I pulled from memory and I dont' use it in practice. I'd like to go back and review the assumptions implied in that version.

MS La Moreaux

elect_eng,

If the righthand side of your equation is replaced by the symbol for EMF, the equation will be Lorentz's, which is correct. The version of Faraday's Law which is the subject of this thread is E = -d(phi)/dt, where the left side is EMF and phi is the magnetic flux.

Mike

OmCheeto

Can you show me a picture of a homopolar generator where the magnetic lines of flux are parallel to the plane of the circuit. I have always pictured them as being perpendicular to the current flow.

Prologue

http://en.wikipedia.org/wiki/File:Faraday_disc.jpg

This is the imagery.

elect_eng

OK, there are a couple of questions here.

First, I was asking you to provide a version of equations that you feel is correct, but you provided the one which is under discussion that you feel is wrong. Am I correct about that? If so, do you have an equation that you feel is correct, or are you just saying the given one is wrong?

As far as the equation you gave, it looks like you are saying E is emf, and B is total flux. One confusing thing about this is that I normally use E for electric field and B for magnetic fields, so I want to make sure I'm understanding this. As far as I can tell, the main difference between the equation you quoted and the one I wrote is the location of the time derivative. I wrote the time derivative inside the integral, while you seem to be writing it outside the integral. It occurs to me that we need to be careful about the location because this form is supposed to be valid for time dependent surfaces. There is a difference between the equations, and perhaps the one I gave is wrong. Again, I will look at this more carefully.

What this discussion is telling me is that we need to be careful about distinguishing between the fundamental form of Faraday's Law and the correct integral formulation under a given set of assumptions. We don't want to say Faraday's Law is wrong just because we decide to formulate an improper mathematical statement, or to make an approximate statement for practical applications. I'll think about this more, and will have some comments later.

Getting back to some of your other comments.

I see I might be making contradictory statements above, but sometimes you can think about field problems from alternative points of view. My basic way of thinking about the Faraday disk is to see it as based on the Lorentz force. Charges in the disk are moving through a (nearly) constant magnetic field. They basically see no flux change (to first order), however the Lorentz force strongly pushes the electrons radially on the disk and creates a charge differential between the center and the perimeter of the disk. We really do not even need to think about Faraday's law here. There is no time dependent magnetic field to think about (again to first order) and motional changes do not create an effective flux change. A moving charge can move through a perfectly constant magnetic field (dB/dt=0) and experience a force that will oppose the natural repulsive force between like charges. Compressing these charges away from the natural equilibrium (neutral) state generates a voltage.

OmCheeto

I see the circuit is a loop, with the flux lines perpendicular to the disk, with the current flow through the disk being perpendicular to the flux lines. Since you don't have a homopolar generator without the disk, the motive force has to be generated in the disk. Hence the flux lines are perpendicular to the relevant part of the circuit.

Perhaps it is more obvious in Faraday's original:

http://en.wikipedia.org/wiki/File:Fa..._generator.jpg

Prologue

Maybe I can illustrate the OP's point. The claim is that there are two ways to create an emf due to what we perceive as "flux changing". One way was termed to be "transformer induced emf" and the other was "motional emf". The OP is not arguing against both of these phenomena, he is merely saying that the reasons given are wrong. (The transformer induced emf is due to the changing MAGNITUDE of the B field, not the area change, the area change is a motion, and so is a motional part!) So, the mix up seems to be that people are attributing the wrong thing to what actually causes the emf. The argument that Feynman makes is to show that there are actually two ways, and one can't be derived from the other. He attempts to show two systems, one where motional emf is the ONLY one to blame, and one where transformer induced emf is the ONLY thing to blame. Thus, showing that the effects are not derivable from the other. In other words, there are times where an emf is induced and there is not a motional emf, and there are times where there is no flux changing yet an emf is still induced.

The big mix up is this, sometimes you have a changing flux due to area change (but with no B magnitude change) and people say, yeah that is due to the changing flux. But whent hey say "it is due to the changing flux" they are really thinking "it is due to the transformer induced emf effect". That is the problem, there is a breakdown in the language. Yes, there is a changing flux, but changing flux does not necessarily mean it is the transformer effect. Anytime the B field magnitude stays the same and the area changes, that is the motional effect, and when the area stays the same but the magnitude within it changes, that is the transformer effect.

Now, you can imagine a situation where the magnitude of the B field and the inflicted area changes, so you have both effects. For instance, a square ring of conducting wire is forced into a changing (magnitude) B field, then you have both effects.

Ok, so much for the confusion part, now the real question is...was Feynman right? Or, can you actually derive one from the other. I have always had the opinion that he was wrong. My opinion is that the effects are all motional but there are times where separating the total effect into supposed orthogonal effects helps. In the real world, where one convinces themselves that the transformer effect is a real effect, the soleniods are not infinite, and so the wire that you wrap around it to test the effect, is impinged by moving B field lines. But, my opinion is moot for this specific topic.

elect_eng

That is a very good summary. Thank you!

Let's say we start with the point form of Faraday's Law as stated by Maxwell.

[tex] \nabla \times E = {{-\partial B}\over{\partial t}}[/tex]

Does anybody doubt this form of Faraday's Law? When I read the title of this thread, it struck me that it was this basic law that was being questioned. This is the form of Faraday's Law that is taught in classical EM field theory, and it has held up with the developments of special relativity and general relativity, with suitable formulation in the context of differential geometry. It will obviously break down in the quantum regime, as does all classical physics, including GR.

If we agree on this, should we not be able to derive an integral version of the equation valid for both constant surfaces and time varying surfaces? And, with both/either version, shouldn't we be able to describe both "transformer EMF" and "motional EMF"? Of course, there are other Maxwell equations to draw on in solving any problem. Once we solve for the field solutions and charge distribution and current density, we basically have everything we need to know. It's not always easy to find these solutions, but they can be found in principle. As far as potentials, there are clear definitions of the scalar potential and the vector potential, in terms of the electric and magnetic fields.

What am I missing here?

OmCheeto

Language? Is this entire thread an arguement of semantics? In the Physics area of the forum? Should we move this thread to the Social Sciences under Linguistics section?

hmmm...

Let's start over.

premise: E=-d[tex]\Phi[/tex] /dt is wrong.

Game over. Thread closed. What laws are not based on observed data?
What?

And they are?

Sounds like semantics again. But I'm a linguistic idiot. Let's see if I can figure this out:
so a law is a principle and a principle is a law. ie Law = Principle. Therefore there's no way to incorporate two laws into one term of an equation. So the laws of physics have to all have separate equations.

So laws have to be based on laws?

Our understanding of the universe comes from observation. We build mathematical models to describe these observations. There is nothing to understand beyond the reality of the observed.

hmmm......

Perhaps this belongs in the philosophy forum.

elect_eng

Over morning coffee, I had a revelation about these comments.

First, let me write out my interpretation of the equation you are referring to above. This is a direct interpretation of your words and the equation E = -d(phi)/dt.

[tex]
\ointop_{\partial S} (E+v \times B) \cdot dl=-{{d}\over{dt}}\Biggl(\int_S B \cdot ds\Biggr)
[/tex]

This seems to be what you mean. If it is, and if you are saying that this equation is not correct, then I agree - it is not correct. As far as I can tell, this is not a proper representation of Faraday's Law. Is this basically what we are debating here?

Above, I wrote a different equation as follows:
[tex]
\int (E+v \times B) \cdot dl=-\int {{dB}\over{dt}}\cdot ds
[/tex]

This is a version that I pulled from memory as being valid for a moving surface with velocity [tex]v[/tex]. The inclusion of [tex]v \times B[/tex] was not intended to help represent the EMF, but to capture the effects of surface movement. As I mentioned above, I'm not confident that this formula is correct, but I'd like to not even address that issue since it just detracts from the central premise of the thread.

I'll quote the proper integral form of Faraday's Law from the book "Foundations of Classical Electrodynamics", by F.W. Hehl and Y. N. Ovukhov. It is equation I.4 on page 6.

[tex]
\ointop_{\partial S} E \cdot dl=-{{d}\over{dt}}\Biggl(\int_S B \cdot ds\Biggr)
[/tex]

Clearly the equations are different. Please acknowledge whether you agree with the above comments, or provide any necessary corrections. If the above is correct, we are really debating whether a particular equation is a correct representation of Faraday's Law, not whether Faraday's Law is correct. Is this a fair statement?

Prologue

I like your thinking there. You have an electric field and then you have an 'induced' electric field (from the motional magnetic effects). I can't really say for sure that the equation containing vxB is 100% correct, but I think it is damn close. This moving surface business is always a problem for me, how do you do a closed loop when it is moving? Is it instantaneous, etc? I can't say for sure, but it is sounding better. Thanks for the attempt at a quantitative (with formulas) approach to this tricky discussion. I'll try to do some math and see what sticks out to me.

cabraham

First I'll adress the HG. The law of Faraday per Maxwell, i.e. "FLM", is given as :

curl E = -dB/dt.

The HG and FLM are in perfect agreement. FLM can be stated in plain English as:

The rotation (or "curl" if you prefer) of E equals the negative of the time derivative of the flux density.

Keep in mind that this is a vector equation, and in analyzing the HG and FLM, we must stay in the vector mindset. We cannot understand what is going on if we think in scalar terms. Fair enough?

According to FLM, an HG has a -dB/dt that equals zero. Thus we can conclude that in an HG we will encounter zero electric field rotation. The HG works by spinning the disk in between 2 magnetic poles (N & S) and the electrons in the disk, free electrons as the disk is metal, are subjected to Lorentz force. The B field is static, normal to the surface of the spinning disk, and the electron velocity is tangential to the circular motion. Hence the Lorentz force, F = q(u X B) points radially. Thus charges will separate towards the center and periphery. The E field is F/q = E.

This E field is due to discrete charged particles. The E lines start on a +ve charge and end on a -ve charge. This type of E field has no rotation/curl. The curl of E, in the HG case, is exactly zero!!!

But, the magnitude of E, |E|, is non-zero. Hence the induced current per J = sigma*E, is also non-zero as well. The "paradox" is merely as follows. Often, we prefer to think in scalar terms than vectors because it is easier to do so. In conventional motors, generators, & transformers, if the flux is static, of course the curl of E is zero. But the magnitude of E is also zero.

If curl E = 0, then either |E| = 0, or E is non-solenoidal. That is, |E| is non-zero, but the curl is zero due to absence of rotation. In the case of motors, generators, & xfmrs, the magnitude is zero for the E field when the flux is static. Of course a vector with zero magnitude will also have zero curl. So, in these cases, we can use the simplified scalar form of FL, which is:

v = -N*d(phi)/dt, where phi = Ac*B, Ac = area of cross section of loop, B = flux density.

But in the HG case, the scalar simplified version does not work. Here, d(phi)/dt is zero, but v is non-zero. But the vector form is perfectly correct. The vector form of FLM predicts that E has zero curl. It does not predict an E field of zero magnitude.

Thus the full vector form of FLM agrees perfectly with the HG behavior. No paradox here at all. FLM is valid law. It's too easy. No debate at all.

Next you call me on the carpet for not knowing that E & B are related but not causal!!! Dude, get serious! Have you examined my posting history. For a decade of posting on this and similar forums? I've been stating forever the same thing. Many have told me and others about causality, this causes that, and my response has always been, w/o exception, that electric and magnetic fields, under time-varying conditions, cannot exist independently. Neither can be stated as the cause of the other. You're preaching to the choir!

Regarding your loop experiment, you don't state whether we're measuring current or voltage, a picture/sketch would help, etc. I would say that if you place a magnet in the loop, then remove it, the change in flux takes place for a fraction of a second, but is visible on a scope. By the time you remove the magnet, and then throw the switch, the transient has already passed.

To do such a test, I'd recommend measuring voltage under open circuit conditions, and current when short circuited. You can obtain usable readings that way. So take a simple 2 cm X 2 cm square loop, 1 mm high. Let's keep it open with a small gap, and connect a DVM across the terminals. Place a magnet w/ surface 2 cm X 2 cm flush w/ the loop. Now remove it quickly. If "quickly" is 0.05 seconds, what is the transient voltage? For a good magnet, B = 1.0 tesla, and phi = Ac*B. Ac is 2 cm X 2 cm = 4 cc, or 4e-4 m^3. Thus |v| = d(phi)/dt = (1.0)*(4e-4)/(0.05) = 8.0 millivolt. A good DMM with a peak hold can measure this as it is 0.05 seconds in duration. A scope w/ digital storage would work very well.

Anyone can verify what I've stated. Finally, Feynmann stated that the "flux rule" is not always valid. He calls it the flux rule, I call it the simplified scalar form, but we agree that with the HG we cannot assume that zero curl means zero magnitude. Usually it does, but not with the HG.

You bluff and bluster like you hold 4 aces, and your post is less than a pair of deuces. Seriously, you present nothing but fluff and claptrap. Nothing you said remotely challenges FLM. If I've erred, please point it out using valid scientific reasoning. You talk down to me like I'm a high school grad, and you're a Ph.D. Do you understand the difference between rotational & non-rotational E fields? Do you fully appreciate Lorentz force?

I'm not here to "win an argument". I always want to learn new things, and I don't believe that every law currently adhered to is forever immutable. But to knock down FLM, it will take more than what the critics have presented here. FLM cannot be refuted right now at this time. Maybe later, maybe, but not at this moment. Peace and best regards to all.

Claude

bjacoby

You are correct. I just went an checked the description and I made a mistake in describing the experiment.

The correct description would be to start with the magnet under the meter and the short across the center of the rectangle closed. That metered half of the rectangle represents our area over which we integrate the B field to get the flux. It has a large (DC) value. Now open the center divider switch and slide the magnet to the other end of the rectangle, but not outside of the large rectangle. Since the circuit now is just the large rectangular loop and the magnet stays inside the loop there is NO change in flux. At no time during any of these operations does the flux change or the meter move! Now close the center link again. At this point we are left with our original half loop circuit but with no magnet in it so the flux there is now zero. Hence flux has changed over some period of time from Phi to zero and a dPhi/dt exits. You do not need to remove the magnet completely from the second half of the large loop. That is irrelevant. So the bottom line is we have a flux changing in time with no induced voltage from it. The Flux rule (often referred to as Faraday's Law) fails. Feynman points out that the problem is that the flux rule often fails when the actual CONFIGURATION of the apparatus is changing with time. That is certainly the case here!
OK?

I also forgot to mention that if you have a second switch that opens the part of the divided loop away from the meter (where the magnet ends up) If you open that switch you actually CAN totally remove the magnet at the end. Meter never moves or jumps.

If you think about the above experiment you can derive that the "rocking plates" perform an operation exactly the same as that described above only in a repeated micro-incrementing way.

bjacoby

You are saying that an Electric field can be created by a changing magnetic field. Just to be careful about this, let me note that we are NOT talking here about the apparent "measurements" that appear when they are made in a frame in motion with respect to some other set of measurements. We are indeed talking about an equation such as the commonly written form of Maxwell's equation that says Curl E = -dB/dt. Am I correct in this?

OK. Now let us define our differences. You say that E can be created by a changing B field. Which stated another way is that you assert that the above equation is CAUSAL. In other words that B can actually cause E.

I on the other hand have asserted that the above equation while CORRECT, is nonetheless NOT CAUSAL. What I'm saying is that while The curl of E does indeed EQUAL -dB/dt each side does NOT cause the other side. One way this can be proved is to understand that the above equation all happens at the SAME time. The principle of causality is that things that happen at the same time cannot cause each other! Why? Because according to relativity (and all experiments to date) information or energy cannot travel faster than the speed of light. "Action at a distance" does not happen creating the principle.

Thus I am saying that your description is completely wrong! But let me emphasize that this is not so much "my" theory. I am only describing here the work of Oleg Jefimenko. His mathematical proofs of this are straightforward and easy to understand. I won't attempt to lecture on them here, but they can easily be found in his book "Causality, Electromagnetic Induction and Gravitation" pages 6-10. He concludes as follows on page 10.

"It is now clear that the two terms of Maxwell's equation (above) Curl E and dB/dt do indeed have the same common cause: The changing electric current density J."

Hence he concludes that both E and B are created by a current that is the source of BOTH and that is why they are related to each other not because they cause each other.

On Page 16 he concludes: " There is a widespread belief that time-variable electric and magnetic fields can cause each other. The analysis of Maxwell's equations presented above does not support this belief. It is true that whenever there exists a time-variable electric field there also exists a time-variable magnetic field... But as we have seen, Neither Maxwell's equations nor their solutions indicate an existence of causal links between electric and magnetic fields." In a reference he points out this is not a new idea.

Please note that (the late?) Oleg Jefimenko, a professor at West Virginia University, was the author of an excellent textbook on Electricity and Magnetism and certainly does not fall under the "kook" guidelines of forbidden discussions. If there is doubt with regard to his conclusions, then I would suggest the appropriate response would be to examine his work and show the errors in his equations and derivation. I think we'd all be interested in seeing that!

diagopod

This appeals to me b/c it helps me visualize the perfectly symmetrical (in terms of amplitude) propagation of the E and B aspects of an e.m. wave, where one aspect does not seem to lead the other. What I have a hard time picturing though is how, for example, in shoving a magnet through a wire one does not cause an emf, or circulating E-field, but rather that the emf, or new E-field, happens at the same time as the changing magnetic field? Under the interpretation above, would it be more correct to say that the act of shoving the magnet through the wire-loop itself is the cause, and the effect is two-fold: a changing magnetic field and a new electric field? Either way, hope to learn more as you and others chime in on this concept.

Per Oni

DC stands for Direct Current?

During the time you slide the magnet across the short with the centre divider switch open, there will still be a voltage generated, however with a very much reduced current. The value of this voltage is still U=BLV, where L is the length of the short. In this case the voltage will exist across the open contacts of the switch. Therefore an electric field of E=U/d will be generated, where d is the distance between the contacts. The switch acts now as a (small) capacitor.

No not at all.
The rocking plates are at all times in good electrical contact with each other. As I said before: eddy currents are created in the short circuits in the rocking plates, which prevent the meter from registering the proper value, exactly what happened in your earlier example.

The 2 rocking plates are in fact 2 sectors of circles. Imagine completing the full circles. This way you get 2 homopolar generator disks which are in electrical contact, each spinning in the opposite direction. Now install an uniform magnetic field perpendicular to the disks. Opposite spinning results with one disk producing a +ve voltage at the rim and the other a +ve voltage at its centre.
Will there be an emf generated between the 2 centres?

bjacoby

You have the idea. The source of the "action" is a current (or charges). You need to separate in your mind a couple of cases to make it all more clear. Say one has a magnetic field created by a current in a wire (perhaps a solenoid). Faraday found that a current in one wire can induce another current in a second wire. In that case it is a varying current that induces the second current. An investigation of the causality of Maxwell shows that as well. Also a current produces a magnetic field about the current. If the current varies, the magnetic field varies. Now note the important feature here. BOTH the magnetic field AND the induced Electric Field (which is causing the second current) are propagating away from the source current at the speed of light. Now the important feature then is that these two things are EQUALLY "retarded". Hence they happen at the same time. Hence they can not be the cause of each other!

Now your case of the moving magnet is more complex but works by the same ideas. The assumption is that ALL magnetic fields are caused by currents. In a permanent magnet it is supposedly the electrons circulating around the atoms that are the source current. It can be shown that the distributed magnetic dipole moment in the material is equivalent to a surface current around the outside of the magnet (currents cancel except at the surface).

Thus, even with a permanent magnet the source of the magnetic field is a current and one then needs to show that that same current is ALSO the source of the induced electric fields. This can be done. I"m not going to do it here, but it can be shown that a moving current even at constant velocity actually induces not only magnetic field but also an electric field about itself that is related to the velocity of one frame with respect to the other. [One frame being the magnet and the other being the coil]. In such a case the E field generated by the frame differences can once again be shown to be the result of the CURRENT as is the magnetic fields generated. By the same reasoning we again note that the current is the source and although one can find that the VALUE of the induced E field is given by V x B it is not CAUSED by B!