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

[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: [tex]emf = wB \frac{dL}{dt} = wBv[/itex]

w is the width of a square loop of wire. (The part of the loop in motion is a wire w units long.)
L is the length of the loop.
B is a magnetic field, uniform in strength perpendicular to the loop
v is the velocity of the wire in the L direction.

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

One of the two basic laws Feynman refers to is Fraday's Law,


$$\nabla \cross \textbf{B} - \frac{\partial \textbf{E}}{\partial t} = \textbf{J}\ \ , where \ \textbf{J}=0$$

so of course he doesn't imply it'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

 

[cabraham]

Claude,

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

Mike

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

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

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

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

Claude

 

[MS La Moreaux]

Claude,

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

Mike

 

[cabraham]

Claude,

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

Mike

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

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

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

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

Claude

 

[chrisphd]

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

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

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

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

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

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

 

[cabraham]

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

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

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

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

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

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

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

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

Claude

 

[WiFO215]

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

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

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

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

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

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

Faraday's law is

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

or in integral form can be written as

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

and is not to be confused with

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

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

 

[chrisphd]

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

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

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

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

 

[cabraham]

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

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

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

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

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

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

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

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

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

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

Claude

 

[Archosaur]

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

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

 

[MS La Moreaux]

Claude,

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

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

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

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

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


chrisphd,

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


anirudh215,

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


Archosaur,

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

Mike