# Maxwell-Faraday Law & Stealth Magnets: Exploring EMF Induction

• I
• MS La Moreaux
In summary, the author argues that the emf in a closed path is not the result of a flux change, but is instead due to the changing magnetic flux linking the closed path.
MS La Moreaux
Consider a closed path consisting of a loop of wire with a nonconducting gap that completes the closed path. The wire is threaded through a toroidal permanent magnet, magnetized around the toroid (what I call a stealth magnet). The magnetic flux is considered to be confined to the magnet. The flux links the closed path. Now, slip the magnet off one end of the wire loop so that it now is threaded by the nonconductive part of the closed path. Then pull the magnet out away from the loop so that it crosses the nonconductive part of the path. An emf should be induced in the closed path while the magnet is crossing the path because the magnetic flux linking the closed path changes with time. This is in accordance with the Maxwell-Faraday Law, which is one of Maxwell's equations.

There is a problem, however, because the nonconducting part of the closed path does not have to be the shortest route between the wire ends. It can bow out (or in). In other words, it is arbitrary. So when does the emf appear?

MS La Moreaux said:
Consider a closed path consisting of a loop of wire with a nonconducting gap that completes the closed path. The wire is threaded through a toroidal permanent magnet, magnetized around the toroid (what I call a stealth magnet). The magnetic flux is considered to be confined to the magnet. The flux links the closed path. Now, slip the magnet off one end of the wire loop so that it now is threaded by the nonconductive part of the closed path. Then pull the magnet out away from the loop so that it crosses the nonconductive part of the path. An emf should be induced in the closed path while the magnet is crossing the path because the magnetic flux linking the closed path changes with time. This is in accordance with the Maxwell-Faraday Law, which is one of Maxwell's equations.

There is a problem, however, because the nonconducting part of the closed path does not have to be the shortest route between the wire ends. It can bow out (or in). In other words, it is arbitrary. So when does the emf appear?

Welcome (back) to PF.

Is this question related to your old threads that were closed for cause?

MS La Moreaux said:
Let us shed a little light on the subject by considering a case simpler than a coil, namely the Faraday Paradox. This employs two disks, say of the same size. One is made of copper and the other is a magnet with its faces the poles. These disks are arranged face to face, close but not touching. Each is mounted on an axle like a wheel and the axles are colinear. If the copper disk is spun while the magnet is stationary, a non-electrostatic emf appears between the copper disk's center and rim. If the magnet is spun and the copper disk remains stationary, there is no emf in the copper disk.

No, this is a new topic. By the way, the addition to my title, which I did not write, is wrong. There is no motion of the wire segment.

If you can post a compelling enough case for this new question, it should be allowed. Also, what is your background in E&M and using calculus to solve the differential equations involved in such problems? Thanks.

The closed thread was about the fact that Faraday's Law falsely implies that a changing magnetic flux linking a circuit is responsible for the motional emf in some cases.

The new question is about an application of one of Maxwell's equations. The equation in question is related to Faraday's Law, being a special class of cases, but that is where the similarity ends.

I have a bachelor's degree in electrical engineering from the University of Michigan.

Dale
MS La Moreaux said:
The closed thread was about the fact that Faraday's Law falsely implies that a changing magnetic flux linking a circuit is responsible for the motional emf in some cases.
Falsely?

Yes. Motional emf is never the result of a flux change.

MS La Moreaux said:
I have a bachelor's degree in electrical engineering from the University of Michigan.
Which means you are in a position to overthrow all of physics? I'm not so sure I buy that.

I found your description impossible to fathom. It reminds me of the idea that the reason we haven't built a perpetual motion machine is that past attempts just weren't complicated enough.

There are three things you could be trying to do:
1. Showing Maxwell's Equations do not match experiment. In this case, you need a real experiment, not a thought experiment.
2. Showing Maxwell's Equations are inconsistent. Too late - they are known to be consistent.
3. Trying to understand something you don't understand. Then show the simplest possible setup, perhaps with a drawing, in the words of Art Fleming "cast your response in the form of a question" and restrict yourself to physical measurements - i.e. "what will this ammeter read?"

berkeman and russ_watters
Obviously, your level of understanding is not sufficient.

Ibix and weirdoguy
MS La Moreaux said:
By the way, the addition to my title, which I did not write, is wrong. There is no motion of the wire segment.
I updated the title to make it clearer that the motion is relative.

I think you have a C-shaped piece of wire and you have a toroidal magnet with a toroidal magnetic field that is only non-zero within the material of the torus. You move the magnet through the gap in the C in a plane perpendicular to the line that would notionally close the C into an O. I don't understand what you want to know about this scenario.

berkeman said:
I updated the title to make it clearer that the motion is relative.
The wire segment does not move. How can I be any clearer?

MS La Moreaux said:
The wire segment does not move. How can I be any clearer?
Relative to what? You have a BSEE from the U of M, so you know that there is no such thing as absolute motion. If the test coil and the toriod are moving relative to each other, that is what matters, no?

MS La Moreaux said:
Yes. Motional emf is never the result of a flux change.
MS La Moreaux said:
Obviously, your level of understanding is not sufficient.

Well, please state your question more clearly with an appropriate diagram. It sounds like it has something to do with a wire segment moving in relative fashion near a toroidally magnetized ferrite toriod. Can you please clarify exactly what the situation entails, and what your question is about? The more math and diagrams you can post, the better we can help you with this question.

Ibix said:
I think you have a C-shaped piece of wire and you have a toroidal magnet with a toroidal magnetic field that is only non-zero within the material of the torus. You move the magnet through the gap in the C in a plane perpendicular to the line that would notionally close the C into an O. I don't understand what you want to know about this scenario.
When the magnet is situated so that the nonconductive part of the closed path passes through the hole in the magnet, the magnetic flux of the magnet links the closed path. When the magnet moves so that the portion of it that was inside the closed path crosses the closed path and ends up outside the closed path, there is no longer any flux linking the closed path. This should result in an emf in the closed path. The nonconductive portion of the closed path, however, is arbitrary. One cannot expect that the emf will appear when the magnet crosses a line that one has only imagined!

MS La Moreaux said:
When the magnet is situated so that the nonconductive part of the closed path passes through the hole in the magnet, the magnetic flux of the magnet links the closed path. When the magnet moves so that the portion of it that was inside the closed path crosses the closed path and ends up outside the closed path, there is no longer any flux linking the closed path. This should result in an emf in the closed path. The nonconductive portion of the closed path, however, is arbitrary. One cannot expect that the emf will appear when the magnet crosses a line that one has only imagined!
So, still without any diagram we are forced to try to guess and ask if we are guessing correctly. This is getting tiresome, and you are risking having yet another thread closed for cause.

So here's my guess -- your C-shaped wire segment with the open gap large enough to be slid over the toroid is moved from encircling the toriod body to a position away from the toroid and you are asking what the induced EMF is in that wire segment. Is that basically correct?

If so, you can model this wire segment as that conducting wire and a parasitic capacitor that is formed across the open "non-conducting" portion of that C-shaped wire segment. Do you understand how to calculate that parasitic capacitance and how to use that in your DE calculations of the voltage induced in the wire segment?

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MS La Moreaux said:
The wire segment does not move. How can I be any clearer?

I am reasonably convinced that the setup is as follows. We have a small toroidal magnet (shown from the side as a red line). We have a piece of wire curved into a C shape (blue). We can always draw an infinite number of arbitrary imaginary lines that connect the ends of the wire and pass through the hole in the toroid (one such is shown as a fine green line).

The blue and green lines together form the perimeter of a surface ##\Sigma## through which one side of the magnet passes.

I think that the relevant analysis is this: we can always choose an arbitrary green line arbitrarily close to the edge of the magnet. Thus any motion of the magnet takes it outside this particular loop, meaning that ##\iint_\Sigma\frac\partial{\partial t}\vec B\cdot d\vec S\neq 0##. Thus by the integral form of Maxwell's third equation, ##\oint\vec E\cdot d\vec l## around the blue+green loop is also non zero for such a choice of green line, wherever the magnet is and whenever it is moved.

I also think that @MS La Moreaux thinks that ##\oint\vec E\cdot d\vec l## should be non zero for only one choice of green line, but doesn't know how to select the "correct one". If so, the resolution is to note that any choice of green line will do. If not, OP needs to provide a better description of the problem.

(It's telling that after 17 posts, 7 by the OP, in a thread about electromagnetism, I'm the first one using LaTeX.)

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Ibix said:
(It's telling that after 17 posts, 7 by the OP, in a thread about electromagnetism, I'm the first one using LaTeX.)
And first with a picture

hutchphd, berkeman, Vanadium 50 and 1 other person
Dale said:
And first with a picture
Yeah, but that's already been pointed out several times. The lack of LaTeX was forcibly brought to my attention because I had to do the preview-then-refresh trick to get it to render.

OP - you are going to find it very difficult to communicate about physics if you refuse to use maths and diagrams.

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berkeman said:
Relative to what? You have a BSEE from the U of M, so you know that there is no such thing as absolute motion. If the test coil and the toriod are moving relative to each other, that is what matters, no?
The laboratory frame. No, relative motion is not what matters. Change of
berkeman said:
Relative to what? You have a BSEE from the U of M, so you know that there is no such thing as absolute motion. If the test coil and the toriod are moving relative to each other, that is what matters, no?
Relative to the laboratory frame. Relative motion is not what counts. The Maxwell-Faraday Law does not address motion of the closed path.

Ibix said:
I am reasonably convinced that the setup is as follows. We have a small toroidal magnet (shown from the side as a red line). We have a piece of wire curved into a C shape (blue). We can always draw an infinite number of arbitrary imaginary lines that connect the ends of the wire and pass through the hole in the toroid (one such is shown as a fine green line).
View attachment 313236
The blue and green lines together form the perimeter of a surface ##\Sigma## through which one side of the magnet passes.

I think that the relevant analysis is this: we can always choose an arbitrary green line arbitrarily close to the edge of the magnet. Thus any motion of the magnet takes it outside this particular loop, meaning that ##\iint_\Sigma\frac\partial{\partial t}\vec B\cdot d\vec S\neq 0##. Thus by the integral form of Maxwell's third equation, ##\oint\vec E\cdot d\vec l## around the blue+green loop is also non zero for such a choice of green line, wherever the magnet is and whenever it is moved.

I also think that @MS La Moreaux thinks that ##\oint\vec E\cdot d\vec l## should be non zero for only one choice of green line, but doesn't know how to select the "correct one". If so, the resolution is to note that any choice of green line will do. If not, OP needs to provide a better description of the problem.

(It's telling that after 17 posts, 7 by the OP, in a thread about electromagnetism, I'm the first one using LaTeX.)
Thanks for the great diagram. You are thinking correctly. Upon further reflection, I was able to answer my question. There is an infinite number of simultaneous nonconductive portions of the closed path which includes the wire. As the magnet moves, it crosses one after another. Sometimes the emf will be in one direction and sometimes in the opposite direction. I suspect that they all cancel each other out and that there is no net emf in the wire.

berkeman
MS La Moreaux said:
Sometimes the emf will be in one direction and sometimes in the opposite direction. I suspect that they all cancel each other out and that there is no net emf in the wire.
Did you understand my comments about the parasitic capacitance? It is not some imaginary thing that varies with the path chosen. It is a real thing that is integrated over all of the paths between the two ends of your C-shaped wire...

MS La Moreaux said:
Relative to the laboratory frame. Relative motion is not what counts.
Seriously?

MS La Moreaux said:
I suspect

What we seem to have is a calculation that you didn't do but are guessing at the answer doesn't agree with your intuition of what the answer should be.

vanhees71 and berkeman
berkeman said:
So, still without any diagram we are forced to try to guess and ask if we are guessing correctly. This is getting tiresome, and you are risking having yet another thread closed for cause.

So here's my guess -- your C-shaped wire segment with the open gap large enough to be slid over the toroid is moved from encircling the toriod body to a position away from the toroid and you are asking what the induced EMF is in that wire segment. Is that basically correct?

If so, you can model this wire segment as that conducting wire and a parasitic capacitor that is formed across the open "non-conducting" portion of that C-shaped wire segment. Do you understand how to calculate that parasitic capacitance and how to use that in your DE calculations of the voltage induced in the wire segment?
I was not asking what the induced emf was.

MS La Moreaux said:
I was not asking what the induced emf was.
MS La Moreaux said:
Yes. Motional emf is never the result of a flux change.
MS La Moreaux said:
Sometimes the emf will be in one direction and sometimes in the opposite direction. I suspect that they all cancel each other out and that there is no net emf in the wire.
I'm getting dizzy...

vanhees71
MS La Moreaux said:
The wire is threaded through a toroidal permanent magnet, magnetized around the toroid (what I call a stealth magnet).
BTW, since you are an EE, you do understand how a ferrous core transformer works, right? Is a permanently magnetized toroidal magnet any more "stealthy" than a toroidal core that has a primary coil with a DC current flowing through it?

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vanhees71
"Stealth toroid" is an anagram for "It's tool hatred".

berkeman

## 1. What is the Maxwell-Faraday Law?

The Maxwell-Faraday Law, also known as Faraday's Law of Induction, is a fundamental law of electromagnetism that describes the relationship between a changing magnetic field and an induced electric field. It states that a changing magnetic field will induce an electric field in a closed loop, and the magnitude of the induced electric field is directly proportional to the rate of change of the magnetic field.

## 2. How does the Maxwell-Faraday Law relate to EMF induction?

The Maxwell-Faraday Law is the basis for understanding electromagnetic induction, which is the process of creating an electric current in a conductor by changing the magnetic field around it. EMF induction is the result of the Maxwell-Faraday Law, as a changing magnetic field induces an electric field that can cause a current to flow in a conductor.

## 3. What are stealth magnets and how do they work?

Stealth magnets are a type of magnet that can shield or block magnetic fields. They work by using a special arrangement of magnetic materials that can redirect the magnetic field around the object, making it "invisible" to outside detection. This is achieved by creating a magnetic field that is equal and opposite to the external field, effectively canceling it out.

## 4. What are some practical applications of the Maxwell-Faraday Law and stealth magnets?

The Maxwell-Faraday Law has many practical applications, including generators, transformers, and electric motors. It is also used in technologies such as wireless charging and induction cooktops. Stealth magnets have applications in industries such as aerospace, defense, and medical imaging, where the ability to shield or redirect magnetic fields is crucial.

## 5. Are there any limitations or drawbacks to using stealth magnets?

While stealth magnets have many useful applications, they also have some limitations. They are only effective against static or slowly changing magnetic fields and are less effective against rapidly changing fields. Additionally, they can only shield or redirect magnetic fields, not electric fields. There are also challenges in designing and manufacturing stealth magnets, making them more expensive than traditional magnets.

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