Changing magnetic field and a point charge, seems unresolvable

[Dale]

I think it is this E field that is produced by the changing magnetic field, which contains this physical real momentum, so at-least in this case it is different than the E field produced by a charge ! What do you think?

The momentum density of the field is ExB, not just E. Again, there is only one E field, not two separate kinds.

 

[universal_101]

I think I understand your point here - even in the absence of the peripheral charges there is field angular momentum owing to the mix of quasistatic B and -dA/dt E fields arising solely in response to the coil's dying current. Not actually so here. Note the E field lines are circularly symmetric about the coil axis, while the lines of B, evaluated through any plane lying in and including the coil axis, lie entirely in such planes. So the nominal Poynting vector field for such crossed E & B fields always itself lies in such a plane, and therefore has no azimuthal component as required to account for angular momentum. The coil itself initially does carry mechanical angular momentum owing to the circulating current. That angular momentum was earlier injected during whatever means were used to set up the supercurrent in the first place. During the current decay process, cooper-pairs (which comprise the supercurrent) breakup and thence behave as normally conducting electrons which subsequently resistively interact with the lattice structure and this transfers momentum to the lattice. So in effect the 'invisible' angular momentum in the current finishes up as 'visible' momentum in the lattice - i.e. there is a minute but detectable rotation induced in the coil. But no net change in overall angular momentum is involved. Note also that the azimuthal -dA/dt E field is not inducing any overall mechanical momentum as the coil is electrically neutral.

Your point is valid, that there is NO azimuthal component of the angular momentum as required for peripheral charges, therefore there is NO angular momentum for peripheral charges unless they themselves are present. Alright.

But then, how does the presence of peripheral charges changes the scene ? And wouldn't it then mean, that peripheral charges produces angular momentum for themselves in the presence of magnetic fields or changing magnetic fields !

Whereas on the other hand, I perfectly understand the minute rotation due to stopping of moving electrons while the current decays.

I agree there is a real issue here that imo has been swept under the rug so to speak. Just to highlight the intrinsically different character of demonstrably real radiative momentum to this notional static field momentum, consider something as closely analogous to circulating S_stat = 1/μ₀E_stat × B_stat as can be. A traveling-wave (aka 'ring') resonator. When energized to a steady-state condition, there is a circulating flow of essentially reactive power density S_rad = 1/μ₀E×B and momentum density S_rad/c in what is basically a section of waveguide closed back on itself. Place a tiny strip of power absorbing or reflecting material in the path of this power and momentum flow, and it will variously heat up and move in the direction of power flow, in so doing causing a concomitant loss and/or reflection of power and momentum in the radiative stream. Try the same thing with the notional power and momentum 'flow' in the crossed static fields case, and, no real surprise, nothing whatsoever is detected. This mysterious momentum and power flow has the annoying knack of evading all attempts at physical detection! Does make some folks wonder.

So, we can't detect the angular momentum due to static crossed fields! but the bigger question is why are we searching for one ? Do we have any experiment that suggest the disc in the Paradox should rotate ? After-all even the Feynman disc experiment seems very simple to perform!

 

[Q-reeus]

Your point is valid, that there is NO azimuthal component of the angular momentum as required for peripheral charges, therefore there is NO angular momentum for peripheral charges unless they themselves are present. Alright.

That will do.

But then, how does the presence of peripheral charges changes the scene ? And wouldn't it then mean, that peripheral charges produces angular momentum for themselves in the presence of magnetic fields or changing magnetic fields !

What can be really said is that in such an arrangement as Feynman disk, there is a net production of mechanical angular momentum owing to the interaction between decaying coil current and the peripheral charges. Mediated by the azimuthal E field that owes it's origin to that decaying coil current, and is associated with a time-changing B field, the association between E and B being given by Faraday's law curl E = -dB/dt. With E itself being given here by -dA/dt, as was part of discussions back around #10-#14.

Whereas on the other hand, I perfectly understand the minute rotation due to stopping of moving electrons while the current decays.

Glad that one is bedded down.

So, we can't detect the angular momentum due to static crossed fields! but the bigger question is why are we searching for one ? Do we have any experiment that suggest the disc in the Paradox should rotate ? After-all even the Feynman disc experiment seems very simple to perform!

Personally I have no doubt it will rotate, but the forces induced will be very weak. As said in an earlier post, transformer action really requires that charges in the secondary windings are being pushed around by those -dA/dt E fields.
While the physical scenario is a simple one, the implications continue to create heated debate in various circles, and understandably so. A majority simply accept the primacy of the conservation law involved here - angular momentum, and are happy to accept this demands physically real momentum in those static crossed fields. Others, including myself, are not so readily satisfied.
[There are various alternate arrangements - one example given earlier in a link. Some involve apparent creation of linear momentum, but in such cases there is inevitably another player in the game - so-called hidden momentum that counteracts any 'overt' mechanical momentum. Static field momentum here rarely if ever enters the equation as a 'necessary balance'.]

 

[universal_101]

What can be really said is that in such an arrangement as Feynman disk, there is a net production of mechanical angular momentum owing to the interaction between decaying coil current and the peripheral charges. Mediated by the azimuthal E field that owes it's origin to that decaying coil current, and is associated with a time-changing B field, the association between E and B being given by Faraday's law curl E = -dB/dt. With E itself being given here by -dA/dt, as was part of discussions back around #10-#14.

Whereas I don't think that something like that can be done. I have my own issues

Personally I have no doubt it will rotate, but the forces induced will be very weak. As said in an earlier post, transformer action really requires that charges in the secondary windings are being pushed around by those -dA/dt E fields.
While the physical scenario is a simple one, the implications continue to create heated debate in various circles, and understandably so. A majority simply accept the primacy of the conservation law involved here - angular momentum, and are happy to accept this demands physically real momentum in those static crossed fields. Others, including myself, are not so readily satisfied.
[There are various alternate arrangements - one example given earlier in a link. Some involve apparent creation of linear momentum, but in such cases there is inevitably another player in the game - so-called hidden momentum that counteracts any 'overt' mechanical momentum. Static field momentum here rarely if ever enters the equation as a 'necessary balance'.]

I think all this has to do with a fundamental misconception in classical electrodynamics, anyway, I should thank you for the very detailed and interesting discussion.

 

[Q-reeus]

I think all this has to do with a fundamental misconception in classical electrodynamics, anyway, I should thank you for the very detailed and interesting discussion.

Thanks in return, but I just hope you really ponder transformer action!