My problem comes from this thread: Does a rotating disk develop a potential difference between the centre and rim?

My issue is that I don't see why the assumption of equilibrium commented by Cag must be done. I mean: how do we know that we should expect the electrons to be in equilibrium? Isn't it possible that a steady state current is produced by the electrons which are thrown away from the disk by the centrifugal force? I know that the drag forces in the case of an applied electric field lead the electrons to move really slowly due to the collisions with the metal lattice, but still I don't see why a current is impossible to be produced.

Another question that I make to myself (and to you) is the following: is the electric force produced by the center of the disk at the rim stronger along the disk itself or along the conducting wire? If the answer to the second question is positive, the electrons might jump the potential barrier at the rim and a DC current might be set up.

I must admit that this problem has troubled me since long, because I still see holes in the answers I find.

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    $\begingroup$ If the disk is in a magnetic field? Yes. That's called a homopolar generator en.wikipedia.org/wiki/Homopolar_generator. You can try it yourself at home with an electric drill, a flat metal disk, a magnet, a couple of wires and a simple voltmeter. It's kind of a cute and simple experiment. Why does it work? Because a charge moving in a magnetic field experiences an electric field. Relativity at home! $\endgroup$ – CuriousOne Dec 25 '15 at 20:58
  • $\begingroup$ Please make the second question more clear. I cannot make any sense out of "is the electric force produced by the center of the disk at the rim stronger along the disk itself or along the conducting wire?". $\endgroup$ – Bruce Lee Dec 25 '15 at 22:18

There will be an equilibrium and no steady state current which keeps generating. The reason is that after some of the electrons get deposited on the rim, then they give rise to an electrostatic potential difference between the rim and the centre, the centre having a positive potential due to the loss of electrons, while the rim having a negative potential due to excess electrons. The force due to this potential difference is opposite to the direction of motion of moving electrons and repels the further flow of electrons happening from the centre to the rim and after the potential difference becomes sufficiently high further motion of electrons is stopped and thus an equilibrium is reached where electrons do not further move towards the rim.

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  • $\begingroup$ Excuse me for the ambiguity in my second question. What I meant is the following: I can understand that the total force will be zero after a certain distribution of negative charge will be accumulated on the rim. However, a null force still enables electrons to move at constant speed from the rim to the center of the disk and from there to the rim again, closing the cycle. However, it seems this is not possible, so a DC current cannot exist. Why? $\endgroup$ – Eden Dec 27 '15 at 21:09
  • $\begingroup$ zero force won't allow an electron to keep moving with some constant speed as its kinetic energy would decrease to zero after collisions with atoms in its path. So a null force won't allow a steady state current. $\endgroup$ – Bruce Lee Dec 27 '15 at 23:27
  • $\begingroup$ I neglected the collisions with the metal lattice, but we can add these interactions to the problem: in this case, why are we sure that the centrifugal force will always compensate the repulsion from the electrons on the rim? $\endgroup$ – Eden Dec 28 '15 at 14:03
  • $\begingroup$ @Eden because if centrifugal force is lesser than the force due to electrons at the rim, then they would never have been there at the first place. If it is more than the force at the rim, then similarly they will go on and deposit at the rim. If they are equal, then they have reached equilibrium and that is why no further current will flow. $\endgroup$ – Bruce Lee Feb 1 '16 at 15:19
  • $\begingroup$ Therefore, why doesn't the same occur when a magnetic field is present? A certain amount of electrons will also accumulate at the rim, right? Let's say, if the total force is non-zero (dragging + centrifugal + rim) and at the beginning of the motion this is necessary non-zero, how do you know that at certain moment the electrons will not move anymore? Sorry, I don't say you aren't right, but I don't see the point of your reasoning. A net zero force doesn't imply non-existence of motion! $\endgroup$ – Eden Feb 2 '16 at 20:13

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