Creating a Poleless Magnet Ring

[MS La Moreaux]

Has anyone heard of a permanent magnet in the shape of a ring or toroid with no poles? I believe that one could be made by winding a ring of magnetic material, such as steel, with a wire winding, like one winding of a toroidal transformer. DC current could then be passed through the winding for a sufficient length of time and then the winding removed. One would then have a magnet with no poles, the flux circulating around the ring. I believe that if the ring were uniform and symmetrical, there would be no magnetic field external to the ring. I cannot think of a practical use for such a magnet but just am interested in the principle. Comments?

Mike

 

[Drakkith]

Is this material a hollow torus or a solid?

 

[pallidin]

Remember those old horseshoe shape magnets with a soft iron "keeper" connecting the poles?
There you have it.
Note that there is still some external magnetism, however.

 

[MS La Moreaux]

Drakkith,

I was thinking of solid, but I do not believe that it would make any difference.


pallidin,

Yes, it is similar, but the maximum symmetry of the torus is necessary to eliminate any external field.

Mike

 

[Bob S]

Has anyone heard of a permanent magnet in the shape of a ring or toroid with no poles? I believe that one could be made by winding a ring of magnetic material, such as steel, with a wire winding, like one winding of a toroidal transformer. DC current could then be passed through the winding for a sufficient length of time and then the winding removed. One would then have a magnet with no poles, the flux circulating around the ring. I believe that if the ring were uniform and symmetrical, there would be no magnetic field external to the ring.

B_inside is everywhere parallel to the boundary between air and the magnetic material. If H-tangential is continuous across this boundary, then the tangential B_air = B_inside/μ, where μ is the relative permeability.

I cannot think of a practical use for such a magnet but just am interested in the principle. Comments?

Would there be an Aharanov-Bohm effect

http://en.wikipedia.org/wiki/Aharonov–Bohm_effect

on any charged particle going through the hole in the ring? Is there a practical use?

Bob S

 

[granpa]

Aharonov–Bohm effect:

Schematic of double-slit experiment in which Aharonov–Bohm effect can be observed: electrons pass through two slits, interfering at an observation screen, with the interference pattern shifted when a magnetic field B is turned on in the cylindrical solenoid.

http://en.wikipedia.org/wiki/Aharonov–Bohm_effect

 

[stevenb]

pallidin,

Yes, it is similar, but the maximum symmetry of the torus is necessary to eliminate any external field.

Mike

As pointed out by Bob S, even toroidal symmetry will not eliminate the external field if you only have a permanent magnet.

You could encase the torus in a superconductor to shield the magnetic field, and truly confine it.

A tightly wound toroidal coil with DC current is a cheaper way to have field inside and essentially zero field outside.

... DC current could then be passed through the winding for a sufficient length of time and then the winding removed ...

In other words, don't remove the windings from the ring, and don't turn off the current. Basically, the field from the current will cancel the field from the core, on the outside of the ring. (you can also think of this in terms of the boundary condition mentioned by Bob S, but now include the sheet linear current density K: i.e. Ht1-Ht2=K, which allows Ht2=0 on the outside)

 

[MS La Moreaux]

The lack of an external field is the result of symmetry, not the particular source of the field. The lack of poles implies no external field. If there were an external field, there would be poles. If there is an external field, what does it look like?

Mike

 

[Bob S]

The lack of an external field is the result of symmetry, not the particular source of the field. The lack of poles implies no external field. If there were an external field, there would be poles. If there is an external field, what does it look like?

If there are no surface currents (coils), Curl H is continuous across the boundary between air and the ring (magnetic material), meaning Curl H = 0, or tangential H_air = H_ring.. So B_air = μ₀H_air = B_ring/μ, where μ is the relative permeability of the ring material at field B_ring.

Bob S

 

[MS La Moreaux]

Bob S,

So what does the field look like? What is its shape?

Mike

 

[Phrak]

As pointed out by Bob S, even toroidal symmetry will not eliminate the external field if you only have a permanent magnet.

You could encase the torus in a superconductor to shield the magnetic field, and truly confine it.

Now, that's an interesting proposal. But will the counter-currents in the superconductor, required for cancelation of external fields, also cancel all internal fields?

 

[thehacker3]

http://unitednuclear.com/index.php?main_page=product_info&cPath=70_71&products_id=290

 

[pallidin]

http://unitednuclear.com/index.php?main_page=product_info&cPath=70_71&products_id=290

Most commercial ring magnets actually have the poles on the "flat" sides.
The same is true for the above link, but harder to envision.

 

[thehacker3]

Most commercial ring magnets actually have the poles on the "flat" sides.
The same is true for the above link, but harder to envision.

Well then I'm puzzled by the question - what defines a pole? Like what makes the north pole of a magnet a pole, and not the middle of it?

 

[stevenb]

Now, that's an interesting proposal. But will the counter-currents in the superconductor, required for cancelation of external fields, also cancel all internal fields?

That's an interesting question about an "interesting proposal". Keep in mind that the proposal is not my invention. I've just read discussions on the Aharonov–Bohm effect that talk about using superconductors to remove any doubt that the electron is traveling in a field free region.

I'm not very knowledgeable about superconductor theory so I hesitate to answer definitively. My best guess is that generally the internal fields won't cancel, and that the internal field will always be strengthened. But, I wouldn't be overly surprised if an expert comes here and tells us that it is possible to configure a superconducting shield with a particular core material in a way that cancels both internal and external fields. It seems counter-intuitive to me, but my intuition has failed me often enough that I'm not surprised when it happens.

 

[stevenb]

Well then I'm puzzled by the question - what defines a pole? Like what makes the north pole of a magnet a pole, and not the middle of it?

That's actually a good question. A magnetic "pole" is one of those things that everyone talks about and assumes is straightforward, until they try to define it. I like to think of a pole as the part of a magnet that has the most concentrated field that is typically coming mostly perpendicularly to the surface.

For example, a typical bar magnet or a spherical magnet (like the earth) are like dipoles, and the dipole field pattern (you can look it up in any EM book) has clear poles. Magnetic field lines are always closed, so the north poles field lines circulate back to the south pole.

The OPs example is interesting because there is no clearly identifiable pole, due to the symmetry. The field lines internal to the toroid just circulate back on themselves always. The external field lines also circulate back on themselves.

However, typical ring magnets aren't magnetized in this way. They can be magnetized so that the top and bottom (think heads and tails of a coil-like object) are the north and south poles. Also, they can be magetized so that one side of the circular cross section is the north pole and the oposite side is the south pole. Think about a two dimensional version of the Earth (circle rather than sphere) with a north and south pole.

 

[granpa]

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/toroid.html#c1
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html#c1

 

[MS La Moreaux]

All magnetic field lines of a permanent magnet must pass through the magnetic material, since the iron atoms are the source of the field lines, and therefore the lines must pass through the iron atoms. Any external field lines must therefore pass through the surface of the torus. There is no way for this to happen without violating symmetry. Thus, there can be no external field.

Mike

 

[pallidin]

All magnetic field lines of a permanent magnet must pass through the magnetic material, since the iron atoms are the source of the field lines, and therefore the lines must pass through the iron atoms. Any external field lines must therefore pass through the surface of the torus. There is no way for this to happen without violating symmetry. Thus, there can be no external field.

Mike

Uh... I don't think that's true. Field lines do not have to stay within a material, though a majority will.
For example, take a horseshoe permanent magnet and bridge the north/south poles with a soft iron "keeper''
According to your thoughts, then, there can be no external field.
This is NOT the case.
With that magnet and it's keeper, bring it close, BUT NOT TOUCHING a paper-clip.
The paper-clip WILL be attracted.
Just not as much, by far, if there were no "keeper"

 

[MS La Moreaux]

pallidin,

I did not say that the lines had to stay within the magnetic material; I said that they have to pass through the material. In other words, there cannot be any lines no part of which exist in the material.

Mike

 

[pallidin]

OK, gotcha. We're on the same page of thought.

 

[granpa]

Uh... I don't think that's true. Field lines do not have to stay within a material, though a majority will.
For example, take a horseshoe permanent magnet and bridge the north/south poles with a soft iron "keeper''
According to your thoughts, then, there can be no external field.
This is NOT the case.
With that magnet and it's keeper, bring it close, BUT NOT TOUCHING a paper-clip.
The paper-clip WILL be attracted.
Just not as much, by far, if there were no "keeper"

a horseshoe magnet with a bridge isn't perfectly symmetrical.
A perfectly symmetrical ring magnet with the north south poles aligned along the torus will not and cannot have any external field.

likewise an infinite solenoid will have zero external magnetic field.

 

[MS La Moreaux]

Thank you, pallidin and granpa.

Mike

 

[stevenb]

In other words, there cannot be any lines no part of which exist in the material.

Ah, good point. So, actually, there is no discrepancy with the boundary condition, since there is an effective current sheet running on the surface of the magnet, which allows the boundary condition to be matched, and the external field to be zero.

Sorry, I forgot about that aspect of magnets. The internal dipoles act like tiny little current loops. The internal loops all cancel out, but the outer surface has nothing to cancel it out. (self-inflicted head slap)

 

[MS La Moreaux]

Thank you, stevenb.

I guess we could call it a "stealth magnet."

I have thought of one use for it. It perfects my counter example to Faraday's Law (see Post #51 to my locked thread, "Faraday's Law Is False!," last post March 10, 2010, in this forum). Substitute the toroidal permanent magnet for the core and primary winding.

Mike

 

[granpa]

why no link?

https://www.physicsforums.com/showthread.php?p=2404015#post2404015

 

[MS La Moreaux]

granpa,

Sorry, I did not realize that I could do that. Thanks for providing it.

Mike

 

[stevenb]

I have thought of one use for it. It perfects my counter example to Faraday's Law (see Post #51 to my locked thread, "Faraday's Law Is False!," last post March 10, 2010, in this forum). Substitute the toroidal permanent magnet for the core and primary winding.

Mike

I'm not able to fully comprehend the mechanism, based on your description, but it sounds like you are saying that if you wrap coils around a toroidal core magnet (magnetized in the way you describe), and devise a method to keep electrical connections while you unwind the coils (so that the number of turns encircling the field steadily decreases), there will be no EMF despite the fact that there is a time changing flux.

However, you haven't provided a good reason why there would be no EMF. Motional and transformer EMF are just words used to classify. Whether or not you find that your experiment fits either category is not important. Whether or not others agree or disagree with your classification is unimportant. What is important is that Faraday's law says there will be EMF if flux changes in time, and if there is no EMF as you change encirclements in time, then the law would be invalid in that case.

So, there are two logical questions we are forced to asked here.

1. Have you actually done the experiment and confirmed your notion?

2. If so, why in heaven's name have you not published your amazing result?

Surely you realize such a publication would immortalize your name. Whenever Faraday's name is mentioned in future, your name would logically follow.

Remember that Faraday was an avid experimentalist and believed that experiments are the only source of new scientific discovery. He would never accept any mathematical or logical explanation for a new discovery. Although later history has shown some exceptions with theory driving discoveries, all scientists look to experiments to prove a discovery.

The experiment would need to show that (1) there is no EMF and (2) that the number of encircling loops truly is decreasing. Determining encirclement can be very tricky in some circumstances. Although I don't consider myself an expert, I've done a number of experiments that involve Faraday's Law. If not careful, you can miscalculate encirclements. They can be there when you think they are not there and they may not be there even when you think they are there. I've seen people a lot smarter than I literally pulling there hair out trying to make sense of some arrangements.

In any event, the process is simple. Do the experiment. Clearly show the experimental setup, methods and results. Then let others read a write-up and try to make sense of the result. They will then repeat the experiment to see if they can reproduce the result. If they can't explain why there is no EMF and can't show that the number of wraps is constant, then you are instantly famous.

 

[MS La Moreaux]

stevenb,

No, I have not done the experiment, but it should not be necessary. There are two forms of induction. One is motional emf, which is just a direct application of the definition of a magnetic field. A conductor moves through a magnetic field in such a direction that it cuts the field lines. The free electrons experience magnetic forces on them along the length of the conductor, resulting in an emf. Notice that there is no primary electric field. (There may be a secondary electrostatic field due to the emf, but this is irrelevant.) The other form of induction is transformer emf and is prescribed by one of Maxwell's classic four equations. It states that an intrinsically time varying magnetic field induces a non-electrostatic electric field. A closed path (not necessarily conductive, and suitably oriented) in that electric field will have an emf. These two forms of induction include all the possible cases. They are independent of each other. There is no principle that a change in flux linking a circuit due solely to motion induces an emf in the circuit. Any emf in the circuit due to motion caused flux change is motional emf and not due to the flux change which happens to accompany it. In my counter example, the flux change linking the circuit is solely due to motion. There is no intrinsic change in the flux in the magnet. No electric field is induced. There is no motional emf because the winding is not in the magnetic field. Since induced emf must be either transformer or motional, there is no emf in this case. Faraday's Law supposedly includes both motional and transformer emf. It is not claimed to include anything else. Since Faraday's Law specifies an emf in this case, it is falsified.

Mike

 

[stevenb]

stevenb,

No, I have not done the experiment, but it should not be necessary.

Thank you for answering my first question. Above I explain why I'm of the opinion that it is necessary to do the experiment to prove your point. Keeping it still simpler. You are saying Faraday's Law is wrong because another law (or set of rules), which logically can not be Faraday's Law, gives a different answer. How do you choose between two theories, that each give different answers, except by experiment? You are obviously giving greater credence to the other law, but how do you convince someone else who believes that Faraday's Law is a more fundamental law?

I guess I'll rephrase my second question, since I originally made it contingent on whether you had done the experiment.

2. Since you are confident that you can disprove Faraday's Law and have not done the experiment, why wouldn't you next do this relatively simple experiment, publish the results and get the credit for a great discovery? Or, perhaps that is your plan?

 

[stevenb]

No, I have not done the experiment, but it should not be necessary.

I should also point out that there is another aspect to this question. In addition to doing the experiment, you also need to show your application of Faraday's Law and demonstrate that threre is a discrepency between the law and the experiment.

I've been rereading your description of the experiment, and I now think I understand your setup. Now that I understand it, I actually agree with you that there will be no EMF, but this still does not invalidate Faraday's Law. When I apply Faraday's law to the problem, I get EMF=0. In effect, as counterintuitive as this will sound, there is no change in number of encirclements, and hence no time changing flux.

In order to see the error in your logic, I would propose a slight modification to your experiment. Instead of using a slip-ring and brush, let a long length of wire run by the brush (in contact) as you pull the wire through. From this viewpoint, you can see that you will never unwind the coil. The coil stays on the toroid with the same number of turns, provided you have a very long length of wire to keep feeding into the stream. The slip ring example is analyzed from the same point of view. As the ring spins, it traces out additional loops.

Having read some of your other posts, I know you don't accept this type of explanation, but this is the correct way to apply Faraday's Law. In order to provide you another viewpoint, consider how your arrangement with the slip ring would decrease the number of encirclements. Since the number must be an integer, how do you gradually go from 100 to 99 to 98 turns etc.? In other words, if you have 100 turns and the length of the circumference of one turn is 1 cm, and you pull the wire by 0.1 cm, you can't say that you've encircled the field by 99.9 turns.

Anyway, I know you won't accept this, so let's just agree to disagree on this. The bigger issue here is not whether you are right or wrong. I think you actually have provided a very interesting thought experiment, that is worthy of thinking about. The main point here is that it's ok to challenge a law with a thought experiment, but you should not make the claim that a firmly established law is invalid without following a reasonable scientific approach. You need to carefully explain the experiment, carefully do an analysis, carefully do an experiment, and then (most importantly) allow others to examine all of this, they/we can then reproduce your experiment, check your analysis and validate your idea. That's how the scientific process works.

 

[MS La Moreaux]

stevenb,

The two principles upon which Faraday’s Law is supposed to be based, namely motional emf and transformer emf, are principles of nature. Faraday’ s Law is not based upon any principle. It does include transformer emf, but its apparent inclusion of motional emf is just a mathematical or geometrical coincidence. Faraday’s Law is just a numerical equality, not a mathematical description of a principle, and the numerical equality does not even always hold true. The Lorentz equation does what Faraday’s Law only claims to do (and the latter only for circuits). It includes both transformer and motional emf and does it properly by the sum of separate terms. Faraday’s Law tries to cram them both into a single term, which is logically impossible because they are independent.

Your idea that the number of turns has to be an integer is not true. Without the device of the slip ring there has to be an integral number of turns, but with the slip ring the flux linking the winding gradually and smoothly decreases as the coil is unwound. I do not see how there could be any confusion concerning encirclements. When the coil is fully unwound there will be no more flux linkage. (The slip ring always has its own constant flux linkage, but it is a separate circuit. Its spinning has no effect.)

I independently determined that Faraday’s Law is false, but it was know to be the case way before that. Richard Feynman pointed it out. A physics professor recently told me that above the undergraduate level, the matter is made clear, but that Faraday’s Law is an oversimplification for undergraduate students. My view is that if simplification is desired, Faraday’s Law should just be eliminated. It would not be missed since it is redundant.

Mike

 

[stevenb]

A physics professor recently told me ...

Feel free to mention the name of the Prof and the school he teaches at. Can you give the reference to the grad level textbooks which you/he are talking about?

above the undergraduate level, the matter is made clear, but that Faraday’s Law is an oversimplification for undergraduate students.

I have noted just the opposite of what you said. My undergrad text on EM theory simplifies the presentation of Faraday's Law, while my three grad level texts show Faraday's law as one of the four Maxwell Equations. I'm tempted to quote them all, but I know you will still not be convinced. So for the benefit of others, I'll just mention Jackson, which is well respected here. I'm on my cell phone now, so later I'll paste in the page and equation number.

 

[MS La Moreaux]

stevenb,

His name is Professor Keith Riles of the Physics Department of the University of Michigan at Ann Arbor. I do not know the titles of the textbooks to which he referred. I do not believe that he is aware of the lack of widespread awareness of the situation. I am aware that many textbooks call that one of Maxwell's Laws Faraday's Law, which only adds to the confusion surrounding induction. Professor Riles does the same, as did Richard Feynman. The version we have been discussing in this thread is just that one with the partial derivative changed to the total derivative, which is obviously suspect on the face of it. Actually, it makes sense to call that one of Maxwell's Laws Faraday's Law, since the other version is false.

Mike

 

[MS La Moreaux]

stevenb,

I found an email sent to me by Professor Riles. Here is part of it:


"My own approach to teaching Faraday's Law depends on the
level of the class. In elementary courses for premeds and
engineers, I always point out that the EMF in moving
circuits can be derived from motional EMF while presenting
the traditional "Faraday's Law" approach at the same time,
but I don't draw special attention to the mathematical
machinery that allows both approaches to give the same
answer. When I teach honors physics majors at the elementary
level or teach upper level or graduate E&M courses, I do
draw attention to the "trick" that allows Faraday's Law to
give the right answer even when, strictly speaking, it
doesn't apply.

"The nation's most popular textbook for junior/senior E&M courses
for physics majors is David Griffiths' "Introduction to
Electrodynamics". On page 303 (3rd edition) he does explicitly
draw attention to the different mechanisms and states that
he does not regard a loop of wire drawn through an inhomogenous
B field to be an instance of Faraday's Law. Griffiths notes that
this "peculiar accident" of mathematical agreement led Einstein to
special relativity.

"I also checked the text I used as an undergraduate (Reitz, Milford
& Christy, "Foundations of Electromagnetic Theory", 3rd edition).
It too drew attention to the different phenomena involved in
what is loosely called Faraday's Law.

"So I think most physicists do receive the education you would like
them to receive on these subtleties. It's when the subject is
taught at the elementary level that the treatment is typically
superficial. Although I realize that bothers you, it may help to
realize that there is a great deal of pedagogical oversimplification
in those elementary courses. For example, we usually simplify the
presentation of angular momentum and moment of inertia as if
rotations occur about a single axis. We don't present relativistic
transformations of E and B fields or the notion of "retarded time".
At most we only touch upon the magnetic vector potental, and so on."

Mike