Faraday's disk and "absolute" magnetic fields

[Buckethead]

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

 

[Drakkith]

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.

 

[Buckethead]

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.

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.

 

[Drakkith]

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.

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

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?

Not really, no.

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.

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

 

[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.

 

[Buckethead]

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

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.

 

[Buckethead]

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.

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.

 

[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?

 

[Drakkith]

Well, yes, but the phrase "moving in a magnetic field" implies that one part of a magnetic field can be distinguished from another part.

It does not.

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?

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.

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.

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.

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.

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.

 

[Paul Colby]

Are you saying that if the disk is not moving but the magnet is, there will be a current?

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. [edit] and your correct. There is no E field as a result of spinning the magnet according to the wiki.

 

[sweet springs]

Hello.

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?

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 ?

 

[pervect]

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.

 

[Buckethead]

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.

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?

You are aware that field lines don't actually exist right?

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.

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.

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.

 

[Buckethead]

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.

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?

 

[Buckethead]

First how did you know magnetic field generated by rotating current in magnets of no rotation are not rotating ?

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

 

[Buckethead]

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.

This is very well written and understood. Thanks for the preciseness. I can say that intuitively this works for me.

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.

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?)

 

[Dale]

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

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

 

[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.

 

[Drakkith]

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.

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.

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?

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.

 

[Paul Colby]

OK, I'm fine with just saying

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.

 

[Buckethead]

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

I thought the charge of a poem was 42.

If it can be said that the property of rotation does not apply to a field then concerning this thread the concept of whether or not a field is real is probably beside the point. What is important is whether or not the disk rotates relative to the magnetic field and I think you answered that. It does not. To paraphrase: Is an electron attracted to a poem?

 

[Dale]

What is important is whether or not the disk rotates relative to the magnetic field

I would say that what is important is whether or not the disk rotates relative to an inertial frame where there is a magnetic field.

 

[vanhees71]

For an exact relativistic treatment of the case of a homogeneously magnetized ball, see

http://th.physik.uni-frankfurt.de/~hees/pf-faq/homopolar.pdf

 

[Buckethead]

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.

I understand this as i alluded to earlier in my "Mystique" analogy. But this applies to a magnet moving through a coil. On a Faraday disk, while whether one is rotating with the disk relative to the magnet or vice versa can determine if we are looking at an M or a E field, it is irrelevant with regard to current flow. Only when the disk absolutely rotates is there current. Again, whether the current is due to an E field or an M field doesn't matter. It all comes down to the absolute rotation of the disk.

 

[TSny]

It all comes down to the absolute rotation of the disk.

There is no meaning to absolute rotation of the disk. As Paul Colby points out in post #20, the return path must also be considered.
Here is a video that shows various cases of parts of the setup moving relative to other parts.

The demo starts at time 0:30

 

[Drakkith]

I understand this as i alluded to earlier in my "Mystique" analogy. But this applies to a magnet moving through a coil.

No, it applies to all movement through an electromagnetic field.

On a Faraday disk, while whether one is rotating with the disk relative to the magnet or vice versa can determine if we are looking at an M or a E field, it is irrelevant with regard to current flow. Only when the disk absolutely rotates is there current.

The difference is that if the magnet is generating a rotationally symmetric field, then the field doesn't change as you rotate the magnet, so no force is felt by the electrons. Rotating the disk now causes the electrons to move through the magnetic field and Lorentz's law applies.

If it can be said that the property of rotation does not apply to a field then concerning this thread the concept of whether or not a field is real is probably beside the point. What is important is whether or not the disk rotates relative to the magnetic field and I think you answered that. It does not.

As Dale said, it would be better to talk about the disk rotating relative to an inertial frame in which there is purely a magnetic field. Trying to assign a frame of reference to the field itself is problematic and will mislead you later on down the road. It may seem pedantic, but it's important.

 

[Buckethead]

I would say that what is important is whether or not the disk rotates relative to an inertial frame where there is a magnetic field.

That does seem to be a reasonable conclusion.

However, I need to change my mind on what we talked about earlier. I'm thinking that a magnetic field does have the property of rotation but that the angular velocity is always 0. Here is my reasoning:

Imagine a large disk magnet not rotating, but rather moving in a circle such that the radius of the circle is much less than the radius of the magnet. A small piece of wire enveloped by the field but not experiencing any flux strength change, will nevertheless experience a current (The current will be AC in nature). Any particular line of flux (whether imaginary or not) will be moving in a circle relative to the wire, but the relationship between lines of flux is such that no field line can be said to be orbiting any other field line from the point of view of a disk that is not rotating.

If what I'm saying makes sense, then it's as if lines of flux are "bound" to an inertial frame with regard only to the orbital relationship between field lines. And again if what I'm saying makes sense, then this relationship between these field lines and the inertial frame is of interest.

 

[Drakkith]

Imagine a large disk magnet not rotating, but rather moving in a circle such that the radius of the circle is much less than the radius of the magnet. A small piece of wire enveloped by the field but not experiencing any flux strength change, will nevertheless experience a current (The current will be AC in nature). Any particular line of flux (whether imaginary or not) will be moving in a circle relative to the wire, but the relationship between lines of flux is such that no field line can be said to be orbiting any other field line from the point of view of a disk that is not rotating.

As far as I can tell, you are moving the magnet and the field strength will thus change at every point in space, even if only a tiny amount. In terms of flux, the flux strength will indeed change.

If what I'm saying makes sense, then it's as if lines of flux are "bound" to an inertial frame with regard only to the orbital relationship between field lines. And again if what I'm saying makes sense, then this relationship between these field lines and the inertial frame is of interest.

I'm sorry I don't see any "orbital relationship" between field lines. What are you referring to?

 

[Buckethead]

The difference is that if the magnet is generating a rotationally symmetric field, then the field doesn't change as you rotate the magnet, so no force is felt by the electrons.

It sounds as if you are saying that the field rotates when you rotate the magnet, but I don't think that's really what you mean. Is it?

As Dale said, it would be better to talk about the disk rotating relative to an inertial frame in which there is purely a magnetic field. Trying to assign a frame of reference to the field itself is problematic and will mislead you later on down the road. It may seem pedantic, but it's important.

I agree that this is the best way to look at the cause of the resulting current in the disk. See what I said however in #27. The reason we can't dismiss the field entirely is because translational movement of the field seems to be real and so the relationship to parts of the field with itself must be real as well.

 

[Buckethead]

As far as I can tell, you are moving the magnet and the field strength will thus change at every point in space, even if only a tiny amount. In terms of flux, the flux strength will indeed change.

I suspected you were going to call me on that. Replace the magnet with the Helmholtz apparatus such that the wire is always in the homogeneous area of the field.

I'm sorry I don't see any "orbital relationship" between field lines. What are you referring to?

Sorry, that was a bit vague. The difficulty I'm having is the fact that if I move an electron across field lines or field lines across an electron, the electron will feel the Lorentz force, so the field lines seem to have a property of being able to translate through space. Does that make them real? I just don't know, but, if they have the property of translation then one field line must have the ability to orbit any other field line (with respect to a non-rotating frame), but it doesn't. A line drawn between any two field lines will not rotate relative to an object with a 0 angular velocity. I originally liked the idea of rotation of a field being undefined, but it seems inconsistent with the idea of field lines being able to have the property of translation.

 

[Buckethead]

There is no meaning to absolute rotation of the disk. As Paul Colby points out in post #20, the return path must also be considered.
Here is a video that shows various cases of parts of the setup moving relative to other parts.

The demo starts at time 0:30

Thanks for the video. Case #5 was interesting. However this does not lead to the conclusion that there is no meaning to the absolute rotation of the disk. Case #5 generates a voltage because the upper part of the stator is moving through the magnetic field and the strength of this field is less at this point than it is near the path between the electrodes on the disk.

 

[TSny]

Thanks for the video. Case #5 was interesting. However this does not lead to the conclusion that there is no meaning to the absolute rotation of the disk. Case #5 generates a voltage because the upper part of the stator is moving through the magnetic field and the strength of this field is less at this point than it is near the path between the electrodes on the disk.

The following two cases produce the same emf:
(1) Rotate the disk at 10 rad/s with respect to the lab while keeping the stator and external parts of the circuit at rest relative to the lab.
(2) Keep the disk at rest with respect to the lab while rotating the stator and external parts of the circuit at 10 rad/s in the opposite direction relative to the lab.

If you rotate both the disk and the external circuit in the same direction at the same angular speed, no current is induced.

So, it's not absolute rotation of the disk that matters. What matters is the relative motion of the disk with respect to the external circuit. At least that's how I see it.

 

[sweet springs]

Hi. Tensor equation of Lorentz Force

Assures that frames of reference does not matter with physics. Best.

 

[Buckethead]

The following two cases produce the same emf:
(1) Rotate the disk at 10 rad/s with respect to the lab while keeping the stator and external parts of the circuit at rest relative to the lab.
(2) Keep the disk at rest with respect to the lab while rotating the stator and external parts of the circuit at 10 rad/s in the opposite direction relative to the lab.

If you rotate both the disk and the external circuit in the same direction at the same angular speed, no current is induced.

So, it's not absolute rotation of the disk that matters. What matters is the relative motion of the disk with respect to the external circuit. At least that's how I see it.

What you did not take into account is that when you rotate the stator and leave the disk stationary, the stator now becomes the disk and the disk the stator, so the disk rotates in both cases.

Also I want to add that the two situations are not symmetrical. When you rotate the disk you are rotating one wire (the disk) through the field, when you rotate the stator you are moving two wires through the field and the two wires oppose each other. Normally this would result in a null current, however because the two wires are in different parts of the field they will see different flux strengths so the net result is you get current.

 

[Dale]

I'm thinking that a magnetic field does have the property of rotation but that the angular velocity is always 0.

I don't see any value in this distinction, but I suspect it probably is harmless.

Imagine a large disk magnet not rotating, but rather moving in a circle such that the radius of the circle is much less than the radius of the magnet. A small piece of wire enveloped by the field but not experiencing any flux strength change

If the disk is moving then I don't see how the flux is not changing.

I originally liked the idea of rotation of a field being undefined, but it seems inconsistent with the idea of field lines being able to have the property of translation.

The fields do not have the property of translation either.