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

[bjacoby]

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?

I used DC in the sense of Direct Current meaning not varying with time. I purposely used the term "DC" as a reminder that even in permanent magnets it is electron CURRENTS that cause the magnetic field.

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

To understand the rocking plates. Look at the circuit of the plates as the area we are calculating flux over. The area changes because the contact point between the two plates changes. See Feynman Fig. 17-3. Draw straight lines from the pivots on the two plates to the contact point. See how they form an expanding triangle? That represents a HUGE flux change. So why does the flux rule fail? Suppose if you will that the plates contact not in a single point but in two points that are very closely spaced. Now you have TWO circuits through the plated. As you rock the plates inward the inner circuit breaks and the new outer one makes contact. If we assume that the outer one makes contact BEFORE the inner one breaks we have a situation exactly like our switched loops above. The plates are making micro-steps by switching between the two "circuits". Feynman doesn't bother to explain this in his book but you can see with a bit of thought that it's true.

 

[Ben Niehoff]

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

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

The key point is that drawing straight lines from the pivots to the contact point is NOT the correct way to complete the circuit. The ambiguity arises because one is using extended conducting objects to form a circuit, rather than idealized, thin wires. Remember that at sufficiently low frequencies, current always travels on the [i]surface[/i] of a conducting object, and does not penetrate. In fact, in an irregularly-shaped object, the current will be concentrated near regions of higher mean curvature; i.e., it will flow along the [i]edges[/i] of the rocking plates, not along the faces. Hence the straight line paths in Feynman's drawing are not the path actually taken by the current.

Edited to add:

There have been a lot of confusing, irrelevant, and probably false statements in this thread, both in favor of and against Faraday's Law. I hope you will read the paper above by Frank Munley, which resolves all of these paradoxes squarely. Faraday's Law applies even to the homopolar generator, despite others' claims (and Wikipedia's claim) that one must resort to the Lorentz force law.

In fact, one can prove mathematically that for circuits, Faraday's Law and the Lorentz force law are completely equivalent. The catch is that one has to provide a clear interpretation of these laws in the case of extended conducting objects.

 

[elect_eng]

There have been a lot of confusing, irrelevant, and probably false statements in this thread, both in favor of and against Faraday's Law. I hope you will read the paper above by Frank Munley, which resolves all of these paradoxes squarely. Faraday's Law applies even to the homopolar generator, despite others' claims (and Wikipedia's claim) that one must resort to the Lorentz force law.

Excellent! This clears everything up perfectly. I apologize for implying that one must resort to the Loretz force law to explain the Faraday disk. My own opinion was that the disk did not disobey Faraday's law, but that Faraday's Law did not explain the operation. I was wrong about that. This description by Frank Munley makes it crystal clear.

So, in protest to the title of this thread, I'd like to yell out,

"FARADAY's LAW IS TRUE!"

 

[MS La Moreaux]

elect_eng,

You asked for correct equations. Maxwell's Law for transformer EMF is E = - \partial\Phi/\partialt, which is correct. The equation for motional EMF is E = (v x B) . l, which is correct.
The Lorentz equation is EMF = \int (e + v x B) . dl, which is correct. (Sorry, I do not have a complete handle on printing equatiions.) The first two, between them, cover every case of the two types of electromagnetic induction. The Lorentz equation covers both the above and is correct. Notice that the Maxwell law uses the partial derivative and not the ordinary. This eliminates the effect of motion. The equation for Faraday's Law that is the topic of this thread is the same as that Maxwell law with the exception that it uses the ordinary derivative rather than the partial. This broadening of the derivative is evidently for the purpose of including motional EMF, but it does not do so accurately. It works in most cases, but not all.

FL is claimed to give the induced EMF, regardless of whether it is transformer EMF or motional EMF. This means that it would have to encompass motional EMF in every instance where motional EMF occurred. It fails to do this and is therefore false.

\Phi is magnetic flux. B is flux density.

Mike

 

[bjacoby]

The meter will jump twice during this procedure: each time the switch is opened or closed! Remember that flux is the B field enclosed times the area,

\Phi = BA

and so its derivative with respect to time is

\frac{d \Phi}{dt} = A \frac{dB}{dt} + B \frac{dA}{dt}

When the switch is opened or closed, the area of the loop changes, and therefore there is a nonzero change in flux! In fact, the faster the switch is opened or closed, the higher the value of dA/dt, and hence the higher the EMF generated. In the ideal case of opening or closing the switch infinitely fast, the EMF will be a delta function (spike), and the needle will quickly flick to one side and back.

Your mathematics is correct it just doesn't apply to the experiment in question! If you open and close the switch the area of the loop most assuredly is changing. But the meter does NOT "twitch". What is missing here is the difference between an EXPANDING loop which changes the flux by changing the area (as talked about in the excellent (but I believe basically incorrect) paper you referenced). If you have a thin wire and pull it out into a large loop you do indeed get a meter movement. The wire thus represents the line integral defining the area where an integration calculates the flux. Hence if you change the area the flux changes. But as Feynman notes in that case the apparatus while moving, is not changing configuration with time. In other words it is not "switching". I can assure you the switched loops, on the other hand, do NOT twitch the meter when switching from one loop size to another. You've got a great theory, but reality does not agree with you.

There is simply NO physical mechanism you can point to that can explain any induced EMF in the wires as a result of shorting and unshorting half a coil! No conductors are moving in a magnetic field, no currents are moving or changing. The bottom line is you are proving the flux rule is correct by starting with the assumption that it works! You have gone in a circle!

 

[MS La Moreaux]

OmCheeto,

I said that FL is based on observed data, not that it correctly reflected all observed data. There is a difference.

If you would read my posts in this thread, you would find two counter-examples. One is the homopolar generator and the other is a modified toroidal transformer with the secondary gradually unwound.

I would say that physical laws tend to be quantitative, whereas physical principles are qualitative. It seems to me that the laws of physics all do have separated equations. Can you give an example of a true physical equation that contains two independent principles in a single term?

I said that there is no principle upon which FL is based. This is not a case of a law being based upon a law; it is the case of a false equation posing as a law and having no foundation. FL is not a model of anything.

Mike

 

[MS La Moreaux]

elect_eng,

The equation you quote from "Foundations of Classical Electrodynamics" is the proper integral form of FL, and it is false.

It is an example of the situation that I addressed in my initial post in this thread.

Mike

 

[elect_eng]

The equation for Faraday's Law that is the topic of this thread is the same as that Maxwell law with the exception that it uses the ordinary derivative rather than the partial. This broadening of the derivative is evidently for the purpose of including motional EMF, but it does not do so accurately. It works in most cases, but not all.

OK, if it doesn't work in all cases, then it is not a correct representation of Faraday's Law. I can't claim to to be able to conclusively answer why this equation does not always work, but I suspect examples where it fails would have to do with the difficulty of defining a path independent EMF in some cases. I quoted a proper representation of FL above and I'll repeat here again, from the book "Foundations of Classical Electrodynamics", by F.W. Hehl and Y. N. Ovukhov. It is equation I.4 on page 6. Note that no reference is made to voltage, EMF or potential here. <br /> <br /> \ointop_{\partial S} E \cdot dl=-{{d}\over{dt}}\Biggl(\int_S B \cdot ds\Biggr)<br /> <br />

I'm quoting this book because it offers a very clear axiomatic based treatment of electromagnetics in a modern formulation that includes general relativity. In this treatment, FL is a direct consequence of very basic experimentally consistent and accepted facts.

1. Conservation of electric charge
2. Existence of the Lorentz force
3. Conservation of Magnetic Flux

The vanishing divergence of magnetic field strength is another result of these. Additional axioms are used to complete the treatment in the context of GR, and some of these, while well-accepted, are not as firmly established. Note that a discovery of magnetic monopoles would require significant changes to the additional axioms. However, FL would still be valid, while the Lorentz force and divergence equation would need alteration.

Denying FL is akin to denying conservation of mass/energy. It represents a very significant claim that requires an extraordinary basis with evidence. It's still not clear to me if you are challenging the proper statement of FL, or only stating that a particular formula may not properly capture the essence of FL.

 

[bjacoby]

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

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

The key point is that drawing straight lines from the pivots to the contact point is NOT the correct way to complete the circuit. The ambiguity arises because one is using extended conducting objects to form a circuit, rather than idealized, thin wires. Remember that at sufficiently low frequencies, current always travels on the [i]surface[/i] of a conducting object, and does not penetrate. In fact, in an irregularly-shaped object, the current will be concentrated near regions of higher mean curvature; i.e., it will flow along the [i]edges[/i] of the rocking plates, not along the faces. Hence the straight line paths in Feynman's drawing are not the path actually taken by the current.

Edited to add:

There have been a lot of confusing, irrelevant, and probably false statements in this thread, both in favor of and against Faraday's Law. I hope you will read the paper above by Frank Munley, which resolves all of these paradoxes squarely. Faraday's Law applies even to the homopolar generator, despite others' claims (and Wikipedia's claim) that one must resort to the Lorentz force law.

In fact, one can prove mathematically that for circuits, Faraday's Law and the Lorentz force law are completely equivalent. The catch is that one has to provide a clear interpretation of these laws in the case of extended conducting objects.[/QUOTE]

I knew someone would bring up the "straight line" assumption being wrong. Yeah it is wrong or at least one might say that the path of the circuit inside the plate is not well defined. But that doesn't quite throw it out. Suppose for example one replaces the plates with just the "rocking" edge of the plates that are attached to a thin "rod" to the pivot. Now the circuit is well defined: down the rods and up the edge to the contact point. One can easily see that while the rods are not moving to the extreme degree as given by the appearance of the former assumed straight-lines, the rods indeed ARE moving and the area defined by them and the rest of the "thin" circuit parts is clearly changing to a reasonable degree. Thus the Munley assumption that only the space between the curves represents changed area would be wrong. Furthermore, they actually think that a small meter movement should be present from that flux change! I am asserting based on my "switching" model that NO meter movement appears even for the relatively large flux change as defined by my proposed rods.

As for lots of confusing, irrelevant and probably false statements, I suggest we begin with the one that low frequency currents travel only on the OUTSIDE of conductors. This is simply not true. Obviously you are referring to the fact that charge in equilibrium only resides on the outside of conductors. But in a dynamic case ESPECIALLY when there is electromagnetic induction this is not the case. Charge is redistributed because an electric field E exists WITHIN the conductor to move said charge. In the case of an open circuit the build up of charge due to that E field creates an opposite balancing E field and equilibrium is achieved. But the CURRENTS DO NOT travel on the outside of conductors except at very high frequencies and for very different reasons.

 

[elect_eng]

elect_eng,

The equation you quote from "Foundations of Classical Electrodynamics" is the proper integral form of FL, and it is false.

It is an example of the situation that I addressed in my initial post in this thread.

Mike

No, you did not address this equation because the one I quoted does not reference EMF in any way. The equation quoted has very strong foundations. Can you quote a specific example where this formula has been proved wrong?

 

[MS La Moreaux]

Prologue,

You have given a great summary of the confusion surrounding FL. I would think that it might help many people who seem to be confused.

At the end of that post, you mention the possibility of the transformer effect being the result of a wire being impinged by moving B field lines. The apparent motion of B field lines during an intrinsic change in the magnitude of the magnetic field is not the same as moving lines. The lines of a changing field have no direct effect on a wire. The wire does not even have to be in contact with the magnetic field to experience transformer EMF because it is the electric field produced by the changing magnetic field that is directly responsible for the EMF in the wire. The closed path of which the wire is at least a part must, however, be flux linked by the magnetic field.

Mike

 

[moderate]

This thread IS being reviewed right now.
Zz.

Don't close this thread - I think that it's an informative and interesting discussion.

 

[MS La Moreaux]

OmCheeto,

In regard to the homopolar generator, the relevance of the flux lines being parallel to the plane of the circuit is that, because of that, there is no flux linkage of the circuit. Therefore there can be no change in the flux linkage during the operation of the HG. Since FL only explicitly involves the change in flux linkage, the EMF it predicts has to be zero. Yes, the flux lines are perpendicular to the current flow in the disk. And yes, the EMF is generated in the disk, by motional EMF, which is not encompassed by FL.

Mike

 

[MS La Moreaux]

elect_eng,

You state that if the equation for FL does not work in all cases then it is not a correct representation of FL. The equation for FL is FL. The equation expressing a law is the ultimately accurate expression of that law. You can certainly argue that FL should be reformulated, but I believe the result would be the Lorentz equation. Some textbooks call Maxwell's Law for transformer EMF Faraday's Law. I have no problem with that. My initial post in this thread stated that this thread is about the other version of FL, and that one is used by many if not most textbooks.

Mike

 

[Ben Niehoff]

Your mathematics is correct it just doesn't apply to the experiment in question! If you open and close the switch the area of the loop most assuredly is changing. But the meter does NOT "twitch".

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

 

[Ben Niehoff]

I knew someone would bring up the "straight line" assumption being wrong. Yeah it is wrong or at least one might say that the path of the circuit inside the plate is not well defined. But that doesn't quite throw it out. Suppose for example one replaces the plates with just the "rocking" edge of the plates that are attached to a thin "rod" to the pivot. Now the circuit is well defined: down the rods and up the edge to the contact point. One can easily see that while the rods are not moving to the extreme degree as given by the appearance of the former assumed straight-lines, the rods indeed ARE moving and the area defined by them and the rest of the "thin" circuit parts is clearly changing to a reasonable degree. Thus the Munley assumption that only the space between the curves represents changed area would be wrong.

Re-read the paper. Munley actually makes exactly the same assumptions you just did: that the current path, for the sake of calculation, follows a line that is fixed relative to each individual rocking plate. So effectively, he removes the plates and replaces them with two wires with circular arcs attached to the end. He then calculates the total change in area due to the rocking movement (including the movement of the two wires, not just the arcs), and shows that it is quite small, thus producing a small EMF.

Feynman's claim was that given large enough rocking plates, one could produce arbitrarily large changes in area with arbitrarily small movements of the plates. Munley demonstrates that in fact the change in area gets smaller as the movements of the plates get smaller, and thus there is no violation of Faraday's law.

Furthermore, they actually think that a small meter movement should be present from that flux change! I am asserting based on my "switching" model that NO meter movement appears even for the relatively large flux change as defined by my proposed rods.

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

As for lots of confusing, irrelevant and probably false statements, I suggest we begin with the one that low frequency currents travel only on the OUTSIDE of conductors. This is simply not true. Obviously you are referring to the fact that charge in equilibrium only resides on the outside of conductors. But in a dynamic case ESPECIALLY when there is electromagnetic induction this is not the case. Charge is redistributed because an electric field E exists WITHIN the conductor to move said charge. In the case of an open circuit the build up of charge due to that E field creates an opposite balancing E field and equilibrium is achieved. But the CURRENTS DO NOT travel on the outside of conductors except at very high frequencies and for very different reasons.

Hmm...yes, you're right. I was thinking of penetration by electromagnetic waves, which has an exponential decay below the plasma frequency.

 

[elect_eng]

f

My initial post in this thread stated that this thread is about the other version of FL, and that one is used by many if not most textbooks.

If I'm understanding you correctly, you are now saying that the formula I quoted is correct, but just above you said it was incorrect. This has to be one of the most confusing threads I've ever read. Which is it? If it is correct and it is the one quoted in most textbooks (all that i own), then that is the one we want to use, and it is the definition of Faraday's Law.

 

[elect_eng]

elect_eng,

You state that if the equation for FL does not work in all cases then it is not a correct representation of FL. The equation for FL is FL. The equation expressing a law is the ultimately accurate expression of that law. You can certainly argue that FL should be reformulated, but I believe the result would be the Lorentz equation. Some textbooks call Maxwell's Law for transformer EMF Faraday's Law. I have no problem with that. My initial post in this thread stated that this thread is about the other version of FL, and that one is used by many if not most textbooks.

Mike

You know, I really think we've reached a point where we need to dispel some of this nonsense. I've quoted a very respected book above. Now I'll quote another very respected book. From "Classical Electrodynamics" 2nd edition by J.D. Jackson on page 210 and 211.

Starting on page 210, EMF is defined as the line integral of the electric field, nothing more and nothing less. Hence he arrives at the following which is a combination of his equations 6.1, 6.2 and 6.3.

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

He then goes on to say, "Let us now consider Faraday's law for a moving circuit and see the consequences of Galilean invariance.", and then he rewrites the equation again (eqn. 6.4), this time leaving out the EMF, which is just defined as the line integral of E. This is valid for motion and non-motion cases, and it is valid in the context of relativity as well. This is the correct representation of FL, period ! Note that the constant k is there because he uses a different convention for units, and we can just set this to unity for comparison to other formulas in this thread.

<br /> \ointop_{\partial S} E \cdot dl=-k{{d}\over{dt}}\Biggl(\int_S B \cdot ds\Biggr)<br />

Note that he says "Galilean invariance" which tells me that anything that follows from this point on can be questioned in the context of relativity, but should be valid in the Newtonian range of physics. Let me be very clear about that. The equations above are always true, while the equations below, are limited to nonrelativistic velocities.

He then expresses equation 6.5 to separate the motion from the local change as follows.

<br /> {{d}\over{dt}}\Biggl(\int_S B \cdot ds\Biggr)=\ointop_{\partial S} (B\times v) \cdot dl+\int_S {{\partial B}\over{\partial t}} \cdot ds<br />

This will then lead to a formula very similar to one I expressed before, only it has partial derivative in the right hand term, rather than total derivative. This needs to be modified for relativistic velocities, which seems implied in Jackson' comment that he is considering Galilean invariance. Anyway he finally arrives at the following, although I've corrected an obvious negative sign typo shown in the book [EDIT! Apologies, the equation was in fact correct!].

\ointop_{\partial S} (E-k v\times B) \cdot dl=-k\int_S {{\partial B}\over{\partial t}} \cdot ds<br />

So, I say once again. Faraday's Law is True !

If the point of this thread is that sometimes EMF is defined incorrectly for the purposes of expressing FL, for example involving a v x B term, then that is a good thing to talk about. Unfortunately, if that is the intent, it has not been made clear and there is much room for people to be misled by this thread.

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

 

[OmCheeto]

OmCheeto,

In regard to the homopolar generator, the relevance of the flux lines being parallel to the plane of the circuit is that, because of that, there is no flux linkage of the circuit.

I'm sorry, but I don't see the term for flux linkage in Faradays law:

E=-d\Phi /dt

Therefore there can be no change in the flux linkage during the operation of the HG.
Since FL only explicitly involves the change in flux linkage, the EMF it predicts has to be zero.

No. Since Faradays law does not include flux linkage in it's most basic form, the EMF it predicts is once again simply E=-d\Phi /dt

Perhaps it is best if you imagined the generator as a device with a unity flux linkage, as silly as that may sound, and it will all make sense.

Yes, the flux lines are perpendicular to the current flow in the disk. And yes, the EMF is generated in the disk, by motional EMF, which is not encompassed by FL.

Mike

It's good to see that you acknowledge that the flux lines are perpendicular rather than parallel as you stated earlier. But I really don't know how you can maintain your argument after accepting that fact.

 

[elect_eng]

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

As another example for the proper definition of Faraday's Law, consider the text "Fields and Waves in Communications Electronics", 2nd edition by S. Ramo, J.R. Whinnery and T. Van Duzer. Once again, this discussion makes the definition of FL clear. It is a law of nature according to our present understanding. This fact should not be clouded by other people who choose to use invalid definitions, or believe that their inability to properly apply the law to a given problem is evidence that the law is invalid.

In section 3.2 titled, "Voltages Induced by Changing Magnetic Fields"

" Before defining Faraday's Law more precisely, we should be clear about several definitions. By voltage between two points along a specified path, we mean the negative line integral of electric field between the points along that path. For static fields, we saw that the line integral is independent of path and equal to the potential difference between the two points, but this is not true when there are contributions from Faraday's Law. When there is a contribution from changing magnetic flux, the voltage about a closed path is frequently called the electromotive forece (emf) of that path."

EMF\equiv {\rm voltage \;\; about \;\; closed\;\; path} \equiv -\ointop_{\partial S} E \cdot dl

It is interesting that they define EMF as the negative of the line integral of electric field, but that is just an issue of convention.


In the next section, titled " Faraday's Law for a Moving System"

"... Faraday gave much physical significance to the flux tubes and lines of force. This point of view can be developed rigorously by writing the time derivative on the right hand side as a total derivative instead of a partial derivative".

Note that here they are referencing back to a previously stated version of FL which they clearly desribes as valid only for non-moving systems. They then write out the general formula as equation 4 on page 117.

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

 

[elect_eng]

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

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

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

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

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

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

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

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

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

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

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

Hence, Faraday's Law is True!

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

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

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

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

 

[Prologue]

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

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

...[/QUOTE]

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

 

[bjacoby]

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

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

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

 

[elect_eng]

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

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

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

 

[Ben Niehoff]

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

I repeat:

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

 

[amyfrog]

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

 

[bjacoby]

I repeat:

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

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

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

 

[elect_eng]

elect_eng,

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

One can see a few issues here.

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

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

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

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

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

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

 

[bjacoby]

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

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

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

"The flux rule does not work in this case. It must be applied to circuits in which the material of the circuit remains the same. When the material of the circuit is changing, we must return to basic laws."

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

Curl E = -dB/dt"

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

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

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

 

[elect_eng]

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

"The flux rule does not work in this case. It must be applied to circuits in which the material of the circuit remains the same. When the material of the circuit is changing, we must return to basic laws."

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

Curl E = -dB/dt"

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

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

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

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

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

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

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

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