Faraday's Law is False!

[M S La Moreaux]

The version of Faraday's Law that purports to encompass both motional and transformer EMF in one term of an equation, namely EMF= -d[math]\Phi[/math]/dt, is false! Richard Feynman pointed this out in his Lectures on Physics, although he called it the "flux rule." It works in most cases, but not all. It has no physical basis. It is just an engineering convenience. It seems that virtually all the physics and electromagnetics textbooks and encyclopedias, at least in the U.S.A., treat it as though it is a true physical law. They also contain a lot of nonsense related to Faraday's Law, such as erroneous derivations and misconceptions. I believe that it is quite an indictment of the status quo and a scandal.

 

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

 

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

 

Mike

[Cap'n Refsmmat]

Could you provide some specific examples of situations where Faraday's Law is improper or fails? You're using different terminology than I used when I learned Faraday's Law. (You're also not using SI units, but that's another story...)

[M S La Moreaux]

Ironically, Faraday's disk dynamo is an example where Faraday's Law fails. It is a steady-state case. The magnetic flux is constant. Therefore, Faraday's Law specifies zero EMF when, in fact, there is one.

 

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

 

Mike

[Cap'n Refsmmat]

Ironically, Faraday's disk dynamo is an example where Faraday's Law fails. It is a steady-state case. The magnetic flux is constant. Therefore, Faraday's Law specifies zero EMF when, in fact, there is one.

 

This is not strictly true. My textbook's definition of Faraday's law has two separate wordings:

 

The induced emf along any moving or fixed path in a constant or changing magnetic field equals the rate at which magnetic flux sweeps across the path.

 

That is, in the Faraday's disk case, we can measure the flux a path on the disk sweeps through in each unit of time, and use that to determine the emf.

 

The book then defines the version of Faraday's Law for a closed loop, which agrees with your version:

 

The induced emf around a closed path in a magnetic field is equal to the rate of change of the magnetic flux intercepted by the surface within the path.

 

However, any closed loop in the disk would necessarily have a zero potential difference, because in a closed loop, the start point and the end point are the same point. (They can't be different points if it's a closed loop.) The law gives the correct result -- the voltage difference across a point is 0 -- but it's not useful at all, since it's not what we're looking for.

 

Physics for Engineers and Scientists, 3rd. ed., Ohanian and Markert.

[M S La Moreaux]

Your quoted definitions are perfect examples of what I described: they are both sloppy and incorrect.

 

In the first case, if the path is not conductive, it may have an EMF induced in it by a changing magnetic field which the path is not in. For example, a closed path looped through a toroidal electromagnet with a time-varying magnetic flux.

 

The second case again specifies that the path be in the magnetic field, which, as in the first case, is unnecessary. it is also incorrect in not forbidding motion of the path. The second counter-example in my previous post refutes this definition.

 

You see, transformer EMF, given by one of Maxwell's classic four equations, and called by some textbooks Faraday's Law, is the result of an electric field produced by a time-varying magnetic field. It is not directly a result of the magnetic field, itself. Faraday's Law (the version which is the subject of this thread) is mistakenly taken to imply a third physical principle of induction, namely that a time-varying magnetic field that is changing solely due to motion always produces an EMF. There is no such principle.

 

As regards the Faraday's disk, the path is fixed and does not sweep. Only the disk moves. Potential differences have no part in this discussion. Faraday's Law only addresses EMF. The closed loop is not entirely in the disk. The closed loop is the circuit, including the external part. As a matter of fact, at least to a first approximation, the magnetic field lines are parallel to the plane of the circuit. Therefore, there is no magnetic flux intercepted by the surface of the closed path.

 

Mike

[Cap'n Refsmmat]

The emf generated by a Faraday disk can be computed using Faraday's law as follows, for a disk of radius r with an angular frequency of [math]\omega[/math]:

 

The arc length s = r θ and the area A = r s can be approximated to be a triangle of height r and base s, so

 

[math]A = \frac{1}{2} r s = \frac{1}{2} r^2 \theta = \frac{1}{2} r^2 \omega t[/math] and

 

[math]\varepsilon = -\frac{d\Phi}{dt} = IR[/math]

 

[math]|I|R = \frac{d\Phi}{dt}[/math]

 

[math]|I| = \frac{1}{R}\frac{d\Phi}{dt} = \frac{B}{R} \frac{dA}{dt}[/math]

 

[math]= \frac{B}{R} \left( \frac{1}{2}r^2 \omega\right) = \frac{B r^2 \omega}{2R}[/math]

 

as given by the solution manual for my homework problem from a week or two ago.

 

It works!

[M S La Moreaux]

It may give the correct answer, but that does not prove that it is physics. Faraday's Law does give the correct answer in most cases, but not because it is a valid principle. If it were valid, it would give the correct answer in every case.

 

Mike

[Cap'n Refsmmat]

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

 

I'm curious; you suggest that there is no motional emf, yet you are unwinding the wire, which should induce a motional emf. (After all, the wire has to move.) Now, the situation you describe is complicated enough that I may be mistaken, but whatever...

 

With the Faraday disk example, it's apparent that misinterpreting Faraday's law and complaining when you get the wrong answer doesn't work. Faraday's Law does work in that situation. The "physicality" of the law is unimportant, anyway -- look at Maxwell's equations, for example. They're not actually Maxwell's, because Maxwell's original equations were horrendously complicated and had a few dozen unknowns. Oliver Heaviside used vector calculus (a mathematical formulation) to create a new formulation that described electromagnetism in just four equations, which became known as Maxwell's equations. But the modern Maxwell's equations are a result of complicated mathematical manipulation, not a direct physical principle.

[Mr Skeptic]

Ooh, someone says that a theory that has stood the test of time nearly 2 centuries. I can't wait for the shocking new revelations! This will revolutionize the world of science, it's not every day that such a well-supported theory gets overturned.

 

However, I'd rather read the peer-reviewed article rather than some random guy on the internet. So where was it published? Science? Nature?

[swansont]

Moved to speculations

[M S La Moreaux]

Cap'n Refsmmat,

 

There is no motional EMF, first because the wire is moving lengthwise, so that any EMF would be across the width of the wire, not its length, and second because the external magnetic field is insignificant.

 

I am not misinterpreting Faraday's Law, you are. It is clear that there is no change in the magnetic flux through the circuit. It seems to me that Maxwell's equations are the expression of direct physical principles, regardless of how they were arrived at.

 

Mr Skeptic,

 

I see that you are one of those who takes authority over logic and reasoning. Is Richard Feynman not authoritative enough for you?

 

swansont,

 

I do not believe that this thread deserves to be moved to the speculations category. Again, this is not something new. Richard Feynman pointed out the fact that Faraday's Law does not always work and gave a couple of examples of this many years ago.

 

Mike

[Cap'n Refsmmat]

How is the wire moving lengthwise when you unwind it? You cannot unwind it without rotating it around the core.

 

Incidentally, Feynman said of Faraday's law:

 

We know of no other place in physics where such a simple and accurate general principle requires for its real understanding an analysis in terms of two different phenomena.

 

(Emphasis mine.) He hardly said it was wrong.

[M S La Moreaux]

The wire is moving lengthwise as it unwinds, not sideways as in motional EMF.

 

If you read a little further you will find that Feynman said that the "flux rule," as he called it, does not always work and gave two examples. I cannot explain the apparent discrepancy. Again, I maintain that one phenomenon cannot be logically explained alternatively in terms of either of two independent principles.

 

Mike

[Cap'n Refsmmat]

Its flux linkage will steadily decrease, but there will be no EMF because there is neither motional nor transformer EMF, thus violating Faraday's Law.

Wait. How can the flux decrease steadily without inducing a transformer emf?

 

Since I do not have Feynman's book, I'm not privy to his examples.

 

Relativity does unite motional and transformer emf as being the exact same phenomenon in different reference frames, so what's the problem?

[M S La Moreaux]

Transformer EMF is produced by an intrinsically changing magnetic flux, not by the changing exposure of a closed path to a constant flux, as is the case with my example.

 

One of the examples Feynman gave was Faraday's disk dynamo. The other involved rocking plates with a moving point of contact. With an insignificant motion of the plates (thereby eliminating motional EMF) the flux linked by the circuit changed a lot without producing any transformer EMF for the reason given in the previous paragraph.

 

I would rather not get into relativity. Faraday's Law was evidently around long before relativity and is simple enough.

 

Mike

[swansont]

One of the examples Feynman gave was Faraday's disk dynamo.

 

In his video lecture he uses this example and says it works by the law of induction. Curious.

[M S La Moreaux]

It seems to me that there are two forms of induction: motional EMF and transformer EMF. Faraday's disk dynamo is an example of motional EMF.

 

Mike

[Cap'n Refsmmat]

And as I pointed out, special relativity makes motional and transformer emf the same thing.

[Chriton]

I am only a simple Electrical Engineer but I was taught that a moving Magnetic field induces EMF in a conductor in a closed loop by inducing the electrons to move through that conductor, in turn a magnetic flux is induced in that conductor, A transformer uses the same principle by alternating the EMF and inducing a EMF in an external conductor, all moving Fluxes and Alternating Fluxes cause the same effect, In a non (or semi) conductor the EMF can be produced and stored by exchanging charged particles to discharge when a circuit is realised, a DC current would not induce an EMF unless it was moving or collapsing, if collapsing then it would induce an EMF in the opposite direction, Faraday's Law is still true.

I remember when I was being taught Electrics, I questioned everything as well...

Did you know that water moving through your taps at home cause an EMF in the pipes as anything that strips electons causes EMF and Faraday's Law still applies.

Edited April 21, 2010 by Chriton

[M S La Moreaux]

Cap'n Refsmmat,

 

I am not that up on relativity, but I do not see how it could apply to transformer EMF, since transformer EMF does not involve motion.

 

Mike

[M S La Moreaux]

I have realized that my purported counter example involving the toroidal transformer is flawed. The circuit splits at the slip ring and then rejoins. This is not addressed by Faraday's Law.

 

Mike

[M S La Moreaux]

I have concluded that Faraday's Law is not a law but rather a mathematical identity. If the change in magnetic flux linkage of the circuit is due to motion of the circuit, the resulting emf is just motional emf and is not a result of flux change. Essentially, the quantities that are multiplied together to get the emf are the flux density, the length of the conductor, and the speed of the conductor. These are the same quantities multiplied together to calculate the rate of change of the magnetic flux linkage. Faraday's Law may give the correct result, but it is not the expression of a physical principle, which I believe is a requirement of a physical law. Now, if the circuit is stationary and the magnetic flux changes, an emf will be induced in the circuit, and Faraday's Law will give this as a result. But this case is covered by the Maxwell-Faraday Law, which is one of Maxwell's equations. Between them, motional emf and the Maxwell-Faraday Law cover every case of induction. Faraday's Law is not just a combination of these two principles: Faraday's Law applies only to a circuit. Neither motional emf nor the Maxwell-Faraday Law do. Motional emf only requires a conductor, and the Maxwell-Faraday Law does not even require that.

[swansont]

Faraday's observation came ~30 years before Maxwell's equations , which incorporated and generalized Faraday's law.

 

It's a law because it's a simple mathematical expression that holds for some phenomena. That's really all it took in classical physics.

[M S La Moreaux]

I have personally discovered that Faraday’s Law of Electromagnetic Induction is not a law.  I am referring to the version of Faraday’s Law which uses the ordinary time derivative and not the partial derivative, which version is called the Maxwell-Faraday Law and is one of Maxwell’s equations.

Faraday’s Law is not a law because it is not an expression of a physical principle.  There are two physical principles which are called induction.  The first is motional emf, which is an extension of the definition of the magnetic field and consists of a conductor moving through a magnetic field such that it cuts the magnetic field lines.  It is responsible for the operation of generators.  The second is the Maxwell-Faraday Law, one of Maxwell’s Equations, and is responsible for the operation of inductors and alternators.  These two principles are independent of each other.  It is unfortunate that both are called induction because it leads to confusion.  Faraday’s Law only partially includes both and in a way which obscures the cause and effect.  Neither of the principles of induction requires a circuit, but Faraday’s Law does.  Faraday’s Law gives the same result whether the change in magnetic flux linking the circuit is strictly due to a time-varying magnetic field or is due to movement of the circuit.  A time-varying magnetic field is accompanied by an electric field.  It is this electric field which results in an emf in the circuit.  A moving circuit in a magnetic field experiences an emf due to the motion of the conductor through the magnetic field.  Of course, the magnetic field has to be non-uniform or the shape of the circuit has to change with time.  The same mathematics is that is used to calculate the time derivative of the magnetic flux linking the circuit is used to calculate the motional emf.  Thus, Faraday’s Law is just based on mathematics and not physics.  It is misleading because it implies a cause and effect which does not exist.  Also, Faraday’s Law can be derived.  This proves that it is not a law because physical laws cannot be derived, only inferred.

I believe that Faraday’s Law does not belong in the textbooks.  It is superfluous and serves no purpose except to confuse the issue.

[swansont]

!

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