Bar Magnets

It is much easier to draw a bar magnet with magnetic field lines surrounding it than helices of electrons traveling largely in a circular fashion. Well here is a drawing.

This drawing is a poor way to convey the circular path an electron takes around a bar magnet. Between the two magnets there are interactions between the two curling fields of electrons moving with opposing curls. It is likely that these fields interact and scatter matter such that a negative relative pressure is created. This lack of pressure pulls the two bar magnets together.

The Maxwell-Gauss magnetism equation traditionally defines this elliptical field. That is to say if we take the vector calculus curl of the electron movement fields we arrive at the magnetic field strength and direction. That vector field can be related to the Maxwell-Gauss magnetism equation. Otherwise, the Maxwell-Gauss magnetism equation is simply a vector calculus identity to be found in any vector calc text book.

Between the two bar magnets, in the gas or vacuum, there is likely to be centrifugence where the electrons leave the bar magnet and centripetence where the electrons enter the opposing bar magnet.

It will be harder to draw like poles of bar magnets repelling.