Apologize for asking: Isn't this analysis (with frames), when applied to the rotational version of the Faraday Experiment supposed to predict a zero measurement, although the observed one is non zero?

If we imagine the classical Faraday Unipolar generator, with "infinite radius" then a small portion of the far rim is approximatively this linear device, isn't it?

It would be if you kept the magnets/magnetic field stationary in the laboratory frame of reference. In which case in the laboratory frame there is no electric field and a force $q\vec{v} \times \vec{B}$ on the charged particle. In the stationary frame of the charge particles there is an electric field $\gamma \vec{v}\times \vec{B}$ and a magnetic field of $\gamma \vec{v}\times \vec{B}$ that the particles are not moving with respect to. Hence $\vec{F}' = q\gamma \vec{v}\times \vec{B}$ (note that Lorentz force is not invariant).

In the Unipolar Generator, even if the field is rotated with the disc a voltage is measured. How is this different to this linear experiment? If we replace the "infinite" disc, with an "infinite"rod, then isolate a small portion at the tip, wouldn't that be the exact device I'm proposing?

If the area of the magnet is slightly larger than the one of the copper plate, wouldn't this lead to a non zero measurement? As you mention, in case the area of the magnets is infinite, then there will be indeed a separation of charge ... well ... what if it is not infinite, but say "larger"?

@CMarius this experiment is not related to the homopolar generator. Not even in the approximation you mention. In the homopolar generator the magnet and the conductor have a relative velocity. Here they are comoving.

@Dale the faraday paradox is related tot the unipolar generator like this: in the homopolar generator even if the field is co-moved with the disc, the same effects are observed as to the case in which the field remains stationary. I will exemplify how this relates to it ...

@CMarius do you have a reference for that? One other major difference is the lack of current in your scenario. And a minor difference is that the edge of a rotating reference frame is non-inertial, whereas this is inertial. I do not think they are equivalent. At least their equivalence is not apparent simply by handwaving arguments. You would need a proper derivation to show the differences don’t matter

@Dale Reference for the voltage in the unipolar generator if the field is co-moved? I think this is the paradox itself! I've just added a picture in the post in which I've partitioned the disc to show it's equivalence (more or less) to my design

@CMarius you are not supposed to change a question after it receives an answer in a way that invalidates the answer. In any case your description of the equivalence is problematic. An infinite disk has no edge, and for a finite disk as the radius becomes large the angular velocity goes to zero, and the homopolar generator produces no voltage if it does not rotate. And if the radius is not large then it is substantially non-inertial. You are trying to claim a paradox by claiming a contradictory equivalence

@Dale. I haven't modified the question, per se, but added additional arguments for the expected results, or just say: "improved my work done". I hope that is acceptable. Regarding the equivalence ... yes! I am not saying that it is perfect, but that it is just the reason I think one way or another ...

@Dale: If the disc is arbitrarily large ... the angular velocity becomes arbitrarily small indeed assuming a bounded velocity of the rim. Nice approach! But if you fix the speed of the rim (what ever that is), the Lorenz force in the rotation case, does not depend on the radius ...

@CMarius that is a judgement call, I feel like it is changing the question because now ProfRob's answer seems incomplete when it was a complete answer to the original question. I think that I need to study this a bit more before commenting further. However, I don't think that the idea that the edge of a big disk is approximately inertial holds water. It is a false equivalence in general, and clearly causes problems here

@Dale I appreciate your approach! Although I do not know what I have added to change the meaning ... Why do you think ProfRob's answer is more incomplete now as opposed to "before"? This was the question the whole time ... I admit that I am not a physician, but I just hold my argument and intuition to the best of my abilities.

@ProfRob Please stop rolling back to some previous version of the question, where the phenomenon is less clear. What is wrong is the subsequent additions?

@ProfRob Do you think your answer is no longer valid? Should I ask another question? I want the answer to this version of question!

@CMarius I agree with ProfRob here. Now his answer is incomplete because he doesn't address the things you added since you added them after he answered. I think it is entirely reasonable for him to roll it back to the version that he answered since your edits make his answer incomplete

What is that? At this moment I do not know what invalidates the answer of ProfRob! He uses the fact that the edge of the magnet gives rise to a component which cancels the Lorenz force. Is that phenomenon now now no longer valid if I just say that the copper plate should be well within the field? or?

@CMarius as I said, this is a judgement call, but my judgement is that your additional material makes ProfRob's response incomplete. He didn't address the additional material. If you believe that it doesn't make the answer invalid then why do you insist on adding it? You already got a complete answer then.

@CMarius What edge of what magnet? The Lorentz force is $q(\vec{E} + \vec{v}\times\vec{B})$ and it is zero in both frames of reference, as I demonstrated.

@ProfRob: I'll ask another question, alright! From here researchgate.net/publication/… and here pure.psu.edu/en/publications/… it seems to me (I'm not a physician) that the underlying explanation for why the translation and rotation are not the same is "something" related to the "edge" of the magnetic field. I did not see this in your answer.

Besides, it also "seems" to me, that the linear case is "somehow" the limit case of the rotational one. I'll address this better someplace else. Anyway, thanks a lot for your attention! I'll return for sure to this answer to analyse it from a different perspective!

@CMarius Correct, it forms no part of my answer since rotation was not part of the original question. The reference was to show you that the rectilinear motion experiment has been done and there is no voltage produced.