B Faraday's disk and "absolute" magnetic fields

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1. Jun 28, 2017

I've posted this here because I think it might be related to the absoluteness of acceleration and rotation.

I've been educating myself on the Faraday Disk and was very surprised by one aspect of it. If we have a solid metal disk mounted on a shaft with two electrical brushes contacting the disk rim and the disk center and a round magnet with a hole in the center (and with poles on opposite ends of the hole) also mounted on the shaft such that the shaft goes through the magnet hole and the disk center, then we have a Faraday disk. If the magnet is held stationary and the disk is rotated, we get the expected current flow from the center to the edge of the disk resulting in a voltage across the brushes. The reason is because the electrons in the disk cut across the stationary magnetic field.

The part that surprised me was if you allow the magnet to spin with the disk, then you get the same current flow. This indicates that the magnetic field remains non-rotating regardless of the angular velocity of either the disk, magnet or both.

This made me wonder if the magnetic field of a magnet is absolute in the same sense that the forces felt by an object rotating or linearly accelerating are absolute. This led me to a few questions:

1) (I was going to assume this, but I've learned on PF to never assume unless you can back it up ;) Is this non-rotating magnetic field described above non rotating relative to an object that is also non-rotating? If so is there an inherent reason to believe this or has it been shown to be true empirically or with calculations?

2) Is the relationship between a non-rotating magnetic field and the forces (not) felt by a non-rotating object significant or are they just coincidences? In other words, does the magnetic field not rotate for the same reason that a non-rotating object does not feel proper acceleration?

3) Is there any relationship between the described magnetic field and a non rotating object that would give me an understanding of why the magnetic field does not rotate?

Thanks

2. Jun 28, 2017

Drakkith

Staff Emeritus
I'm hesitant to say that a field rotates or does not rotate. I prefer to think of the field as either changing or static. Rotating the magnet causes no part of the field to change, so there should be no observed effects. When rotating the magnet and disk, the field is not changing but the electrons in the disk are now moving through a magnetic field and thus feel a force.

Conversely, when moving a magnet towards or away from a coil causes the magnetic field within that coil to change, imparting a force on the electrons and causing current to flow. I wouldn't even say that the field itself is moving, only that its values at any point in space are changing over time.

3. Jun 28, 2017

In the case of the coil and magnet, if there is current flow, any given point on the coil experiences a modulation in the flux strength. However, in the Faraday disk, the flux strength is uniform. Perhaps the field has tiny modulations in it that are non-rotating relative to an object that is also not rotating (more like a wave in water (a modulation in a field)) or perhaps the field can be left out of the equation entirely and the relationship is directly between the electrons in the spinning disk and the reference frame that is part of a non-rotating physical object. In other words perhaps the field can't be said to rotate (or not) because it is not a property that can be assigned to a magnetic field but instead the relationship between the electron and an absolutely non rotating frame (in the presence of this type of magnetic field) is what causes the current flow. Does this make sense? If that is the case then there seems to be a direct relationship between an electron that has an angular velocity (a proper acceleration) and a non rotating frame when in the presence of a magnetic field (of which rotation is undefined) that causes the electron to flow as current.

4. Jun 28, 2017

Drakkith

Staff Emeritus
Yes, but charged particles feel a force either when the magnetic field changes or when they move through the field. The latter is what they're doing in the Faraday disk when it rotates. The fact that the flux isn't changing doesn't matter since they are moving. You can set up a Helmholtz coil, which has a nearly perfectly homogenous magnetic field, and watch charged particles circle around in a vacuum tube. Just see the picture of the purple ring in the glass bulb in this article: https://en.wikipedia.org/wiki/Helmholtz_coil

Not really, no.

I'm fairly certain the electrons are just experiencing the Lorentz force because they are moving in a magnetic field.

5. Jun 28, 2017

Paul Colby

I agree the Faraday disk is quite interesting. One comment, in the stationary frame a rotating magnet will produce a radial electric field which gives rise to the observed current. This is because the magnetic field of the magnet are, after all, the result of charges and currents within the magnet which are now in relative rotation to the observer frame.

6. Jun 28, 2017

Well, yes, but the phrase "moving in a magnetic field" implies that one part of a magnetic field can be distinguished from another part. In other words it seems there has to be a property of the magnetic field such that when an electron moves through it, it has something to respond to such as crossing distinct magnetic field lines. If an electron can't witness some change in the field, then how can it respond to it?

In addition these field lines can move in a linear direction. For example in the cool Helmholz Coil (thanks for that link) if a short wire rolls through the field on stationary rails that are perpendicular to the field lines and the rails exit the field to go to a ammeter, then a current will be seen. Likewise if the coil itself is moved along with the short wire, then the current stops as the lines of force are not crossing the wire, even though they (and the wire) are moving through the laboratory.

So it can be shown that field lines can move, so movement can be a valid property of field lines in a linear direction, but they cannot seem to rotate as if rotation is undefined for field lines as (I think) you suggested. It's curious that the field lines seem to align to some stationary absolute rather than the rotating magnet or even by a reverse emf from the disk.

7. Jun 28, 2017

Are you saying that if the disk is not moving but the magnet is, there will be a current? It is my understanding that this is not the case.

8. Jun 29, 2017

jartsa

Let us consider a copper block. When the block stands still, electrostatic forces are in balance, I mean every particle feels zero net force from other particles. When the block moves, there are also Lorentz forces between particles, and those the Lorentz forces are in balance.

Now let us consider a Faraday disk. We can guess that Lorentz forces between particles are not in balance in this case.

So I got rid of the problem simply by replacing "magnetic field" by "Lorentz forces between particles". There are Lorentz forces between moving charged particles, aren't there?

9. Jun 29, 2017

Drakkith

Staff Emeritus
It does not.

Why wouldn't it? It's directly in the Lorentz force law and an observed fact. As I said earlier, to experience a force, the field can either be changing or the charged particle can be moving through the field. The latter criteria does not require that the field be inhomogeneous, as the Helmholtz coil demonstrates.

Sure. The magnetic field is not changing in the coordinate system (reference frame) of the wire, though it is in the coordinate system of the lab.

You are aware that field lines don't actually exist right? They're just a handy visualization/calculation tool. If you take a cylindrical magnet and move it towards or away from a coil, the field lines "move" because the field is changing in the reference frame of the coil. If, however, you rotate the magnet while keeping it otherwise stationary, the field lines don't "move" because the field is rotationally symmetric and rotating the magnet does not cause a change in the field at any point.

10. Jun 29, 2017

Paul Colby

I'm saying if there's a current there is an electric field and visa versa. All fields in the problem are created by moving charges in the magnet and disk. The confusing bit is forgetting this connection. And I agree it's confusing.  and your correct. There is no E field as a result of spinning the magnet according to the wiki.

11. Jun 29, 2017

sweet springs

Hello.

Magnets generate magnetic field by rotating current of electrons in atoms.
First how did you know magnetic field generated by rotating current in magnets of no rotation are not rotating ?

12. Jun 29, 2017

pervect

Staff Emeritus
First off I think we need a description of what "absolute means". The working definition I'm using is that an absolute quantity is one that is independent of any choice of an inertial frame.

Magnetic fields by themselves are not absolute. Magnetic fields transform into electric fields, and vice-versa. This implies magnetic fields cannot be absolute by the above definition, which requires that they be independent of the choice of inertial frame. Magnetic fields do depend on the choice of inertial frame.

A combination of both electric and magnetic fields called the "Faraday tensor" might be regarded as absolute, in that the object itself is regarded as something that is independent of any choice of inertial frame (and more generally still, any choice of coordinates , a more general statement that removes the restiction of only doing physics in inertial frames). So I believe it's reasonable to say that any tensor quantity is absolute by the definition I suggested. I'm a bit concerned that the definition I'm suggesting may not be the same as whatever intuitive notions the OP has, also, while I attempted to come up with a reasonable definition of what "absolute" really means, it's not sure how standard what I suggested is, though I did do some research in coming up with the definition I suggested.

A further concern is that it may be well and good to talk about the Faraday tensor, but it is probably not a good way to communicate with the OP. Unfortunately, I don't currently see how to avoid talking about it :(.

While the electromagnetic field expressed via the Faraday tensor could reasonably be called absolute , it's not clear to me what the tensor representation of the conductive disk would be. The geometric description that comes to mind for the rotating disk is a congruence of worldlines, but that's not quite a tensor - see below.

It makes sense to me to ask whether or not a congruence rotates or not - there is a tensor associated with the congruence that vanishes if and only if the congruence does not rotate. It doesn't make any sense to me to ask whether or not a tensor quantity rotates. The tensor description of a phenomenon doesn't demand that one analyze the problem in some special inertial frame (which implies that the frame cannot rotate) - it works in any set of coordinates. Rotating or not, it doesn't matter, rotation refers to the coordinates, not the tensor itself.

This is perhaps most clear in empty space. Empty space has a representation via its metric tensor. One can have a metric tensor for rotating coordinates, and a metric tensor for non-rotating coordinates. But the coordinate choice doesn't matter to the physics at all - empty space is still empty space, it doesn't suddenly change it's nature depending on what human convention one uses to assign coordinates to it. The components of the metric tensor one chooses vary depending on the state of rotation of one's coordinates, but the rotation itself is a property of the coordinate choice, not a property of empty space.

This underscores the difference between the congruence (which can rotate), and the electromagnetic field, as described by the Faraday tensor, where the question of whether it rotates or not seems to be inapplicable.

So in short, at the moment I can't assign any meaning to the question of whether a magnetic field "rotates" or not. It just is. We can talk about whether or not the conductive disk rotates, though.

13. Jun 30, 2017

In the case of the Faraday Disk the first criteria can be ignored since there is no changing magnetic field in the apparatus. Regarding the second, the charged particle does in fact move through the field when the disk is rotated. However it seems the magnetic field is bound and we cannot create a situation where the magnetic field moves across the electron in a non rotating disk. What is the reason we cannot do this? Why is the magnetic field bound like this and what is it bound to?
I am not. What exactly is it electrons pass through to feel a force if not something real. I understand that magnetic fields can morph into electric fields depending on your frame of reference, but that to me just says these fields are related to the X-woman Mystique who can change if you look at her the wrong way.

Again, ignoring any movement that would change the flux strength, you can rotate the magnet and nothing happens, but if you rotate the coil around the magnet something will (although the effect will be small due to the small slant of the coil wires). So again, no changing flux strength, yet a go/no-go voltage depending of if you rotate the coil or the magnet indicating what appears to me as some kind of absolute reference.

14. Jun 30, 2017

OK, I'm fine with just saying we need moving electrons. But what are the electrons moving relative to? I don't have a problem with just eliminating the concept of fields if we are to look upon them as something imaginary and just get to the nuts and bolts. If we do so then we can whittle this down to this: The electrons are NOT moving relative to the magnet, since rotating the magnet or rotating the disk is not a symmetrical situation. One generates a voltage and the other does not. Therefore the disk is moving relative to something else. What is that something else?

15. Jun 30, 2017

Because if it was, it would generate a current in a stationary disk.

16. Jun 30, 2017

This is very well written and understood. Thanks for the preciseness. I can say that intuitively this works for me.
If I'm getting your concept (and I admit it's really pushing my brain) the concept of a rotating (or non-rotating) magnetic field is not a reasonable concept and only the rotation of the disk is of concern which is why rotating the magnet is also of no concern since it is not really associated with a rotating or non-rotating magnetic field. If I'm not mistaken then it seems that some of my earlier remarks about just looking at all of this as if a field not only does not exist, but is not even necessary in thinking about the original questions. So again, if I'm getting this right, then the absolute rotation of the disk (i.e. whether if feels rotational forces or not) is the only factor involved so thinking about a relative motion between the disk and the field is just not necessary, or even useful as it really plays no part in answering my original questions. This must mean (although I was told no earlier) that the absolute nature of rotation of an object (the disk) is the only thing that gives rise to the current when a magnet is present. No angular velocity - no current, period! (So in my original question #1 my assumption was right?)

17. Jun 30, 2017

Staff: Mentor

Fields aren't imaginary, they just don't have rotation. It is like talking about the charge of a poem.

18. Jun 30, 2017

sweet springs

Hi. To #15
Let us think of a simple model of magnet whidh consists of two same sized positive and negative chargted rings in the same position. One rotates and generates magnetic field. The other is still so that electric field generated by the two is cancelled. There remains only magnetic field and the pair is regarded as magnet of non rotation.
When we rotate this magnet, one ring changes its rotation more or less and the other also starts rotation. TOR says not only change of magnetic field but appearance of electric field due to break of the cancellation.
So we should regard these changes as of electromagnetic field not as rotating magnetic field.
Best.

Last edited: Jun 30, 2017
19. Jun 30, 2017

Drakkith

Staff Emeritus
Your general idea is correct. All observers will agree that a particle moving through an electromagnetic field will experience a deflection. They just may not all agree on how much each component of the electromagnetic field (electric vs magnetic) affects the particle.

Perhaps think of it this way:

We assign several values to every point in a coordinate system to represent the electric and magnetic components of the electromagnetic field at that point. Now, observers in other coordinate systems moving with respect to this initial coordinate system will instead have different values for these components. However, the combined effect that each component has on a charged particle moving with respect to the original coordinate system results in all observers seeing the charged particle accelerate in exactly the way they would expect. That is, no matter what the motion of the particle is like with respect to a coordinate system, the E&M field values for each coordinate system all end up causing the particle to accelerate in a way that makes sense to all observers.

Hopefully that makes sense. I put it in these terms to illustrate that even though the EM field components change for different coordinate systems, they change in such a way as to make the particle always accelerate in a way that all observers will agree with. So even though we can have an infinite number of coordinate systems and observers, there is still only one electromagnetic field. It's just that the values of each of its components changes. And just like there is no preferred frame of reference, there is no preferred way of assigning electric and magnetic field vectors. An observer moving with a magnet will see a non-changing magnetic field, while an observer watching the magnet move towards them will see a changing magnetic field (and a resulting electric field). Both are equally valid and end up producing the exact same effects.

20. Jun 30, 2017

Paul Colby

I recommend reading the wiki on the Faraday Disc. There is a modern "explanation" which includes the return path of the current which includes stationary brushes. It''s safe to conclude I'm confused as well. As I said, the Faraday disk is an interesting discussion.