I Magnet falling though copper pipe

[Orthoceras]

@Orthoceras, Am I right?

No, I don't think of electrons as being tiny magnets. My idea is rather plain, and it is best summarized by the image below. The force F_Lor pushes the electrons down. I don't think the controversy in this thread has much to do with my idea, the controversy just got a life of its own.

 

[DaveE]

No, I don't think of electrons as being tiny magnets. My idea is rather plain, and it is best summarized by the image below. The force F_Lor pushes the electrons down. I don't think the controversy in this thread has much to do with my idea, the controversy just got a life of its own.
View attachment 296384

The electrostatic repulsion between conduction band electrons is powerful. I don't think they can move to the bottom in a metal tube and collect there to any significant degree. Maybe a bit near the magnet as it falls, but that equilibrium will be established very quickly and will be hard to "see".

 

[Swamp Thing]

Sorry Orthoceras, I didn't notice that mohamed_a's question was directed to you as the OP... Since my posts were the most recent activity on the thread (after some long inactivity), I sort of thought he was asking me.

That said, the general tone of the discussion has been a bit dismissive about your original question, whereas to me it still feels pretty intriguing and I find myself thinking about it now and then.

 

[hutchphd]

Saying something is incorrect is "dismissive" of necessity.
The fundamental point here is that any solid contains both plus and minus charges. The structure maintains its integrity because they interact strongly. To deal only with the electrons, particularly when the mass matters will take you to a wrong place. Also the classical picture of conduction works for a limited subset of circumstances. The anomalously high conductivity of metals was one of the reasons QM was important.
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[vanhees71]

Well, nevertheless the Drude model is qualitatively not too bad. In this simple classical picture you can consider a metal as consisting of a positively charged lattice of ions with the conduction electrons moving quasi-freely within this lattice. Due to (thermal) lattice vibrations and other "defects" the conduction electrons are also scattered, leading to a friction force. Since for usual household currents and of course also for the here considered situation of a magnet falling through a cylindrical-shell conductor the drift velocities are very tiny (order of 1mm/s) the usual "Stokes friction" (friction linear in the momentum of the electron) is good enough, and this leads to the usual constitutive equation $\vec{j}=\sigma \vec{E}$ (neglecting the Hall effect, which must be reintroduced if you want a relativistic description, which however here is completely irrelevant).

 

[hutchphd]

But the Drude model foundational assumption of quasi-free electron transport in the lattice makes no sense in a classical context. And for electrons in that periodic structure the notion of momentum is supplanted by "crystal momentum" which requires the presence of the massive periodic structure. So notions of momentum conservation of the electrons are fraught. That being said I do often think of electrons as little blue Drudish spheres...

 

[vanhees71]

Well, you can do everything quantum theoretically with a very similar qualitative result ;-).

 

[hutchphd]

Yes I like the blue electrons in my head ! But neglecting the background periodicity and the comcommitant surrender of rigorous momentum conservation leads directly to the incorrect analysis here. It is a very useful model, except where it isn't...

 

[vanhees71]

Of course momentum is not conserved, because there are forces acting on the electron. It's an effective description of the underlying microscopic many-body dynamics, and it's amazingly good. Of course, as with any effective model, the parameters are not predicted from first principles but taken as parameters to be determined empirically (in this case electric conductivity).

 

[hutchphd]

Of course they are not free in reality. But it seems to me that the major source of confusion for the OP is the assumption that conduction electrons are "free" particles until they hit the end of the conductor. He then uses momentum conservation for the electrons alone (they are, after all, just free Drude particles) to reach some dubious conclusions. It is the model that takes him down this path.