Maxwell-Faraday Law & Stealth Magnets: Exploring EMF Induction

[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?

 

[berkeman]

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?

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.

 

[MS La Moreaux]

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.

 

[berkeman]

How so? Can you please compare and contrast your two questions? I'm only asking because this new thread start of yours was reported as too similar to your previously closed thread.

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.

 

[MS La Moreaux]

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.

 

[berkeman]

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?

 

[MS La Moreaux]

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

 

[Vanadium 50]

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?"

 

[MS La Moreaux]

Obviously, your level of understanding is not sufficient.

 

[berkeman]

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.

 

[Ibix]

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.

 

[MS La Moreaux]

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?

 

[berkeman]

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?

 

[berkeman]

Anyway, back to your question in this thread now...

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

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.

 

[MS La Moreaux]

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!

 

[berkeman]

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?

 

[Dale]

The wire segment does not move. How can I be any clearer?

With a good picture, for one. I don’t follow your description.

 

[Ibix]

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.)

 

[Dale]

(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

 

[Ibix]

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.

 

[MS La Moreaux]

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

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.

 

[MS La Moreaux]

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]

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...

Relative to the laboratory frame. Relative motion is not what counts.

Seriously?

 

[Vanadium 50]

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.

 

[MS La Moreaux]

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.

 

[berkeman]

I was not asking what the induced emf was.

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

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...

 

[berkeman]

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?

 

[Vanadium 50]

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