Theory of Magnetism

Between two parallel conducting wires at distance R, surface free electrons are repelling each other with electrostatic force F=Ke x ee/R^2. That repulsion force transfers electric force between the two conductors. If current move in one conductor, it will induce an opposite direction current in another conductor. The strength of the induced emf is proportional to the voltage and inversely proportional to the distance squared.

A magnet carries circular electric force. One magnet pole has clockwise electric force, the other pole has counterclockwise electric force.

A current in a wire does not create a circular magnetic force in the space, it induces the circular electric force in the compass, makes the compass move to 90 degrees.

Every magnetic domain contains two atoms. Two connect atoms of a ferromagnetic matter before magnetizing, we know the charges in them as 00. Use circular current to induce it, if one electron moves from one atom to the next atom and stays there as -1+1, the two atoms become a magnetic domain, it carries a special property now, we call it magnetic force. -1+1, -2+2, -3+3 are all magnetic domains but carry different magnetic force strength. Same direction magnetic domains attract, opposite direction magnetic domains repel. Before magnetizing, atoms in the magnet are all neutral.  After magnetizing, all atoms become magnetic domains and line up into concentric rings across the magnet from pole to pole.