NEW DISCOVERY OF VOLTAGE INDUCTION

[F6FLT]

I don't know,can't explain. Just it came to my mind.
This thing is said to have unusual geometric properties.
...

These special properties only concern the surface topology, not the conduction of electrons, for which an ordinary or Möbius strip is the same.

[F6FLT]

...
Sadly, this confirms to me that the vector potential does not offer an induction effect when charge is moving through a "static" vector potential changing only due to the movement of the charge.

On a closed circuit and static A, one cannot expect an EMF because a force deriving from a potential is conservative.

But I think that a variation of A in time is well accompanied by a gradient in space seen from a moving charge and vice versa.

To do the integral over a circuit in a A gradient, with the variation of A in time seen from the charge, as if it were a real ∂A/∂t seen from an observer at rest with respect to the circuit, is to mix values seen from different reference frames, it can only lead to false results.
If the integral over a circuit is done in the reference frame of the charge moving in a A gradient, then the charge sees ∂A/∂t BUT also a moving circuit, so the calculation cannot be done as in the case of the circuit at rest with respect to the observer.

[Smudge]

I quickly setup an experiment using the eccentric loop idea. I ran the motor at its rated 24V DC which as labeled makes it spin at 3500 RPM. I also used slightly thicker coper loop opposed to the copper tape I used previously. This proved to be much better as the measured voltages were much more stable.

The result I got was in the range of 0.5mV, essentially a null result. Regardless of how I placed the brushes even next to each other the same value was seen which tells me the this very low voltage was due to eddy currents rather than the change of the vector potential. From my crude calculation I should have seen a value in the 30mv range.

Sadly, this confirms to me that the vector potential does not offer an induction effect when charge is moving through a "static" vector potential changing only due to the movement of the charge.

I have just created the A fields near the surface of your PM and I agree with the magnitude you got near the outer edge.  In the image of your experimental set up you don't see any brushes.  Could you please explain what you used for brushes and where did you place them?  Thanks.
Smudge 

[broli]

I have just created the A fields near the surface of your PM and I agree with the magnitude you got near the outer edge.  In the image of your experimental set up you don't see any brushes.  Could you please explain what you used for brushes and where did you place them?  Thanks.
Smudge

I used braided wires and my own hands to hold them. I could easily slide the brushes around like that and going from 180° till the brushes almost next to each other gave the same result. What's surprising is that Weber's electrodynamics also predicts such longitudinal field yet the experimental setup shows none.

[Smudge]

@Broli
OK, I think I have solved the dilemma.  F6 and I have had earlier discussions about the vector potential on my Marinov Generator thread.
We agreed that it should be possible to derive classical induction for homopolar motion within a magnetic field directly from the A field that creates B (B=curl A).  When I initially did this I got only 1/2 the correct value.  To get the correct value you have to take account not only of the changing magnitude of the A field along the movement trajectory but also its changing angle relative to the trajectory.  This is somewhat akin to the Coriolis force for movement within a rotating frame.

For Broli's experiment, treating qA as some form of hidden momentum I have a method for deducing force by taking the change in A over a small distance dx of charge movement as dA, taking the angle between A and dx as Θ then using E_x=-v*dA*cos(Θ)/dx.  If Θ changes value over that movement I take the average of the two values in the cos function.  I got a voltage induction that agreed with Broli's deduction from Weber dynamics.  That is OK but it is important to note that a changing angle represents a rotating vector, and a rotating momentum vector creates a force even if the magnitude stays constant, and that force direction is at right angles to A.  So I have now deduced an additional force by taking the change in Θ over the movement dx as dΘ, taking the average magnitude of A over dx as |A|, then using E_x=-v*|A|*dΘ*sin(Θ)/dx as the addition.  This cancels out the induced voltage.  Note this is for the field close to the magnet where B=curl A.  So within that particular A field pattern there is no longitudinal induction along the movement path, only at right angles to it.  It remains to be seen whether the same thing applies to a non-curl A field.

Smudge 

[Smudge]

@Broli,

I have rechecked my method of taking the actual A field at different points around the circle (not the component wrt to velocity direction).  Then taking the change in magnitude over the time increment between two points as dA/dt, and that is an E vector pointing in the mean direction of the two A vectors.  The component of that E along the velocity direction is then one component of induction.  I also look at the change in angle of the A vector over the time increment between points (omega) and that gives me another E vector given by omega*A.  This E vector is at right angles to the mean direction of the two A vectors.  That gives me another component to be added to the first one.  And the two components have opposite signs and cancel each other.  So not surprising you found zero induction.

I then took another trajectory for a slip-ring mounted alongside the magnet as depicted in my modification to your image below.  I am doing this in a 2D program so my magnet is infinitely long in the z direction, thus there is zero magnetic field external to the magnet.  But there is a non-curl A field there and now my two E field components don't cancel.  The second image shows that external A field and my integration line.  This predicts a voltage across the diameter and I got such a voltage in my Marinov Generator work.  I would ask you to modify your experiment to do this test using your large magnet and see what you get.

Smudge

[broli]

@Broli,

I have rechecked my method of taking the actual A field at different points around the circle (not the component wrt to velocity direction).  Then taking the change in magnitude over the time increment between two points as dA/dt, and that is an E vector pointing in the mean direction of the two A vectors.  The component of that E along the velocity direction is then one component of induction.  I also look at the change in angle of the A vector over the time increment between points (omega) and that gives me another E vector given by omega*A.  This E vector is at right angles to the mean direction of the two A vectors.  That gives me another component to be added to the first one.  And the two components have opposite signs and cancel each other.  So not surprising you found zero induction.

I then took another trajectory for a slip-ring mounted alongside the magnet as depicted in my modification to your image below.  I am doing this in a 2D program so my magnet is infinitely long in the z direction, thus there is zero magnetic field external to the magnet.  But there is a non-curl A field there and now my two E field components don't cancel.  The second image shows that external A field and my integration line.  This predicts a voltage across the diameter and I got such a voltage in my Marinov Generator work.  I would ask you to modify your experiment to do this test using your large magnet and see what you get.

Smudge

Do you have a ball park figure on the estimated voltage of this as I have calculated before?

[Smudge]

Do you have a ball park figure on the estimated voltage of this as I have calculated before?

Yes, my figure is 6mV.  If you could arrange some crude fixed brushes then you can hand hold the magnet and move it around.  You could try smaller magnets.  Of course the acid test is with a magnetized ring core as shown in the image below (shown without the toroidal winding).  You must have some wound cores lying around in your workshop  .  Then there is no magnetic field, only the A field at the slip ring.  I have been waiting years for that test to be done.

Smudge

[broli]

Wanted to get back to this topic as I've recently got around to performing the experiment where the magnet was  positioned outside the rotating ring.

Now sadly this was inconclusive. The readings jumped around up to 4mV-5mV and sometimes flipped sign too and this was around 1000 RPM indicating a not so ideal brush assembly. I'm not the best builder around.

However I'm still skeptical about the vector potential inducing any voltage here.