Yes, that's the key.The electrons and the nuclei don't enjoy the same freedom. The electrons can move around; the nuclei can't. This breaks the symmetry. Electrons and their distribution conform to the boundary condition of 0 net charge by acquiring a greater proper distance between them, but the nuclei cannot do this.
That's a very interesting question, I've to think about.@vanhees71, in one of your comments on your article, you mentioned, "The battery must deliver some net negative charge (i.e., electrons)." How is the charge (in the wire frame) accounted for in the case of a superconducting loop in which a current is induced?
We call it electromagnetic force. This is because, as you have noted, how the electromagnetic field splits into an electric and a magnetic field is frame dependent.a neutral current-carrying wire creates an electrostatic force for a test charge moving relative to the wire/current, which we call the magnetic force.
The force is created due to how the material reacts to the external magnetic field by creating induced currents.If we replace the test charge with a chunk of ferromagnetic material, we find that it experiences a magnetic force even if both it and the wire are uncharged, and even if it is stationary relative to the wire.
Ordinarily we associate induction with a changing magnetic field. Here, we have a static magnetic field. Is it that the field is always changing for the moving electrons in the ferromagnetic material? And, that the resulting currents set up a calculable electric-charge buildup on the surface of the material, and an opposite charge on the wire, which causes the wire to attract the material?The force is created due to how the material reacts to the external magnetic field by creating induced currents.
Ferromagnetism is explained by the fact that elementary particles (in this case the electron) do not only carry electric charge but also a magnetic dipole moment, related to their spins. A permanent magnet is a material, where a macroscopic number of spins is oriented in one direction, because (at the given temperature) it is energetically more favorable for the associated magnetic moments being directed in one direction than being in random orientation as is the case in usual materials. To understand this completely from first principles you need quantum many-body theory (in this case the non-relativistic version is sufficient).This thread has shown how a neutral current-carrying wire creates an electrostatic force for a test charge moving relative to the wire/current, which we call the magnetic force. Excellent, thank you.
But I seek a more complete understanding.
If we replace the test charge with a chunk of ferromagnetic material, we find that it experiences a magnetic force even if both it and the wire are uncharged, and even if it is stationary relative to the wire.
How is this explained in terms of electrostatic forces and the Lorentz transform? The PF threads I've reviewed, and the linked resources (such as http://physics.weber.edu/schroeder/mrr/MRRtalk.html), only discuss test charges; and all explanations I've found of ferromagnetic materials appeal directly to the magnetic force, with none of that relativistic goodness. Perhaps Purcell covers it, but I don't have that book. Does it have to do with eddy currents?
Summary:: Why a test charge at rest in the lab frame does not experience a force from a current
I am intrigued by the special-relativity explanation of magnetic force discussed here (linked from the physicsforums FAQ): http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Length_Contraction
Naively, from this explanation, it seems that a test charge at rest in the lab frame should experience a force from a current-carrying wire, since the electrons' fields are Lorentz-contracted relative to the test charge, but the nuclei fields are not. And, that the test charge should experience no force only if the positive and negative charges in the wire are moving in equal and opposite directions relative to the test charge, i.e., when the test charge is moving along the wire at 1/2 the drift velocity. But that's not what happens. What am I missing?