I The Faraday disk in the context of the theory of relativity

[Ivan Nikiforov]

Good afternoon! I would like to understand how the Faraday disk works and get answers to two questions. The working conditions are as follows: 1) we rotate the external circuit with a voltmeter relative to a stationary disk; 2) the external circuit is not in a magnetic field. Questions: 1) will an electric current flow in such a system? 2) what forces will act on the external circuit with the voltmeter? I would like to consider these processes precisely from the point of view of the theory of relativity, since the Faraday disk is based on the principle of relativity of simultaneity. Thank you in advance!

 

[anuttarasammyak]

On external circuit which does not include the disk, Lorentz force of v X B appears and makes electrons move where v is r$\omega$.

 

[TSny]

View attachment 356917
Good afternoon! I would like to understand how the Faraday disk works and get answers to two questions. The working conditions are as follows: 1) we rotate the external circuit with a voltmeter relative to a stationary disk; 2) the external circuit is not in a magnetic field.

Here is an elaboration of @anuttarasammyak's comment.

By the "external circuit," I think you mean this part

This part of the circuit is in a magnetic field. The field of the magnet extends to this part.

Questions: 1) will an electric current flow in such a system?

Yes.

2) what forces will act on the external circuit with the voltmeter?

As the external circuit rotates in the direction shown in the figure, the free charge carriers in the external circuit move through the B field. So, a carrier with charge $q$ and velocity $\mathbf v$ experiences a magnetic force $\mathbf F = q \mathbf v \times \mathbf B$. For simplicity, imagine the B field to be uniform:

In the horizontal parts $ab$ and $cd$, the magnetic force on electrons is toward the axle: from $b$ toward $a$ and from $c$ toward $d$. See this video for a discussion of the motional electromotive force (emf) induced in a rod rotating in a B field. Since $ab$ is longer than $cd$, the emf in $ab$ is greater than in $cd$. Thus, the net emf in the external circuit drives electrons in the external circuit in the counterclockwise direction: $d$ to $c$ to $b$ to $a$. Electrons arriving at $a$ flow down the axle and back to $d$ through the stationary disk.

I would like to consider these processes precisely from the point of view of the theory of relativity, since the Faraday disk is based on the principle of relativity of simultaneity. Thank you in advance!

I'm not clear on what you want here.

 

[Ivan Nikiforov]

On external circuit which does not include the disk, Lorentz force of v X B appears and makes electrons move where v is r$\omega$.

Thanks for the comment. By the condition of the problem, the external circuit is not in a magnetic field, therefore the Lorentz force cannot appear.

 

[Ivan Nikiforov]

I'm not clear on what you want here.

Thanks for the comment. Yes, you understand correctly which part of the system rotates. I would like to understand how this system will work if the external circuit is not in a magnetic field. Let's say that due to the design, we will make it so that the magnetic field bypasses the external circuit.
The following is stated in the literature: "An observer moving at a velocity u, relative to a medium with magnetization M, detects an electric moment P equal to:

At the same time, it is not claimed that the moving observer must be in a magnetic field. Based on this statement, we can give a slightly abstract example. A magnet with a conductive surface (a metal magnet) lies motionless on the table. A copper wire moves relative to the magnet, at a great distance from it and perpendicular to the magnetic field lines. An observer located in a copper wire detects an electric field on the sides of the magnet. If a copper wire is connected by brushes to the sides of a magnet, current will flow in a closed circuit. At the same time, the copper wire is not in a magnetic field. Is this interpretation correct?

A magnetic field can be closed in addition to an external circuit, for example, like this.

 

[anuttarasammyak]

Thanks for the comment. By the condition of the problem, the external circuit is not in a magnetic field, therefore the Lorentz force cannot appear.

Then apply B=0 to my comment, please. No B No emf.

 

[Ivan Nikiforov]

Then apply B=0 to my comment, please. No B No emf.

I generally agree with you. At the same time, it turns out that everything is not so obvious. If in this model (when the external circuit is not in a magnetic field) we start rotating the disk relative to the external circuit again, an electric current is likely to flow. According to the principle of relativity, the rotation of the disk and the rotation of the external circuit are equivalent. Indeed, in empty space we cannot understand whether the disk is rotating or the external circuit is rotating. We can only say that there is relative motion between the disk and the external circuit. Therefore, we come to the conclusion that the rotation of the circuit, which is not in a magnetic field, relative to the disk, leads to a current. Is this interpretation correct?

 

[anuttarasammyak]

Rotation of the circuit where B=0 and rotation of the disk where B$\neq$ 0 should be investigated independently. You don't have to think of the correlation between.
There are three things; maget, disk and circuit. What kind of motion involving the three are you interested in ?

 

[Ivan Nikiforov]

In the literature, the occurrence of electric polarization is explained as follows. It is argued that the magnetic field is a set of elementary circuits with an electric current. This refers to the rotation of an electron around an atom. It is argued that an elementary circuit with an electric current at rest in the reference frame S0 acquires an electric moment in the moving reference frame S. In a simplified way, this is explained as follows. For a moving observer, the time of movement of an electron in the direction of motion differs from the time of movement of an electron in the opposite direction. At the same time, it is not claimed that the moving reference frame S should be in a magnetic field.

 

[Ivan Nikiforov]

Rotation of the circuit where B=0 and rotation of the disk where B$\neq$ 0 should be investigated independently. You don't have to think of the correlation between.
There are three things; maget, disk and circuit. What kind of motion involving the three are you interested in ?

Thank you. An interesting explanation. I'll think about it.
I am interested in the motion of the external circuit relative to the magnet and the disk (the magnet and the disk are one).

 

[anuttarasammyak]

Then as said no B no emf.

 

[Ivan Nikiforov]

Then as said no B no emf.

Then it turns out that the rotation of the disk and the rotation of the external circuit are not equivalent. Why? How can this be explained from the point of view of the theory of relativity?

For example, such a model is given in the literature. The picture shows a metal band that moves inside an inductor, that is, in a magnetic field. At the edges of the tape, sliding contacts of an external circuit are connected, which is not in a magnetic field. In this model, the metal band and the external chain have a rectilinear uniform relative motion, that is, they represent inertial reference frames. So, in the general case, we cannot understand whether the tape is moving or the external circuit is moving. There is only a relative motion at which current flows. Therefore, if we move only the outer circuit, we will get the same result. Is this statement true?

 

[Ivan Nikiforov]

In fact, the first question of the topic can be formulated as follows. An electric current circuit is fixed in the laboratory (reference frame S0). Relative to this circuit with an electric current and at a great distance from it, a material point (reference frame S) is moving. The material point is not located in a magnetic field. An observer located in the frame of reference S of a material point discovers that a circuit with an electric current has an electric moment:

Is this interpretation correct?
I would like to get an answer to this question precisely in the context of the theory of relativity.

 

[Nugatory]

According to the principle of relativity, the rotation of the disk and the rotation of the external circuit are equivalent. Indeed, in empty space we cannot understand whether the disk is rotating or the external circuit is rotating. We can only say that there is relative motion between the disk and the external circuit.

The principle of relativity says that inertial frames are equivalent, but a rotating frame is not inertial. Even in otherwise empty space, we can determine whether the disk is rotating; an accelerometer attached to the disk will show non-zero proper acceleration if the disk is rotating.

Then it turns out that the rotation of the disk and the rotation of the external circuit are not equivalent. Why? How can this be explained from the point of view of the theory of relativity?

Because the theory never claimed that they were equivalent.

 

[Ibix]

Then it turns out that the rotation of the disk and the rotation of the external circuit are not equivalent

Of course. Attach a mass on a spring to each component - if one is spinning the spring will extend.

How can this be explained from the point of view of the theory of relativity?

It's only inertial frames that are all equivalent. Acceleration is absolute - that is, detectable in an arbitrarily small closed box with something like my mass on a spring.

Whether you are sliding in a straight line past a straight rail or the rail is sliding past you is unanswerable. Moving along a curved rail has an answer - one or more of you will be accelerating.

 

[Ivan Nikiforov]

The principle of relativity says that inertial frames are equivalent, but a rotating frame is not inertial. Even in otherwise empty space, we can determine whether the disk is rotating; an accelerometer attached to the disk will show non-zero proper acceleration if the disk is rotating.
Because the theory never claimed that they were equivalent.

Thanks for the comment. I mean equivalent rotation in terms of electromagnetism, not mechanics. In comment No. 12, I specifically indicated a model in which the metal band and the external chain move evenly and in a straight line. This model is essentially a Faraday disk, if you make a geometric sweep of it. Is it possible to apply your arguments to the model mentioned in comment No. 12?

 

[Ivan Nikiforov]

Whether you are sliding in a straight line past a straight rail or the rail is sliding past you is unanswerable.

Thanks for the comment. It also seems to me that with uniform rectilinear motion, it doesn't matter if the disc is moving or the external circuit is moving or if they are moving simultaneously towards each other. However, the fact is that the electromagnetic processes occurring during the rectilinear motion of the disk and the external circuit are completely identical to the electromagnetic processes occurring during the rotation of the disk and the external circuit. This has been proven experimentally.

 

[anuttarasammyak]

Then it turns out that the rotation of the disk and the rotation of the external circuit are not equivalent. Why?

Why do you think equivalent ?

I am interested in the motion of the external circuit relative to the magnet and the disk (the magnet and the disk are one).

From your figure I interpret the motions here are rotation. Spinning magnet is an advanced matter so I would set Magnet is at rest with no spin in a IFR. In this IFR,
Disk : spinning with angular velocity $\Omega$ where $B\neq0$
Circuit : spinning with angular velocity $\omega$ where $B=0$

$\Omega$ contribute to emf with integrated contribution of $r \Omega B$ where r is radius of a part of Disk.
$\omega$ has nothing to do with emf due to $B=0$.
"Relative rotation" angular velocity $\Omega-\omega$ does not show as you might have expected.

[EDIT]
Now we know $\omega$ is irrelevant. Let’s think of relativity on $\Omega$. On Disk inherent FR which is not a IFR but a rotational FR, magnet is spinning with $-\Omega$. emf is observed as it is in the IFR.

The next configuration : in a IFR Disk is at rest and Magnet is spinning with $-\Omega$. Is emf observed? I do not think so because v=0 but it is worth doing an experiment.

 

[Ivan Nikiforov]

Why do you think equivalent ?

The model is shown in comment No. 12. If the disk is expanded (geometrically transformed) into a straight part, then we get the same thing. If in the model of comment No. 12, the movement of the metal band and the external circuit are equivalent, then the rotation of the disk and the external circuit are also equivalent. In this case, as I understand it, acceleration is not taken into account, since it does not affect electromagnetic processes (electric and magnetic fields).

It has been experimentally proved that the electromagnetic processes for a rotating disk and an external circuit are completely identical to the electromagnetic processes occurring during the rectilinear motion of a magnet and an external circuit. If you roll up the magnet in this picture into a ring, we get a disk.

 

[anuttarasammyak]

You start from rotation but the figure shows linear motion. I do not think it is a good way to visit different topics at a time if you really want to study.

 

[Ivan Nikiforov]

You start from rotation but the figure shows linear motion. I do not think it is a good way to visit different topics at a time if you really want to study.

Excuse me, but in the literature, when considering the electromagnetic processes occurring in a Faraday disk, it is argued that this is the same thing - the rotation of the disk and the translational motion of the magnetic bar. That's not my opinion. I am only referring to sources and based on them I am trying to build a correct interpretation in relation to the conditions of the problem.

 

[Ibix]

The model is shown in comment No. 12. If the disk is expanded (geometrically transformed) into a straight part, then we get the same thing.

If you make your disc infinitely large you make its angular velocity zero. What results would you expect from a Faraday disc with zero angular velocity?

 

[Ivan Nikiforov]

If you make your disc infinitely large you make its angular velocity zero. What results would you expect from a Faraday disc with zero angular velocity?

Please forgive me, these are probably translation features. I was referring to a geometric transformation in which a disk turns into a rectangle (a magnetic bar, a metal ribbon). This explains the transition from rotational motion to rectilinear motion, and vice versa. Ultimately, this shows that the models in comments No. 12 and No. 19 are equivalently converted to a disk. In the literature, these models are used to explain the electromagnetic processes occurring in the Faraday disk.

 

[Ivan Nikiforov]

In this book, in chapter 22, the question of how applicable to rotation are the results obtained for rectilinear motion is discussed in detail. It is stated that for rotational and rectilinear motion are the same: 1) all the results concerning the possible variants of the relative motion of the magnetic field, the metal bar and the external circuit; 2) the electromagnetic process of production and the magnitude of the electromotive force. Thus, for my problem, rotation and rectilinear motion are equivalent.

In this book, in chapter 21, paragraph 178a, it is stated that the detection of an electric field when moving relative to a magnetic field, as well as the detection of a magnetic field when moving relative to an electric field, is a first-order relativistic effect that depends on u/c, and is a consequence of the relativity of simultaneity.

 

[anuttarasammyak]

Chapter 22 of my Panofsky-Phillips second edition is "Radiation, scattering and dispersion" which seems not our topics. What is the chapter title of your book ?

Referring to these books, what is your own conjecture in OP setting for which you have posed only questions ?

 

[Ivan Nikiforov]

Chapter 22 of my Panofsky-Phillips second edition is "Radiation, scattering and dispersion" which seems not our topics. What is the chapter title of your book ?

Referring to these books, what is your own conjecture in OP setting for which you have posed only questions ?

My book was translated into Russian in 1963. It is possible that the chapter numbers do not match the original. In my book, chapter 22 is called "The covariant form of field equations for material media and conservation laws." This chapter describes how the electrical polarization of a circuit with an electric current occurs, which is detected by a moving observer.
This chapter also discusses the extent to which the results obtained for rectilinear motion are applicable to rotation.
The chapter titled "Radiation, Scattering, and Dispersion" in my book has the number 21.
As I understand it, according to the rules of the forum, I can only ask questions. If I state my own understanding, it may be a violation. Therefore, at the end of the text, I write the phrase: "Is this true?"
Based on literary sources, I came to the following conclusion. When the external circuit moves relative to the disk, an electric current must flow in the system. That is, the answer to the first question of the topic is in the affirmative. On the second question of the topic, about what forces will act on the external circuit in this case, I do not yet have an accurate understanding. Just speculation. Therefore, I wanted to address these issues on the forum and understand: 1) am I drawing the right conclusions on the first question; 2) get opinions on the second question.

 

[anuttarasammyak]

Based on literary sources, I came to the following conclusion. When the external circuit moves relative to the disk, an electric current must flow in the system

Yes, as stated in post my #2 and @TSny ‘s #3 and also Panofsky Philips the figure of which you quoted in #19 with B there , but you said no B in #4. By which condition shall we go ?

 

[anuttarasammyak]

This chapter also discusses the extent to which the results obtained for rectilinear motion are applicable to rotation.

I do not find such a discussion in my second edition. Maybe I am a careless reader. I should appreciate it if someone who has the book check it also.

 

[Ivan Nikiforov]

Yes, as stated in post my #2 and @TSny ‘s #3 and also Panofsky Philips the figure of which you quoted in #19 with B there , but you said no B in #4. By which condition shall we go ?

In comment No. 19, it is said that, in relation to the conditions of the problem, rotation and rectilinear motion are equivalent. The model in comment No. 19 is given solely to demonstrate that the electromagnetic processes in the disk are completely identical to the electromagnetic processes in the magnetic bar. The very formulation of the first question of the topic remains unchanged: will current flow if the moving external circuit is not in a magnetic field? I came to the conclusion that the current will flow.

 

[anuttarasammyak]

will current flow if the moving external circuit is not in a magnetic field?

As I answered in #11, no.

 

[Ivan Nikiforov]

I do not find such a discussion in my second edition. Maybe I am a careless reader. I should appreciate it if someone who has the book check it also.

The following is literally written in this fragment.

"Consider the so-called "Faraday disk" (Figure 22.4). Its action is based on the phenomenon discussed in paragraph 9.5. Many properties of the Faraday disk are consistent with the conclusions of this paragraph. In particular, all the results summarized in Table 9.1 regarding the possible relative movements of the field source and the external circuit remain correct. The important conclusion also remains valid that the rotation of the magnetic field source does not affect physical phenomena if the field remains constant. As before, the electromotive force can be found from Faraday's law (9.2), determining the change in the magnetic flux through the circuit along which the current carriers move. The correct answer is also provided by a consideration based on the "effective force acting on an electron." However, this is where the commonality of inertial and non-inertial reference systems ends."

Ниже я привел фрагменты из книги, на которые указаны ссылки в тексте выше.

 

[Ivan Nikiforov]

As I answered in #11, no.

Thanks for the comment. I will take it into consideration and try to understand the error of my conclusions.

 

[anuttarasammyak]

The second bottom line of the table 9.1 means movement of galvanometer circuit only. Horizontal metal part of circuit moving u in magnetic field B. You see it in the figure.

 

[Ivan Nikiforov]

The second bottom line of the table means movement of galvanometer circuit only. Horizontal metal part of circuit moving u in magnetic field B. You see this part is in B in the figure.

Regarding the understanding of Table 9.1, I completely agree with you. But I set myself the task of finding out whether an electric current will be observed if the horizontal metal part of the circuit is not in the magnetic field B. That's the whole point of the question.
The fact is that upon further consideration of the electromagnetic processes occurring in a magnetic bar, nowhere is the requirement that both frames of reference must be in a magnetic field stated or mentioned. Moreover, the process of the appearance of an electric field on the sides of a magnet, which is detected by a moving observer, has nothing to do with whether this moving observer is in a magnetic field.

 

[anuttarasammyak]

What kind of configuration for an example to make B=0 at the circuit ?

 

[Ivan Nikiforov]

What kind of configuration for an example to make B=0 at the circuit ?

A possible version of this configuration is indicated in comment No. 5. The figure shows that the magnetic field is concentrated in a magnetic core, while the external circuit is not in a magnetic field.
For the figure in comment No. 5, the logic of my conclusions is as follows: 1) if we rotate the disk in this model, then electric current will flow in the system; 2) rotation of the disk and rotation of the external circuit are equivalent; 3) therefore, if in this model we rotate the external circuit, then electric current will flow in the system as well.

 

[Ivan Nikiforov]

I understand the physics of the process as follows. When the disk rotates relative to the magnetic field, an observer located in the disk detects an electric field on the sides of the magnetic field. This electric field passes through the disk and closes to an external circuit, as a result of which an electric current flows in the system. When an external circuit rotates relative to the magnetic field, an observer located in the external circuit detects an electric field on the sides of the magnetic field. This electric field passes through an external circuit and closes onto a disk, as a result of which an electric current flows in the system. Thus, the process of detecting an electric field is the same in both cases, with the only difference being that in the first case, the observer is in a magnetic field, and in the second case, the observer is not in a magnetic field.
This understanding of the process fully corresponds to the fundamental statement: "An observer moving at a speed u relative to a medium with magnetization M detects an electric moment P equal to:

This fundamental statement does not specify that the observer must be in a magnetic field.

 

[renormalize]

This understanding of the process fully corresponds to the fundamental statement: "An observer moving at a speed u relative to a medium with magnetization M detects an electric moment P equal to:
View attachment 357079
This fundamental statement does not specify that the observer must be in a magnetic field.

Perhaps I missed it earlier, but could you please cite a specific source for this statement, preferably written in English? Thanks.

 

[anuttarasammyak]

A possible version of this configuration is indicated in comment No. 5. The figure shows that the magnetic field is concentrated in a magnetic core, while the external circuit is not in a magnetic field.

I am afraid metallic surface (blue lines) is kept equipotential during the process so no emf observed. If I misunderstand the configuration please correct me.

 

[TSny]

Regarding the figure in post #5, Maxwell's equations do not allow the B field to have the pattern shown. In particular, boundary conditions for $\mathbf B$ are violated at the interface between the core and the vacuum.

For example, in region $a$ shown above, the normal component of B is discontinuous at the interface. This violates $\nabla \cdot \mathbf B = 0$.

At the interface in region $b$, the tangential component of B is discontinuous. This violates $\nabla \times \mathbf B = \mu_0 \mathbf J + \varepsilon_0 \mu_0 \dfrac{\partial \mathbf E}{\partial t}$ assuming that there are no surface currents on the interface.

 

[anuttarasammyak]

Re:#31
I found a correspong page in my book "18-6 Transformation properties of the partial fields". I observe in "Fig.18-6 Faraday disk illustrating unipolar induction in rotation" that B perpendiculat to paper exist for both disk and galvanometer circuit. So I am not surprized that it behaves same as Table 9-1 of linear case.

 

[Ivan Nikiforov]

Regarding the figure in post #5, Maxwell's equations do not allow the B field to have the pattern shown. In particular, boundary conditions for $\mathbf B$ are violated at the interface between the core and the vacuum.

View attachment 357086

For example, in region $a$ shown above, the normal component of B is discontinuous at the interface. This violates $\nabla \cdot \mathbf B = 0$.

At the interface in region $b$, the tangential component of B is discontinuous. This violates $\nabla \times \mathbf B = \mu_0 \mathbf J + \varepsilon_0 \mu_0 \dfrac{\partial \mathbf E}{\partial t}$ assuming that there are no surface currents on the interface.

Thanks for the comment. Below, I have provided several drawings showing various generator options. In general, the design of a practical model can vary in a wide range of options. But this has nothing to do with the original question. For now, we may not consider the specific design at all, but simply set the initial condition: the external circuit is not in a magnetic field.

 

[Ivan Nikiforov]

Re:#31
I found a correspong page in my book "18-6 Transformation properties of the partial fields". I observe in "Fig.18-6 Faraday disk illustrating unipolar induction in rotation" that B perpendiculat to paper exist for both disk and galvanometer circuit. So I am not surprized that it behaves same as Table 9-1 of linear case.

I made a link to this part of the book in order to argue that, as applied to the problem, rotation and rectilinear motion are equivalent. This is exactly the doubt you originally had. I did not claim that this picture shows a variant in which the external circuit is not in a magnetic field. Moreover, you were able to make sure that the disk and the magnetic bar, as applied to the task, are the same thing.

 

[Ivan Nikiforov]

It seems to me that considering this process in the framework of the theory of relativity well explains why a charged particle moves along a circular trajectory under the influence of the Lorentz force. Usually, the reasons for the circular motion of a particle are not considered in detail in the literature. I'll make the following assumption. At the initial moment of time, an observer located in a charged particle detects an electric field on the sides of the magnetic field. This electric field acts on the particle and deflects its velocity vector. As a result of changing the direction of the velocity vector, the vector of the electric field that the particle detects changes. This in turn leads to a further deviation of the velocity vector. This process occurs continuously, as a result of which the charged particle moves along a circular trajectory. This assumption is in good agreement with the conclusions mentioned in comment No. 37 and may be their confirmation.

 

[anuttarasammyak]

I made a link to this part of the book in order to argue that, as applied to the problem, rotation and rectilinear motion are equivalent. This is exactly the doubt you originally had.

I believe I am not included in "you". I just said "no B no emf". I refer rotation only in [EDIT] of #18 for another context.

Moreover, you were able to make sure that the disk and the magnetic bar, as applied to the task, are the same thing.

It should be mentioned that Panofsky Philips said in the end as the difference with SR,
" "absolute" rotational motion of the disk (i.e. the motion relative to an inertial frame )
can in principle be dermined ".
[EDIT]
Rotation does not have same relativity as translational motion in SR has.

 

[renormalize]

I did not claim that this picture shows a variant in which the external circuit is not in a magnetic field.

I find the back and forth discussion here confusing. Could you please clarify what you're asking by describing your configuration in very general terms? In particular, can you answer the following:

1. Does your configuration of interest consist of at least two subsystems, each made of uncharged but electrically-conductive materials (e.g., metal wires, plates, disks, etc.)?
2. Are these subsystems in relative motion with respect to each other?
3. Are these subsystems immersed in an external magnetic field and/or electric field, or are they in no field whatsoever?

Thanks!

 

[Ivan Nikiforov]

I find the back and forth discussion here confusing. Could you please clarify what you're asking by describing your configuration in very general terms? In particular, can you answer the following:

1. Does your configuration of interest consist of at least two subsystems, each made of uncharged but electrically-conductive materials (e.g., metal wires, plates, disks, etc.)?
2. Are these subsystems in relative motion with respect to each other?
3. Are these subsystems immersed in an external magnetic field and/or electric field, or are they in no field whatsoever?

Thanks!

I will provide answers to your questions.: 1) Yes; 2) Yes; 3) The disk (or magnetic bar) is in a magnetic field, and the external circuit is not in a magnetic field. In order to get an answer to the first question of my topic, I suggest not delving into the specific construction yet, as this unproductively complicates the consideration. I suggest using the classic Faraday disk as a basis and simply making the scientific assumption that the external circuit is not in a magnetic field. Will current flow under such conditions if only the external circuit is rotating?

 

[Ivan Nikiforov]

I believe I am not included in "you". I just said "no B no emf". I refer rotation only in [EDIT].

It should be mentioned that Panofsky Philips said in the end as the difference with SR,
" "absolute" rotational motion of the disk (i.e. the motion relative to an inertial frame )
can in principle be dermined "

Please excuse me if I inadvertently made a tactless remark and chastised you in some way. In fact, I am very grateful to you and everyone who participates in this discussion. You can't even imagine how long I've been waiting for the moment to talk about this topic with the scientific community. I can only say that I first started researching this topic back in 2004. You can say that this is my life's work. However, of course, this does not mean that I am right about everything. As Descartes said, "Question everything."

 

[renormalize]

Will current flow under such conditions if only the external circuit is rotating?

Is the rotating external circuit in electrical contact with the disk through something like carbon motor brushes that touch the stationary disk at 2 different points outside of the magnetic field? Or is the circuit like a floating piece of disconnected wire traversing a circular path completely external to the disk?

 

[anuttarasammyak]

https://www.feynmanlectures.caltech.edu/II_17.html
It seems that we can make B at the circuit weak enough by magnet spot in this configuration. Does it help you @Ivan Nikiforov ?