A Treatise on the Magnetic Vector Potential and the Marinov Generator

[broli]

And the double disc magnet version.

[F6FLT]

Thanks for the visualizations, Broli.

I ask the problem on a physics forum. Here is a proposed approximate solution of the torque we can expect.

To simplify, suppose that the variation of A is linear on the path and equal to ∆A on one side, -∆A on the other side.
∆S = π*R  (half-perimeter that is covered on each side)

Assume
I = Q/T        I current, T travel time of charges
v = π*R/T   v charges speed
v = I/Q * π*R

dA/dt ≅ v ∆A/∆S = I/Q * πR * (± ∆A/πR) = ± ∆A * I/Q

The force on the right:
F=Q*E = -Q * dA/dt = - Q * (+ ∆A * I/Q) = - ∆A * I = M*a  (right)

The force on the left:
F=Q*E = - Q * dA/dt = - Q * (- ∆A * I/Q) = + ∆A I = -M*a  (left)

It is thus found a torque of intensity: 4 * R * ∆A * I.

This torque depends on the intensity of the magnet (which gives A and ∆A), the radius of the ring, and the intensity of the current.

It's an approximation but it should give us the order of magnitude, provided that this torque which applies to the electrons is transferred to the ring.

[broli]

After seeing the simulation data my previously corrected version was wrong. After carefully analysing it intuitively the direction in Wesley's paper was in fact correct and is also showing in my simulator. However as Smudge points out this force should induce an EMF on the freely mobile electrons not a Torque. See below simulation and illustration.


This has a huge implication as we can have a stationary coil with many windings. And if we apply a current to it and bring it at the right location this current will get amplified due to the longitudinal E-field over the closed path Integral.

[broli]

This is the mind boggling setup that induces a DC emf in the direction of current flow in a coil which goes around the magnet in an arc and folds back the same path. This is all according to the change of magnetic vector potential experienced by the electron moving around in such wire.


Can we build it? The thing is due to the small EMF's (micro volts /turn) it will need a significant amount of turns. However if this is correct you only need an initial current source and then current would grow due to the EMF which could cause a chain effect because as the current grows the drift velocity increases, which in turn increases the E-field which in turn increases the current.

[Smudge]

I think you have to consider not only the change in the A field component along the semi-circles of wire around the magnets but also around the bends joining the two semi-circles.  As drift velocity is the same everywhere you find that the induction around those sharp bends completely nulls the overall induction.
Smudge