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

[Dadface]

I really don't understand this thread.

I can find situation where the Photoelectric effect doesn't work, Ohm's law doesn't work, 2nd Law of thermodynamics doesn't work, etc.. .etc. In fact, one can say the same about the whole of Newtonian mechanics.

Does that mean that each one of them is "false"? This is absurd! If you truly believe that, get out of your house immediately!

Zz.

I don't think the general opinion here is that they are false,far from it.I think each one has a domain of applicability.Newtonian mechanics domain,for example, is extremely broad but you wouldn't use it to find the KE of particles moving at relativistic speeds.

 

[cesiumfrog]

To get to the integral form of Faraday's law from curl E we have to use Stokes' theorem, which doesn't involve time varying closed paths.

This seems to be in the domain that classical EM is valid, and I don't see a mathematical reason to disallow taking the integral form of any of Maxwell's equations (whether time-varying or steady-state), hence we have that the electric field (in the lab frame of reference) around the circuit sums to zero (regardless of whether the plate turns).

Is the mistake (the paradox) to assume that the total electromotive force is always proportional to merely the electric part (and forgetting the second part of the Lorentz force, namely that the fixed magnetic field constitutes an extra electric force component in the reference frame of the current, and that this becomes unbalanced by different relative motion of the current in the rotor/stator)? (Still, a complete description would presumably use more of Maxwell's equations to obtain the flow of current over the entire disc, rather than just treating the dragging qualitatively.)

 

[atyy]

So if we do surface integrals on both sides of curlE=-dB/dt, then take Stokes law on the LHS to get emf, and changing flux on the RHS due to the time varying boundary, won't it be non-zero?

Maybe for the RHS we can use the "flux transport theorem" given in Chapter 12 of "Advanced Engineering Mathematics" by Jeffrey, after taking dB/dt=0 and divB=0, I seem to get:

d(B-flux)/dt=line-integral-around-time-varying-boundary-of-(B cross v)

where v is the velocity of the boundary, which seems like the Lorentz force law.

The mistake here is that I exchanged the order of integration and differentiation where I shouldn't have. So even with a time varying path, the line integral of E should be zero.

This seems to be in the domain that classical EM is valid, and I don't see a mathematical reason to disallow taking the integral form of any of Maxwell's equations (whether time-varying or steady-state), hence we have that the electric field (in the lab frame of reference) around the circuit sums to zero (regardless of whether the plate turns).

Is the mistake (the paradox) to assume that the total electromotive force is always proportional to merely the electric part (and forgetting the second part of the Lorentz force, namely that the fixed magnetic field constitutes an extra electric force component in the reference frame of the current, and that this becomes unbalanced by different relative motion of the current in the rotor/stator)? (Still, a complete description would presumably use more of Maxwell's equations to obtain the flow of current over the entire disc, rather than just treating the dragging qualitatively.)

Yes, I guess there are two things called "Faraday's law". There's the thing that is one of Maxwell equations (differential and integral forms), and these are never wrong, and emf for a moving conductor actually comes from the Lorentz force law.

Then there's the "sheer luck" form, which has limited applicability and sometimes can be used for moving conductors. Very interesting!

 

[vanesch]

I really don't understand this thread.

I can find situation where the Photoelectric effect doesn't work, Ohm's law doesn't work, 2nd Law of thermodynamics doesn't work, etc.. .etc. In fact, one can say the same about the whole of Newtonian mechanics.

Of course, but here the thing that is at work is more trivial. It are not the "boundaries of applicability of a certain paradigm" in science which is at work, but simply a mis-use of a formula, which, unfortunately perhaps, still gives the "right" result in certain cases, but not all.

 

[lugita15]

I don't have it with me at the moment, but if memory serves me right Griffith explains the real reason behind this apparent "coincidence" in his Introduction to Electrodynamics. Basically, it boils down to the fact that the observed emf is given by the flux rule, regardless of whether it is generated by an induced electric field or an electric force, because the two situations are really the same situation, except that they occur in different inertial reference frames. So special relativity makes the answer the same in both cases.

I read Griffith a couple years ago, so don't quote me on this. BTW, the one thing I was never able to fully understand about this explanation is that it doesn't cover all the cases in which the flux rule applies, so it doesn't fully explain away the "coincidence." For instance, what if you have a coil which is expanding or contracting in area. Or consider a fixed loop through which a magnetic field is directed perpendicular to the plane of the loop, but it is varying in time. Both of these problems obviously obey the flux rule, but can the *deeper* reason for this phenomenon be found using a relativistic analysis?

Another explanation for why the apparent coincidence is given in http://www.iop.org/EJ/article/0295-5075/81/6/60002/epl_81_6_60002.html" .

My high school physics teacher used to say that the reason Faraday's Law yields all kinds of confusing and counter-intuitive results is that it is based in relativity. If you take all the other Maxwell equations, they do not contradict Newtonian mechanics. It is only after you add Faraday's Law that it can be shown that Electric and Magnetic fields do not obey Galilean transformations, but obey Lorentz transformations instead.

 

[MS La Moreaux]

Here is a link to the relevant pages of The Feynman Lectures on Physics, The Definitive Edition, Volume II, sections 17-1 and 17-2, pages 17-1 to 17-3: "[URL

Feynman states, "We have also given the "flux rule," which says that the emf is equal to the rate at which the magnetic flux through such a conducting circuit is changing...First we'll consider a case in which the flux changes because a circuit is moved in a steady field." This indicates that by "flux rule' he means what we are calling Faraday's Law, even though he uses the latter term for the one of Maxwell's Laws responsible for transformer EMF.

He goes on to describe the homopolar generator and states, "Clearly, here is a case where the v x B force in the moving disc gives rise to an emf which cannot be equated to a change of flux."

He gives another counter example to Faraday's Law and then states, "The correct physics is always given by the two basic laws..."[for the Lorentz force and for transformer EMF]. This implies that Faraday's Law is incorrect physics.

Mike

 

[Born2bwire]

I got to echo ZapperZ's sentiments here, what's the point of this thread? The reasons why Faraday's Law does not correctly apply to this situation have already been discussed.

 

[MS La Moreaux]

The point is that virtually all the textbooks seem to treat Faraday's Law as describing a physical principle, namely that a flux change due to an intrinsic change in the flux, or due to motion, induces an EMF in a circuit. This is false. In every instance where the flux changes due to motion, the EMF is actually motional (v x B). The associated flux change is just along for the ride. It is like guilt by association. The change in flux happens to accompany most cases of motional EMF, even though they are independent. In the case of the homopolar generator, the two are separated, in effect, because there is no flux change, just pure motional EMF, and Faraday's Law fails completely. This is not to disparage Faraday. When he formulated Faraday's Law it was an entirely reasonable thing to do. Later on, however, the subject became better understood with Maxwell's Laws and the expression for the Lorentz force. Faraday's Law at that point was obsolete except as an engineering convenience, yet modern physics does not seem to recognize the fact; Feynman seems to have been ignored.

Mike

 

[Per Oni]

The point is that virtually all the textbooks seem to treat Faraday's Law as describing a physical principle, namely that a flux change due to an intrinsic change in the flux, or due to motion, induces an EMF in a circuit. This is false.

This is not false.

In every instance where the flux changes due to motion, the EMF is actually motional (v x B). The associated flux change is just along for the ride. It is like guilt by association. The change in flux happens to accompany most cases of motional EMF, even though they are independent. In the case of the homopolar generator, the two are separated, in effect, because there is no flux change, just pure motional EMF,

How do you think this EMF is generated? (in fact EMF is not the same as v x B).
Do you think there’s a difference in principle when a conductor cuts a homogenous magnetic field, or as in the case of a homopolar generator, the homogenous magnetic field cuts a conductor?

Feynman seems to have been ignored.

And just as well.
Look at Fig. 17-3 of your quoted book.
Underneath he states: “When the plates are rocked in a uniform magnetic field, there can be a large change in the flux linkage without the generation of an emf. “
This is plain nonsense.
Here in the copper plates, eddy currents exist, caused by the EMF’s generated by the change in flux linkages. However there’s no way the galvanometer can measure these EMF’s because of the internal short circuits in the copper plates.

Sometimes a flea bites an elephant.

 

[Phrak]

And just as well.
Look at Fig. 17-3 of your quoted book.
Underneath he states: “When the plates are rocked in a uniform magnetic field, there can be a large change in the flux linkage without the generation of an emf. “
This is plain nonsense.

This is not nonsense. Re-establishing a current requires no eddy currents and does not produce an emf. This can be clearly seen in an arrangment of a series of parallel wires. As the wires are sequencially connected to a galvenometer, so as to change the amount of enclosed flux, Maxwell's equations predict no emf.

 

[Per Oni]

The eddy currents in your parallel wires have already run during the time when you established the magnetic field. Since the energy is now already dissipated no further emf will be observed.
Purely theoretically :If you had 100% ideal diodes in the middle of your wires you would still see a deflection on a 100% efficient galvanometer because during the stet up of this experiment the wires become slightly charged.
To go back to Fig. 17-3 it would be relatively easy to prove that eddy currents are running because of the Joule heating in the plates. Care must be taken not to include heating by friction of the 2 plates against each other. If the plates are heating up it must be that emf’s are generated, in contradiction to what RF states.

 

[MS La Moreaux]

We all agree on the existence of the two principles of transformer EMF (given by the appropriate Maxwell's equation) and motional EMF (related to part of the Lorentz force expression). Per Oni seems to believe in a third principle, that an EMF is induced in a circuit whose flux linkage is changing solely due to the circuit's motion relative to a magnetic field, said EMF being entirely due to the flux change and not due to motional EMF. Since there is motional EMF in such a case, how could it not be the entire EMF?

In the counter example of the rocking plates, the point is that the physical motion is so slight that any motional EMF is insignificant, while the flux change is relatively large. There will not be any significant eddy currents, unless, of course you believe in the third principle.

Mike

 

[Phrak]

The eddy currents in your parallel wires have already run during the time when you established the magnetic field. Since the energy is now already dissipated no further emf will be observed.
Purely theoretically :If you had 100% ideal diodes in the middle of your wires you would still see a deflection on a 100% efficient galvanometer because during the stet up of this experiment the wires become slightly charged.
To go back to Fig. 17-3 it would be relatively easy to prove that eddy currents are running because of the Joule heating in the plates. Care must be taken not to include heating by friction of the 2 plates against each other. If the plates are heating up it must be that emf’s are generated, in contradiction to what RF states.

I don't know where you come up with this idea. Making and breaking contacts will not generate an emf. No emf; no eddy currents. If there is any heating of the plates the generating current will show up on the ammeter.

If you wish to pursue this, show me, using Maxwell's equations where making or breaking a circuit in a static magnetic field will produce current flow.

 

[Phrak]

I'm going to backup a little Mike, and address one of your previous threads since I've only been half paying attention to this thread.

Feynman states, "We have also given the "flux rule," which says that the emf is equal to the rate at which the magnetic flux through such a conducting circuit is changing...First we'll consider a case in which the flux changes because a circuit is moved in a steady field." This indicates that by "flux rule' he means what we are calling Faraday's Law, even though he uses the latter term for the one of Maxwell's Laws responsible for transformer EMF.

The 'flux rule' given by Feynman is derrived from Faraday's Law.

Flux rule: emf = wB \frac{dL}{dt} = wBv[/itex]<br /> <br /> w is the width of a square loop of wire. (The part of the loop in motion is a wire w units long.)<br /> L is the length of the loop.<br /> B is a magnetic field, uniform in strength perpendicular to the loop<br /> v is the velocity of the wire in the L direction.<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> He goes on to describe the homopolar generator and states, &quot;Clearly, here is a case where the <i>v</i> x <b>B</b> force in the moving disc gives rise to an emf which cannot be equated to a change of flux.&quot;<br /> <br /> He gives another counter example to Faraday&#039;s Law and then states, &quot;The <i>correct</i> physics is always given by the two basic laws...&quot;[for the Lorentz force and for transformer EMF]. This implies that Faraday&#039;s Law is <i>incorrect</i> physics.<br /> <br /> Mike </div> </div> </blockquote><br /> One of the two basic laws Feynman refers to <i>is</i> Fraday&#039;s Law, <br /> <br /> <br /> \nabla \cross \textbf{B} - \frac{\partial \textbf{E}}{\partial t} = \textbf{J}\ \ , where \ \textbf{J}=0<br /> <br /> so of course he doesn&#039;t imply it&#039;s incorrect.

 

[Per Oni]

In the counter example of the rocking plates, the point is that the physical motion is so slight that any motional EMF is insignificant, while the flux change is relatively large. There will not be any significant eddy currents, unless, of course you believe in the third principle.
Mike

Instead of the rocking plates think of a flexible wire between the dots where the galvanometer is connected, in the middle sagging through to point P. Now move the middle of this wire from point P to P’. I hope you will agree that an emf will be displayed on the meter due to a change of flux in this circuit.
The rocking plates can be seen as a load of parallel wires. Whether the physical motion is slight or not doesn’t make any difference to the application of Faradays law.

In a similar way one could say that the disk drawn in Fig. 17-2 consist in reality of a huge number of parallel wires. When the disk is rotated each wire will experience a change of enclosed flux, and therefore generate an emf. Again the emf will not be fully displayed due to eddy currents in short circuits.
The point here is that RF writes: "the moving disk gives rise to an emf which cannot be equated to a change in flux." Again I disagree.

 

[Per Oni]

I don't know where you come up with this idea.

During the setup of your experiment you switched on the power supply to the magnet or you moved the wires under the magnet, in both cases emf’s are generated in the wires.

Perhaps more to the point: when connecting different wires to a meter can we still speak of the same circuit, or are there now in fact a load of parallel circuits?

 

[MS La Moreaux]

Phrak, Feynman defines the "flux rule" in section 16-1, and it is the same as what we are calling Faraday's Law. Neither of the two basic laws he refers to is what we are calling Faraday's Law.

Per Oni, flux change due to motion has no effect in itself. It is the motion which has the effect, namely motional EMF. You seem to be using Faraday's Law to argue for the validity of Faraday's Law.

Mike

 

[Per Oni]

Mike

I've asked:

I hope you will agree that an emf will be displayed on the meter due to a change of flux in this circuit.

Can I deduce from your (at least for me) somewhat strange reply that your answer is yes?

Can you explain to me what your reply means?

 

[MS La Moreaux]

Yes, if an actual wire moves in that way there will be an EMF due to motional EMF. Induced EMF is only due to either motional EMF or transformer EMF. Faraday's Law purports to include both of those, but only for circuits. It actually, improperly, includes more, namely the case of flux changing solely due to motion when there is no motional EMF. This is the problem with the rocking plates. One cannot properly approach motional EMF through flux change. Just because it happens to work in most cases, it does not mean that there is a physical basis for it, just a geometric and mathematical basis. Math is essential for physics, but it is not the same thing as physics. If one is not careful to apply or interpret the math according to the underlying physical concepts, one can easily be led astray. For instance, moment is measured in pound feet and work is measured in foot pounds. These are identical mathematically, but completely different physically. Motional EMF requires a conductor, does not require a closed path, involves a magnetic force on the charged particles and requires motion. Transformer EMF does not require a conductor, does require a closed path, involves an electric force on charged particles (if present), and does not involve motion. These two principles are physical principles and, between them, cover all the cases. Faraday's Law is not based upon a physical principle, it just seems that way. It tries to squeeze the two very different and independent principles into a single term of an equation, which, I believe, is impossible.

Mike

 

[Per Oni]

Yes, if an actual wire moves in that way there will be an EMF due to motional EMF. ... This is the problem with the rocking plates. One cannot properly approach motional EMF through flux change.
Mike

You agree that when the rocking plates are replaced with one wire in the manner I described before that an emf is generated. I can describe to you a circuit involving many wires which will replace the rocking plates and each wire in turn will generate an emf caused by a changing magnetic flux through its particular circuit. But it’s a bit boring and I’ve got more to do.

I will end my contribution to this thread by saying sorry if I appeared a bit disrespectful to Mr. Feynman. Personally I think he was a great guy and scientist.
I can only hope that a footnote will be added to 17-2 in case a new edition is published of his lectures on physics.

 

[MS La Moreaux]

I have to believe that the circuit of many wires will not be equivalent to the rocking plates.

Here is another counter example to Faraday's Law. In a toroidal transformer with the primary winding the inner one, the magnetic field external to the primary winding is severely reduced because geometrical symmetry results in its canceling itself out. Now take a toroidal core with a primary winding and loosely wind a secondary winding with one end going to an external circuit (such as a galvanometer) and the other going to a slip-ring loosely fitted around the primary winding. The brush contacting the slip-ring goes to the external circuit. Energize the primary winding with DC current, resulting in a constant magnetic flux in the core. Now gradually unwind the secondary winding. Its flux linkage will steadily decrease, but there will be no EMF in it because there is neither motional nor transformer EMF, thus violating Faraday's Law.

Mike

 

[kmarinas86]

I really don't understand this thread.

I can find situation where...2nd Law of thermodynamics doesn't work, etc...

This claim is entirely baseless and has no founding whatsoever.

 

[kmarinas86]

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'd give more credit to Feynman than the average American science textbook.

 

[ZapperZ]

This claim is entirely baseless and has no founding whatsoever.

Then please explain G.M. Wang et al., Phys. Rev. Lett. 89, 050601 (2002), for example.

Now, I'm not claiming that the 2nd Law has been shown to be wrong, because this occurs under a very specific condition. But that is the exact point being made to condition being given by the OP.

Zz.

 

[cabraham]

I have to believe that the circuit of many wires will not be equivalent to the rocking plates.

Here is another counter example to Faraday's Law. In a toroidal transformer with the primary winding the inner one, the magnetic field external to the primary winding is severely reduced because geometrical symmetry results in its canceling itself out. Now take a toroidal core with a primary winding and loosely wind a secondary winding with one end going to an external circuit (such as a galvanometer) and the other going to a slip-ring loosely fitted around the primary winding. The brush contacting the slip-ring goes to the external circuit. Energize the primary winding with DC current, resulting in a constant magnetic flux in the core. Now gradually unwind the secondary winding. Its flux linkage will steadily decrease, but there will be no EMF in it because there is neither motional nor transformer EMF, thus violating Faraday's Law.

Mike

Is this a joke? For a while, I thought this post was a legitimate questioning of FL. This "counterexample" is proof that this thread is for entertainment purposes only.

Next time you challenge an established law in jest, would you please say so?

Claude

 

[MS La Moreaux]

Claude,

I was entirely serious. Do you have a specific, substantive criticism?

Mike

 

[cabraham]

Yes I do. There will indeed be an emf/mmf. If the flux in the core is constant/dc, and you unwind the secondary, there will be a flux change and an emf. However considering that v = -N*d(phi)/dt, the emf is very small. Unwinding the secondary has a frequency in the sub-Hertz range. While unwinding, you are moving a conductor in the presence of a magnetic field. But the motion involves one turn at a sub-Hertz frequency. Further, what is phi? When wrapped around the toroid, phi can be substantial. But when unwrapped, no longer encircling the core, phi is nanoweber, or less.

The fact that the emf is quite small, and requires good equipment to measure, does not invalidate FL. If phi is 10 nwb, f = 0.10 Hz, N = 1.0 turn, then v = 2*pi*1e-8*1e-1*1e0 = 2*pi*1e-9 = 6.28 nV! These are just off the cuff estimations. A real world scenario may vary by an order of magnitude in either direction. But we are looking at nanovolt levels of emf. Extremely small emf, but still present, is what is going on.

Claude

 

[MS La Moreaux]

Claude,

You are begging the question. You are attempting to use Faraday's Law to validate Faraday's Law. See, this is the crux of the matter. Faraday's Law implies that a flux change due to motion produces an EMF. This is a false principle. The true principles are motional EMF and transformer EMF (given by the one of Maxwell's Laws which is the same as Faraday's Law except in that it uses the partial derivative). One or the other of these true principles covers every case to which Faraday's Law applies. Both of these true principles give an EMF of zero in the case being considered. The partial derivative of the equation for transformer EMF is zero because there is no intrinsic flux change. There is no motional EMF because the wire moves in a direction which results in its not cutting the magnetic flux lines, aside from the fact that the magnetic field is severely reduced external to the primary winding. Faraday's Law specifies an EMF for this case and is thereby proved false. This case is the opposite of the homopolar generator in that in the case of the homopolar generator Faraday's Law gives an EMF of zero where there actually is one, whereas in this case Faraday's Law gives an EMF where there actually is none.

Mike

 

[cabraham]

Claude,

You are begging the question. You are attempting to use Faraday's Law to validate Faraday's Law. See, this is the crux of the matter. Faraday's Law implies that a flux change due to motion produces an EMF. This is a false principle. The true principles are motional EMF and transformer EMF (given by the one of Maxwell's Laws which is the same as Faraday's Law except in that it uses the partial derivative). One or the other of these true principles covers every case to which Faraday's Law applies. Both of these true principles give an EMF of zero in the case being considered. The partial derivative of the equation for transformer EMF is zero because there is no intrinsic flux change. There is no motional EMF because the wire moves in a direction which results in its not cutting the magnetic flux lines, aside from the fact that the magnetic field is severely reduced external to the primary winding. Faraday's Law specifies an EMF for this case and is thereby proved false. This case is the opposite of the homopolar generator in that in the case of the homopolar generator Faraday's Law gives an EMF of zero where there actually is one, whereas in this case Faraday's Law gives an EMF where there actually is none.

Mike

Refer to bold quote. This statement actually affirms FL. If the wire moves so as to NOT cut H lines, then FL predicts 0 emf. Since curl E would then be 0. Since E has no curl, the emf is merely the line integral of E around the closed loop, which is of course 0. Hence FL predicts 0 which you insist is the correct answer. Or, if you prefer to look at it from motional quantities, "u X B", is 0, where "u" is velocity. When the motion is along a flux line, not cutting, then the cross product is 0.

You say 0, & FL says 0. You say you're right, while FL is wrong. You have no case at all.

As far as my using FL to verify FL, what I'm doing is explaining the action, observing the result, and acknowledging the agreement with FL. All science is based on such methods. We observe, postulate, remeasure, and affirm. It happens that FL agrees with observation, so it is valid. Sure, we made initial assumptions. That in itself does not validate FL, nor invalidate FL. But since observation under all known conditions to date verifies FL, it is considered good law.

Claude

 

[MS La Moreaux]

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