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

[Prologue]

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

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

This is the imagery.

 

[elect_eng]

elect_eng,

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

Mike

OK, there are a couple of questions here.

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

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

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

Getting back to some of your other comments.

You state that the operation of the Faraday disk is not based on Faraday's Law. That means that the basis of the operation of the Faraday disk is motional EMF and that motional EMF and Faraday's Law are independent. If they are independent, Faraday's Law cannot include motional EMF, which is what I have been maintaining all along.

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

 

[OmCheeto]

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

This is the imagery.

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

Perhaps it is more obvious in Faraday's original:

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

 

[Prologue]

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

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

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

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

 

[elect_eng]

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

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

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

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

That is a very good summary. Thank you!

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

$$\nabla \times E = {{-\partial B}\over{\partial t}}$$

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

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

What am I missing here?

 

[OmCheeto]

That is the problem, there is a breakdown in the language.

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

hmmm...

Let's start over.

premise: E=-d$$\Phi$$ /dt is wrong.

FL is based on observed data.

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

The problem with it has nothing to do with inability to measure small enough values.

What?

There are three problems that come to mind at the moment. 1. There are counter examples where it does not work at all.

And they are?

2. There is no way to incorporated two independent principles into one term of an equation.

Sounds like semantics again. But I'm a linguistic idiot. Let's see if I can figure this out:

The term law is often used to refer to universal principles

A principle is one of several things: (a) a descriptive comprehensive and fundamental law, doctrine, or assumption; (b) a normative rule or code of conduct, and (c) a law or fact of nature underlying the working of an artificial device.

so a law is a principle and a principle is a law. ie Law = Principle. Therefore there's no way to incorporate two laws into one term of an equation. So the laws of physics have to all have separate equations.

3. There is no principle upon which it is based.

So laws have to be based on laws?

It is just an ad hoc formulation, like Bode's Law, which works for admittedly most cases, but is just an accident of geometry and math. It is an engineering convenience but is superfluous as a law. It adds nothing to our understanding as the principles of motional EMF and transformer EMF cover every possible case.

Mike

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

hmmm...

Perhaps this belongs in the philosophy forum.

 

[elect_eng]

elect_eng,

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

Mike

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

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

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

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

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

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

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

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

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

 

[Prologue]

...

$$\int (E+v \times B) \cdot dl=-\int {{dB}\over{dt}}\cdot ds$$

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

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

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

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

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

 

[cabraham]

Hey, Claude, don't say dumb things and then run off! Where did you ever get the idea that somehow "credentials" are needed to topple Faraday's law? And where did you ever get the idea that real science is only done by spending vast sums of taxpayer money? Are you getting your paycheck from the government or something? And why wouldn't 32 years of engineering background qualify you to challenge Faraday? Hey, you live in the 21st century and Faraday, though smart, didn't know squat compared to you!

The truth is (and I sure hope you are not spreading your errors among the young) that science is done with the MIND! It all starts between the ears. I don't care how much money you spend, if you can't think it won't be science!

And the truth is that Faraday's law as typically stated IS wrong (but interestingly NOT wrong according to how Faraday stated it!). Does anyone here understand how the rocking plates work? Why doesn't the changing flux give a voltage? Here, I'll explain it to you guys. Here's the equivalent idea and one more case where Faraday's supposed law is invalid.

Imagine a large rectangular loop of wire with a meter in the circuit. Imagine a magnet putting a local flux through an area in the end of the loop near the meter. Imagine a wire and a switch connecting the sides of this loop that when thrown cuts it into two loops. Now move the magnet to the other end of the large loop (nothing happens as flux enclosed in loop has not changed). Now close the shorting switch. Remove the magnet. Open the switch. Voila. The flux has gone from max to zero and the meter does not move! Faraday is invalid!

But the error that makes Faraday's law misinterpreted is that one assumes that a changing magnetic field (flux) causes an induced E field. (An E field in a conductor creates a current) Sorry, the equation Curl E = -db/dt or as often stated EMF = -dB/dt are TRUE relations but they are not CAUSAL relations!

You need to understand what that means. It means that while the value of an induced E and a magnetic field are RELATED they DO NOT cause each other. Hence a voltage is NOT repeat NOT created by a changing magnetic field! If one examines the causality of Maxwell's equations one finds that BOTH magnetic and electric fields are BOTH created by ONLY by charges and their motions (currents). Hence an induced EMF is created by a current somewhere as it's source. And that current ALSO creates a magnetic field. BOTH are related (as they come from the same source) by Faraday's law in many cases, but the changing magnetic field is NOT causing the EMF! Indeed even in the case of moving magnets one can show that the EMF is created by the moving atomic CURRENTS that create the fields of the permanent magnets.

Hence, as Feynman clearly states, Faraday's law is NOT valid for all cases. In cases for example where the configuration of our setup is changing (our switching example) it simply does not work. It didn't work in Faraday's time either as proved by the generator bearing his name! Which is why Faraday NEVER said that a changing magnetic field induces an EMF. He said that a changing CURRENT can induce another current nearby! Obviously even though Faraday didn't have much of a clue, he still knew more about the subject than all the "modern" physicists with their PhDs, money, accelerators and scanning microscopes! OK?

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

curl E = -dB/dt.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Claude

 

[bjacoby]

It depends on the size of your short circuit and the sensitivity of your meter whether there’s a deflection. According to Ohms law if your short circuit has a resistance (it has) and a current flows through the short (it does) there will be a voltage across the meter. By the way the current in the short is normally called an eddy current.

Disconnecting the meter temporarily, while you remove the magnet will prove your point as well?

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

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

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

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

 

[bjacoby]

That is completely wrong. An electric field can be created by a changing magnetic field.

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

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

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

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

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

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

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

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

 

[diagopod]

"Neither Maxwell's equations nor their solutions indicate an existence of causal links between electric and magnetic fields."

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

 

[Per Oni]

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

The correct description would be to start with the magnet under the meter and the short across the center of the rectangle closed. That metered half of the rectangle represents our area over which we integrate the B field to get the flux. It has a large (DC) value.

DC stands for Direct Current?

Now open the center divider switch and slide the magnet to the other end of the rectangle, but not outside of the large rectangle. Since the circuit now is just the large rectangular loop and the magnet stays inside the loop there is NO change in flux. At no time during any of these operations does the flux change or the meter move!

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.

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

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

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

 

[bjacoby]

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

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

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

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

 

[Ben Niehoff]

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

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.

 

[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 = - $$\partial$$$$\Phi$$/$$\partial$$t, 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. $$\ointop_{\partial S} E \cdot dl=-{{d}\over{dt}}\Biggl(\int_S B \cdot ds\Biggr)$$

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.

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

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.

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

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.

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

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!].

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

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.

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