If we were able to look down on the Earth from Polaris we would see the North Pole out towards the equator. We would not see the magnetic field surrounding the Earth.
As we watch the Earth spin counter clockwise from Polaris we would note that particles are interacting with the Earth and being accelerated off of the planet. The particles, including electrons, eddie off of the Earth and spin clockwise all around the planet. This clockwise spin or curl in the electron field is observed by our magnetic compass to point North.
All of the particles surrounding the Earth interact and their curls begin to line up with time. At the poles the curl bends back and heads through the Earth's core in the opposite direction. Drawing lines through the mathematical normal to all of these electron curls yields the magnetic field lines.
The Maxwell-Ampere equation confirms the eddie current explanation for the magnetic field. The magnetic field lines are well known to point up from the geographic South pole to the geographic North pole. Using the Maxwell-Ampere equation and the right hand rule and we determine that current flows counter-clockwise when observed from Polaris. Of course electrons travel in the opposite direction to current therefore the eddie current explanation for the magnetic field checks out.
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