Gold Magnet, Earth Magnetic Field, Spin-Orbit Coupling, Polarity Free Repulsion

[Que]

I have been scouring the internet for many hours now and have yet to find any definite conclusion on this. So far Scenario B remains to be the most plausible which also has the most interesting implications.

EDIT: Shortly after making this post I found a paper that was literally published a few days ago: https://www.nature.com/articles/s41598-022-17766-z

I haven't read the whole thing but look at this abstract:

The classical laws of physics are usually invariant under time reversal. Here, we reveal a novel class of magnetomechanical effects rigorously breaking time-reversal symmetry. These effects are based on the mechanical rotation of a hard magnet around its magnetization axis in the presence of friction and an external magnetic field, which we call spin revolution. The spin revolution leads to a variety of symmetry breaking phenomena including upward propulsion on vertical surfaces defying gravity as well as magnetic gyroscopic motion that is perpendicular to the applied force. The angular momentum of spin revolution differs from those of the magnetic field, the magnetic torque, the rolling axis, and the net torque about the rolling axis. The spin revolution emerges spontaneously, without external rotations, and offers various applications in areas such as magnetism, robotics and energy harvesting.

This is so mind blowing, how can such an effect been hidden for so long

Perpetual Motion?

Here's a short video of a small spinning magnet following the magnetic isopotentials of a larger magnet.

The magnetic field is always perpendicular to the magnetic isopotential surfaces.  The isopotentials form concentric circles around the pole of a magnet.  The isopotentials provides much more information than the conventional vector fields of a magnet.  The vector fields are known from the isopotentials.

The small magnet in the video is slightly bound to the paper because of the downward force of gravity on the small magnet towards the paper. Because the small magnet is bound to the paper, it cannot fly directly to the big magnet. But it can spin, and when it spins it begins to move and when it moves it follows the path of least resistance, which just happens to be the isopotential "curve" that it happens to be sitting on when it starts spinning. Once it lifts off the paper, then it flies towards the big magnet. There is a lot going on when you look more closely.  Just looking at the conventional vector fields of a magnet isn't going to explain what is happening in this video!

The small spinning magnet is wobbling on it's magnetic axis as it spins and moves along the isopotential. This is what allows it to follow the magnetic isopotential of the larger magnet.  It takes 0 net energy for a magnet (magnetic dipole) to move along an isopotential (see attached image)!  We can achieve perpetual motion if we can constrain the small spinning magnet from lifting off the paper.  We can map out/trace a specific isopotential using a hall effect sensor.  We can then cut a very small shallow groove in what we traced out.  If the isopotential around the pole is truly a concentric circle, then maybe one of those old grooved vinyl records may work (no hall effect sensor needed).

Que/Gravock

[Verpies]

Here's a short video of a small spinning magnet following the magnetic isopotentials of a larger magnet.

Magnet spin is not electron spin.
The Wesley Gary effect is also an example of a magnet moving along the isopotential neutral line.

[Que]

Magnet spin is not electron spin.
The Wesley Gary effect is also an example of a magnet moving along the isopotential neutral line.

Magnet spin is not electron spin?  The answer is both yes and no depending on how you look at it (see attached image).  A moving electron creates a magnetic dipole, which is a tiny magnet itself.  Electron spin isn't a physical rotation like a spinning top, so a magnet spin is not an electron spin in this sense. However, the electron "acts" like and has "effects" of a spin. The rod rotating in the Einstein-de Haas experiment isn't electron spin either, since electron spin isn't a physical rotation. However, both the spinning magnet I referenced and the Einstein-de Hass experiment shows the "effects" of the so-called electron spin (intrinsic angular momentum).

The spinning magnet I referenced isn't moving along an isopotential neutral line where the magnetic field strength is 0 due to opposing magnetic fields as we find in the Wesley Gary effect.  There is no opposing magnetic fields in the spinning magnet example.  Magnetic isopotential surfaces represent regions of equal "magnetic pressure" or potential around magnetic sources, such as permanent magnets, and are analogous to equipotential surfaces in electrostatics.

The small magnet is spinning counter-clockwise on it's magnetic axis (axial rotation) as it rotates clockwise around the larger magnet (orbital rotation). The small magnet doesn't have a forward spin in the direction of travel/movement.  The axial spin is in the direction that is pointing away from the larger magnet relative to the forward direction it is moving in, which is in the opposite direction of it's orbital rotation.  The small spinning magnet in this example is showing "effects" of electron spin, or it's intrinsic angular momentum.

Que/Gravock

[Verpies]

You get brownie points for mentioning the Einstein-de Haas effect in context.

[Centraflow]

https://www.youtube.com/watch?v=NOG9VOBtpY4

[Que]

https://www.youtube.com/watch?v=NOG9VOBtpY4

Excellent reference video for the spinning magnet!  When viewed from the poles the isopotential lines form concentric circles.  Atomic orbitals match the isopotentials of various configurations of magnets.

When you have two inward counter-rotating magnetic fields in an ac electromagnet, one primary and the other is induced, there is no net magnetic field between them.  One cancels the other out according to Lenz law.  However, the two inward counter rotating fields will push both ferrous and nonferrous metals towards an electromagnet with a copper ring embedded in one end of it.  An attractive "pushing" force with no net magnetic field in that region of space!  Reference video: Non-ferrous magnet 

The reference video isn't directly relevant to the current discussion, but it shows how we must look at both the pressure gradients and the flow (magnetic vector fields and the magnetic isopotentials) in order to better understand electromagnetism and it's effects.  You can't explain the spinning magnet that mimics the electron spin without looking at both. Magnetic vector fields don't tell the whole story.

In meteorology, wind generally flows parallel to lines of constant pressure (isobars) or constant height (isohypses/isopotential lines) in the upper atmosphere, rather than directly across them. It's the same for an electron and the spinning magnet I referenced.  The path of least resistance is with the flow, which are the isopotential surfaces.  The flow in a magnet is the aether/virtual photons, depending on which model one may subscribe to.

Que/Gravock

[Verpies]

In meteorology, wind generally flows parallel to lines of constant pressure (isobars)

Not near the equator where the Coriolis force is low.   ....especially in areas with low surface friction like bodies of water.

[Que]

Not near the equator where the Coriolis force is low.   ....especially in areas with low surface friction like bodies of water.

In meteorology, wind generally flows parallel to lines of constant pressure (isobars).  You're right that it doesn't flow parallel to lines of equipotential surfaces in all cases.  I'm glad you brought this up, because this actually helps to explain the spinning magnet much better.

At the equator, the Coriolis force is zero.  Without this sideways tug to balance the Pressure Gradient Force (PGF), the PGF dominates and the air is pulled directly straight across the lines (nearly perpendicular).  At mid-latitudes the Coriolis is strong, so wind flows parallel to isobars.  In the sub-tropics the Coriolis weakens and the wind starts to angle across isobars.

The dominate force on the smaller magnet as it spins, is the constant pressure of the isopotential (isobar) that it is moving on, which is similar to the sideways tug of the Coriolis.  Once the small magnet lifts off the paper, then the dominate force is the PGF and it will be pulled directly straight across the lines towards the larger magnet (nearly perpendicular).  In other-words, it will follow the path of least resistance and will move along the isopotential it is on, until a greater force dominates it.

Que/Gravock

[Que]

We can map out/trace a specific isopotential using a hall effect sensor.  We can then cut a very small shallow groove in what we traced out.

How to map out a true 3d image of the magnetic isopotential surfaces of a magnet.  However, they're mistakenly calling the isopotential surfaces the magnetic field in that video (see attached image). Since the isopotential surfaces have much more information than the magnetic field vectors and the magnetic field vectors are known from it, then maybe we should be calling it the magnetic field as they are. They did make the connection to the atomic orbitals though.

Que/Gravock

[Smudge]

When you have two inward counter-rotating magnetic fields in an ac electromagnet, one primary and the other is induced, there is no net magnetic field between them.  One cancels the other out according to Lenz law.  However, the two inward counter rotating fields will push both ferrous and nonferrous metals towards an electromagnet with a copper ring embedded in one end of it.  An attractive "pushing" force with no net magnetic field in that region of space!  Reference video: Non-ferrous magnet

That is not how that "Non-ferrous magnet" works.  If you create an electromagnet with a coil around a ferrous core, but the core is actually a cylinder, the flux lines emanating from the annular end surfaces of the cylinder spread out in two directions, some radially outward where the flux lines go aound the outside the magnet to get to the other pole (as in any magnet), and some radially inwards where the flux lines go towards the other pole through the cylinder.  Actually most close through the inner walls of the cylinder, but the important thing is that inside flow that doesn't occur in normal magnets.  That produces the attractive force on the eddy currents induced into the non-ferrous discs, which only occurs over a small area and distance from the magnet.  Further away the force on the induced eddy currents becomes repulsive.  If he had demonstrated a ferrous non-conducting disc (like ferrite) it would show the magnet repulsing the ferrite, not attracting.  All this is easily shown in the free FEMM program that offers true 3D simulation for systems that are axisymmetric, which his demonstration is.  Eddy currents mean the electromagnet is AC driven not DC.  The front cover of the Jeff Moe CD package available for $17 shows his cylinder comprising of multiple rods, probably of Fe where a cylinder would suffer from high induced eddy currents.

Smudge   

[Verpies]

How to map out a true 3d image of the magnetic isopotential surfaces of a magnet.  However, they're mistakenly calling the isopotential surfaces the magnetic field in that video (see attached image).

This is nothing new.  It is just a different representation of the magnetic flux.
The linear force acting on that small magnet in the video is governed by the well-known formula for a force on a small magnetic dipole m in magnetic field (magnetic flux density vector field B):
F = ∇(m · B)
In the magnetostatic case (no free currents, ∇ × B = 0), this simplifies to the equivalent directional derivative form: F = (m · ∇)B.

This equivalence is the key - it means the entire problem reduces to computing the Jacobian tensor ∂Bᵢ/∂x at the dipole's location.
Each X,Y,Z component of the force acting on the dipole m is simply one row of that tensor scaled by its dipole moment magnitude.

All of that is directly derivable from the 3D flux map of the permanent magnet by the Jacobian transformation.

A line connecting points where the small magnet m experiences the same linear mechanical force is the Isoforce line (or Isodynamic line).  It is not the Isopotential line !

Isopotential or Equipotential lines  (surfaces in 3D) are not the same as Isoforce lines/surfaces !!!
The isopotentials of a dipole system are lines/surfaces where the potential energy U = −m·B = const, and the force vector F = −∇U is perpendicular to those lines/surfaces.
The isoforce lines/surfaces (|∇U| = const) are a completely different family of lines/surfaces.

Using the word "isopotential" brings up the connotation of the magnetic vector potential A, which is something very different from the linear force acting on a small magnet m.

To get from A to the force F acting on m you must:
1) Take the curl of A to recover B
2) Form the dot product m·B
3) Take the gradient of that scalar

Here is the full hierarchy:

Object	Symbolic repr.	What it is	SI Units
----------------------------	---------------------	----------------------------------	-------------
Magnetic vector potential	A	Potential field; B = ∇ × A	Tesla·meter
Magnetic flux density	B	Physical field; acts on dipoles	Tesla
Dipole potential energy	U = −m·B	Scalar energy of dipole in field	Joule
Force on dipole	F = −∇U = ∇(m·B)	Gradient of the energy	Newton
Space	s=vt	Prison for your mind	Meter

What I have written above does not refute what Smudge has replied to you.  It is a different, albeit a related subject.
His paper actually addresses the magnetic energy inside the space occupied by ferromagnetic materials.  My reply - does not.

[Que]

That is not how that "Non-ferrous magnet" works.  If you create an electromagnet with a coil around a ferrous core, but the core is actually a cylinder, the flux lines emanating from the annular end surfaces of the cylinder spread out in two directions, some radially outward where the flux lines go aound the outside the magnet to get to the other pole (as in any magnet), and some radially inwards where the flux lines go towards the other pole through the cylinder.  Actually most close through the inner walls of the cylinder, but the important thing is that inside flow that doesn't occur in normal magnets.  That produces the attractive force on the eddy currents induced into the non-ferrous discs, which only occurs over a small area and distance from the magnet.  Further away the force on the induced eddy currents becomes repulsive.  If he had demonstrated a ferrous non-conducting disc (like ferrite) it would show the magnet repulsing the ferrite, not attracting.  All this is easily shown in the free FEMM program that offers true 3D simulation for systems that are axisymmetric, which his demonstration is.  Eddy currents mean the electromagnet is AC driven not DC.  The front cover of the Jeff Moe CD package available for $17 shows his cylinder comprising of multiple rods, probably of Fe where a cylinder would suffer from high induced eddy currents.

Smudge

Thanks for the reply Smudge.  I don't think that is the same non-ferrous magnet I'm referring to after looking at the front cover and your description of that non-ferrous metal magnet.  I didn't pay that much attention to the front cover. That may be why the attraction force is much stronger than anyone else's I have seen.  That's why I chose that video over the others.  Below is a snapshot of the cylinder I was referring to.  It has a copper metal ring embedded in only one end of the cylinder.  That would make it not axissymmetric through the length of the cylinder?  Since this is AC driven, then we'll have an induced rotating field in the non-ferrous metal ring that will push the primary rotating field of the coil outwards.  We now have 2 rotating and opposing fields, if I'm understanding this correctly.  Anyways, I may start a new topic on this so I don't derail your thread more than I already have.  I thought maybe It had some relevancy at first, but I'm going to have to rethink this.

Que/Gravock

[Que]

This is nothing new.  It is just a different representation of the magnetic flux.
The linear force acting on that small magnet in the video is governed by the well-known formula for a force on a small magnetic dipole m in magnetic field (magnetic flux density vector field B):
F = ∇(m · B)
In the magnetostatic case (no free currents, ∇ × B = 0), this simplifies to the equivalent directional derivative form: F = (m · ∇)B.

This equivalence is the key - it means the entire problem reduces to computing the Jacobian tensor ∂Bᵢ/∂x at the dipole's location.
Each X,Y,Z component of the force acting on the dipole m is simply one row of that tensor scaled by its dipole moment magnitude.

All of that is directly derivable from the 3D flux map of the permanent magnet by the Jacobian transformation.

A line connecting points where the small magnet m experiences the same linear mechanical force is the Isoforce line (or Isodynamic line).  It is not the Isopotential line !

Isopotential or Equipotential lines  (surfaces in 3D) are not the same as Isoforce lines/surfaces !!!
The isopotentials of a dipole system are lines/surfaces where the potential energy U = −m·B = const, and the force vector F = −∇U is perpendicular to those lines/surfaces.
The isoforce lines/surfaces (|∇U| = const) are a completely different family of lines/surfaces.

Using the word "isopotential" brings up the connotation of the magnetic vector potential A, which is something very different from the linear force acting on a small magnet m.

To get from A to the force F acting on m you must:
1) Take the curl of A to recover B
2) Form the dot product m·B
3) Take the gradient of that scalar

Here is the full hierarchy:

Object	Symbolic repr.	What it is	SI Units
----------------------------	---------------------	----------------------------------	-------------
Magnetic vector potential	A	Potential field; B = ∇ × A	Tesla·meter
Magnetic flux density	B	Physical field; acts on dipoles	Tesla
Dipole potential energy	U = −m·B	Scalar energy of dipole in field	Joule
Force on dipole	F = −∇U = ∇(m·B)	Gradient of the energy	Newton
Space	s=vt	Prison for your mind	Meter

What I have written above does not refute what Smudge has replied to you.  It is a different, albeit a related subject.
His paper actually addresses the magnetic energy inside the space occupied by ferromagnetic materials.  My reply - does not.

You helped to clarify the force!  However, it's the magnetic isopotential surface that dictates the path, while the isoforce explains the constant speed.

Here is how they work together:
1. The Isopotential (The "Track"):  The small magnet follows the isopotential surface because that is the path where the potential energy is constant.  Since there is no change in potential energy along that circle, there is no magnetic "work" being done to pull it closer or push it away.  It functions like a train on a perfectly level track.

2. The Isoforce (The "Consistency"):  The isoforce line describes the intensity of the B field.  Because the large magnet is axially symmetric (a perfect circle), the isoforce lines happen to overlap perfectly with the isopotential lines.  Since the magnet is traveling along a path of constant force, the "pull" and the "torque" it feels are identical at every second of the rotation. This is why the speed and the wobble stay so perfectly constant.

3.  Why the Isopotential is the "Main Player":  If the large magnet were a square instead of a circle, the isopotential path would be a rounded, "squircle-like" shape and the isoforce (intensity) would vary (stronger at the corners, weaker at the flat sides).  In that case, the magnet would still try to follow the isopotential "track," but its speed and wobble would fluctuate because the field intensity is changing.

4.  The spinning magnet demonstration has a perfect symmetry where the "level track" (isopotential) and the "constant pull" (isoforce) are the same line. That's what creates that spooky, perfect "satellite" motion.

The constant speed is a beautiful visual proof of two things: <---------  If it's not constant, the magnet would still try to follow the isopotential "track," by varying its speed and wobble.

1.  Since the magnet isn't changing its "height" in the magnetic field, its kinetic energy stays constant. It's essentially "coasting" on a magnetic level plane (Conservation of Energy).  The inward pull of the large magnet is perfectly balanced by the outward "gyroscopic" or centrifugal effects of its motion.  The fact that it maintains a steady pace while wobbling (precessing) shows that the system has reached a steady state. It will keep that constant speed until it either loses energy to friction with the paper or "tips over" the edge of the potential well and spirals inward (Equilibrium of Forces).

2.  The spinning magnet doesn't appear to lose energy to friction with the paper, so it must be tipping over the edge of the potential well and spirals inward.  This is why I suggested to use an old vinyl record or to cut a very small and shallow grooved track to keep the magnet from tipping over the well and spiraling inwards.  The grooved track could be seen as a "gravity well" an object exerts on the fabric of space/time.  The area that bends down from the weight of an object.

Que/Gravock

[Allcanadian]

Que

That's funny, I recognized the picture with the cone shaped shaped area of attraction right away. It's the non-ferrous electromagnet of Leonard Crow which I also built and tested. It's an excellent paper with an extraordinary amount of useful information. I still read the paper every now and then and it never gets old. In effect, it's a split shaded pole armature wrapped in a circle which is a brilliant concept.

The article and PDF can be found here, https://www.rexresearch.com/mrmagnet/mrmagnet.htm
Note the date, 1951.

[Verpies]

However, it's the magnetic isopotential surface that dictates the path, while the isoforce explains the constant speed.

Physics doesn't work like that.
Net force always causes acceleration parallel to the force ...not constant speed.

The small magnet follows the isopotential surface because that is the path where the potential energy is constant.

Surface of a table is gravitationally isopotential, too, but that is not the reason an object does not fall. The reason is that the net force on the object is zero even if its weight is not.  If the object slides horizontally with acceleration on the surface of the table then it means that there is a net force component acting on the object horizontally.  If the table were to suddenly disappear, the object would leave the isopotential surface. The isopotential surface has no ability to keep the object confined to it when the force exerted by the table is absent 
The disappearance of the table does not delete the isopotential surface - it deletes the force that opposed the weight of the object.

Just because objects can move without acceleration on a isopotential surface without expenditure of any energy does not mean that this surface keeps or confines this object to that surface.  The only way the object will stay on that surface is when the net normal component of the force to that surface is zero.

Mechanics works the same with magnetic forces and potentials as with gravitational forces and potentials.

[Smudge]

Thanks for the reply Smudge.  I don't think that is the same non-ferrous magnet I'm referring to after looking at the front cover and your description of that non-ferrous metal magnet.  I didn't pay that much attention to the front cover. That may be why the attraction force is much stronger than anyone else's I have seen.  That's why I chose that video over the others.  Below is a snapshot of the cylinder I was referring to.  It has a copper metal ring embedded in only one end of the cylinder.  That would make it not axissymmetric through the length of the cylinder?  Since this is AC driven, then we'll have an induced rotating field in the non-ferrous metal ring that will push the primary rotating field of the coil outwards.  We now have 2 rotating and opposing fields, if I'm understanding this correctly.  Anyways, I may start a new topic on this so I don't derail your thread more than I already have.  I thought maybe It had some relevancy at first, but I'm going to have to rethink this.

Que/Gravock

Are you able to release more details of that system?  From your image I see what looks like a thick walled metal cylinder with a metal rod running through its centre, and the copper annulus within the circular gap.  I presume the coil is within the circular gap hidden below the copper annulus.  I presume the silvery metal is ferromagnetic.  Is the far end gap then closed by a ferromagnetic disc?

I don't follow the concept of an induced rotating magnetic field where the assumed rotation is around the axis.  I understand the induced eddy current and its magnetic field being superimposed onto the primary field resulting in vector sums everwhere but I don't see it as counter rotating fields. 

Smudge

[Verpies]

Are you able to release more details of that system?  From your image I see what looks like a thick walled metal cylinder with a metal rod running through its centre, and the copper annulus within the circular gap. 

Here is the FEMM simulation of that device.

[Smudge]

Here is the FEMM simulation of that device.

On the basis that a good conductor effectively expells an AC magnetic field via the induced eddy currents (much like a superconductor expells any magnetic field) there is a trick that you can do in FEMM to see the field distorted by the eddy currents.  If you give the conducting regions a relative permeability that is much less than 1 to make it diamagnetic (I use 0.001) you then see its effect.  You can take this further and obtain the force on the diamagnetic object (I am assumimg here use of the axisymmetric 3D FEMM).  Obviously this trick will also apply to any other simulation program.  The device will attract even without the copper ring there.  I think a copper ring at the far end helps and it looks as though the Jeff Moe device has that.

What people don't realize is the eddy current magnitude follows the applied field magnitide but the direction of the force on that eddy current depends on the applied field gradient.  The normal magnet and electromagnet has a field that reduces with distance from the pole face, but this field as seen in the FEMM simulation has a small region where it increases with distance.  That is why you get the attraction instead of the normal repulsion.  Nothing to do with contra-rotating fields!!

You can use the same technique to get repulsion of ferromagnetic material over a small region, and even do it with permanent magnets!  In the attached image there is a region of the ferrite PM that has had its magnetization reversed where it now levitates the hatpin.  The second image shows that region.  You can get this reversed region by pressing a strong NdFe disc magnet onto the ferrite billet against repulsion forces (need some jig to do this) and as it gets close there is a sudden switch to attraction when the region below the disc magnet suddenly switches.  Not only has this changed the ferrite but it also changes the NdFe magnet characteristics.

The final image is an FEMM simulation of a soft ferrite billet where its magnetization has been introduced by two coils, one around the outside and one within the ferrite.  The field pattern clearly shows the region where ferrouus material is repulsed (DC current) and where non-ferrous metal would be attracted (HF AC current). 

Having watched the TV program of Aussie Goldhunters I am amazed that no one uses electromagnetic means for gold separation and for analysis of soil looking for fine gold particles.  Dry blowers, wash plants and dangerouus chemical techniques are all the rage.  Electromagnetic repulsion is used in industial recycling plants to separate non-ferrous metals and I am sure it could be used for gold.  Examining soil samples using the old panning method is laborious and takes up time (and precious water).  Watching gold particles jumping is quick and gives an instant indication of the presence of fine gold and could even indicate the volume density without the need to extract the gold from each sample.

Smudge

[Verpies]

Having watched the TV program of Aussie Goldhunters I am amazed that no one uses electromagnetic means for gold separation and for analysis of soil looking for fine gold particles.

If you watch that entire video, to which I have posted the link, then you will see that the attraction is geometry-specific and undersize conductive objects are not attracted (oversize neither).

[Que]

Are you able to release more details of that system?  From your image I see what looks like a thick walled metal cylinder with a metal rod running through its centre, and the copper annulus within the circular gap.  I presume the coil is within the circular gap hidden below the copper annulus.  I presume the silvery metal is ferromagnetic.  Is the far end gap then closed by a ferromagnetic disc?

I don't follow the concept of an induced rotating magnetic field where the assumed rotation is around the axis.  I understand the induced eddy current and its magnetic field being superimposed onto the primary field resulting in vector sums everwhere but I don't see it as counter rotating fields. 

Smudge

Cylo's Garage explains beautifully how this special magnet generates rotating magnetic fields.  When we have sine and cosine waves that are 90 degrees to each other and they're orthogonal, the resultant field is a rotating field (see attached image).  Reference video: Dan Gilbert's Lectures and see attached image.

The cone shape area of attraction also supports the idea that the fields are rotating.  In an Orthographic Projection of the sine and cosine waves (the generator), the base is represented as a circle (when looking directly down), and the tip is a point above it, which is an "orthogonal" view of the cone, but not a description of the structure itself.  Reference video: Orthographic Projection: The Cone.

Que/Gravock

[Que]

Physics doesn't work like that.
Net force always causes acceleration parallel to the force ...not constant speed.

You're thinking of linear acceleration (speeding up or slowing down), but ignoring centripetal acceleration.  In a circular orbit (like the small spinning magnet), the net force is perpendicular to the motion. This force causes centripetal acceleration, which changes the direction of the velocity but not its magnitude (the speed).

A satellite orbiting Earth or the moon orbiting the Earth is under constant net force (gravity), yet it moves at a constant speed. The force is parallel to the acceleration, but both are perpendicular to the velocity. This is exactly what is happening to the spinning magnet as it "falls" around the curve.

Surface of a table is gravitationally isopotential, too, but that is not the reason an object does not fall. The reason is that the net force on the object is zero even if its weight is not.  If the object slides horizontally with acceleration on the surface of the table then it means that there is a net force component acting on the object horizontally.  If the table were to suddenly disappear, the object would leave the isopotential surface. The isopotential surface has no ability to keep the object confined to it when the force exerted by the table is absent
The disappearance of the table does not delete the isopotential surface - it deletes the force that opposed the weight of the object.

Just because objects can move without acceleration on a isopotential surface without expenditure of any energy does not mean that this surface keeps or confines this object to that surface.  The only way the object will stay on that surface is when the net normal component of the force to that surface is zero.

Mechanics works the same with magnetic forces and potentials as with gravitational forces and potentials.

You assume there is no "restoring force" to keep the magnet on the isopotential surface without a physical "table."  In the experiment, the gyroscopic stability (spin) and the magnetic torque create a "virtual table."  If the spinning magnet tries to move off the isopotential line (closer or further from the big magnet), the magnetic torque changes. Because the magnet has angular momentum (spin), it reacts to this change by precessing (wobbling) rather than just flying away.  This precession creates a self-correcting path. The "surface" isn't just a mathematical line, it is a stability valley. If the magnet moves "up" the potential hill, the gyroscopic forces push it back "down."

The table analogy Fails because there is no table.  The magnet is "floating" (skating) on the paper.  If the net force normal to the surface weren't balanced, the magnet would indeed fly to the center.  However, this magnet spins. That spin generates a repulsive torque component or a centrifugal effect that balances the attraction at that specific distance.  The isopotential surface is the "path of least resistance" where these dynamic forces (centripetal, magnetic, and gyroscopic) find equilibrium.

You are right about static blocks on tables, but you are forgetting that rotating dipoles in a gradient field experience vector torques. The magnet doesn't need a 'table' to stay on the isopotential because its own angular momentum converts the inward pull into a circular orbit at constant speed.

Que/Gravock

[Smudge]

If you watch that entire video, to which I have posted the link, then you will see that the attraction is geometry-specific and undersize conductive objects are not attracted (oversize neither).

I am quite aware of how size affects the forces on small particles and you find that for a given product of field magntude and field gradient at any point in the field region that creates the attraction (that product appears in the force equation) the induced eddy current dipole moment (hence also the force) varies with r^-3 (r is the mean radius of the particle).  The mass of the particle follows r⁺³, so the field ability to overcome gravity stays the same for all particle sizes (within the limits determined by the geometry of the system).

[Verpies]

Doesn't FEMM show that eddy currents induced by this device in a small particle, cause it only to rotate ?

[Smudge]

Doesn't FEMM show that eddy currents induced by this device in a small particle, cause it only to rotate ?

FEMM does not show eddy currents, it is simply a magnetic simulation that is a snapshot in time if the field is changing with time.  Neither does it show rotation due to eddy current.  To show the effect of eddy currents you have to apply them which is what the guy did in the simulation you linked to in post #226.  I presume he adjusted his currents applied to the copper disc (shown with a hole in it so he could apply current in two directions into and out of the screen) to get what he considered to be the likely currents or maybe he did a calculation.  That simulation shows the field emanating from the core being squeezed to pass through the small gap around the inner copper disc.  The external field geometry is then maximised for obtaining force on another disc of similar size, which is the wrong thing to do if you want to attract small objects.  The simplest objects to study are spheres where there exists equations telling you the induced dipole moment from which you can deduce the applied force.  So it is not a black art and for fine gold separation or sampling it is certainy feasible.  FEMM will give you the linear force and angular on your object if you apply some predetermined eddy current (so you don't then model a particle, you model a small single turn coil).  But you can get some idea of the force by modelling the particle as highly diamagnetic which it almost is at the right frequency.

[Smudge]

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By controlling the speed, frequency, phase changes, etc. of the rotating magnetic field in the ac master magnet and using another magnet, we can trap/attract/repel/rotate metal flake or fragments (without any physical rotation of an object, except for the magnetic field) based on the Polarity Free Repulsion (PFR) and Magnetic Bound State (MBS) phenomena.  This phenomena is also related to electron spin.  The ac master magnet will more than likely attract tiny metal flakes and fragments with the right parameters, as Smudge said.

You are completely wrong to link these effects using rotating magnets with my writings.  The devices I considered do not use rotating fields.  I tried to point this out tp you but you seem fixated on the perception that creating unusual levitation MUST involve rotating fields, but you are wrong.

Smudge