None more mysterious than the attraction of opposed poles of a magnet. Conversely, like poles repel. We can look at the curl of the electron field and note that opposing poles with opposing orientations in space have electron fields that add constructively in curl.
How does a constructive or additive curl cause magneto-attraction? It is interesting to note that the magnetic force acts similarly in a gas as in a vacuum. I have challenged the whole notion of a vacuum when a magnet or two are present in previous blog posts.
Writers make a big deal of poles never being separated. If poles just represent the orientation of spinning or curling (vector field) of electrons then why does it surprise us that the poles can never be separated? It becomes a trivial statement. This fact is described by the Maxwell-Ampere equation where curl is related to magnetism and movement of electron-charges.
Back to the attraction between magnets. The opposing poles with opposing orientations in space will have additive curl. Electrons will move from one pole to the other but note that the direction doesn't matter. The return path will be through the magnetic material and around the outside of the magnet with the vector curl of the electron field following what we call the magnetic field lines. Both the direct path and the return path for the curling electrons add constructively for attraction.
The curl from the mass of the magnet to the center between the two opposing poles relaxes the curl of the electron field. The field wants to stay together but the mass is loose in the gas or vacuum between the magnets so the electrons spiral outwards. At the same time the return path is curling the other way pushing the electron vector curl field inwards. Eventually the mass of one or both of the magnets seeks to fill the void where the curl is loose (less) and trending towards more.
This phenomenon may be best described by tensors or vector calculus of many dimensions. I will reserve this analysis for another blog post.
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