On Capacitor Earthís Magnetic Field
It is interesting that the Earthís magnetic field lines emerge from its geographic south pole and enter at the geographic north pole. In brief, the geographic south pole is a magnetic north pole, etc. All of which results in a compass needleís north pole pointing toward geographic north (i.e., toward magnetic south).
A second point of interest is that an electric field points down through the atmosphere, toward the Earthís center. This E field is not trivial; as one ascends there is a potential rise of 100 volts/meter! (The Feynman Lectures on Physics, V2, Sect. 9-1.)
Gauss indicates that the surface is negatively charged and the atmosphere is positively charged. We shall model these two charges as concentric spherical shells, with the inner one coinciding with the planetís surface.
At least part of the mechanism for these charges is probably the loss of atmospheric gas electrons to the planetís surface as winds blow over it. Concurrent with this process is the upward discharge of negative charge during lightning storms that constantly occur around the planet. Overall the amount of charge in each shell is more or less constant.
Since the two shells of charge are spinning (along with the planet), each shell engenders a dipolar magnetic field. The negative (surface) shellís dipole moment points toward geographic south, whereas the positive (atmospheric) shellís moment points toward geographic north. Thus at points within the Earth the two B fields tend to oppose one another. But above the surface and between the shells (particularly in the mid-latitudes) the fields tend to reinforce one another. (Beyond the outer shell the fields again tend to oppose one another.)
There is evidence that the planetís net B field has switched polarity in the past. Thus the charges that engender the radial E field cannot be the sole sources of the terrestrial B field. But they certainly modulate the other parts of the net field, and in rather interesting fashion. Note that the negative chargeís B field lines do indeed emerge from the geographic south pole, whereas the positive chargeís lines emerge from geographic north.
Each spinning spherical shell of charge can be modeled as a stack of current loops. As pointed out in other articles, the charge of a current loop is not evenly distributed around the current loop when the loop translates. Consequently, viewed from the Sunís rest frame, the Earthís negative and positive shells of charge are "lop sided" as the planet translates along its orbital path. The concentrations of charge occur on the same side for both signs. But a consequence of this relativistic effect is that, viewed from the Sunís rest frame, the radial E field should be greater on the side where the mutual charge concentrations occur (and the charge densities are greater). Of course with lightning storms and ions being swept along by winds, etc., the tidy current loop concept is no doubt simplistic. Nevertheless this relativistic effect is entertaining to think about.