Date ons 17 januari 2018

A lot of people find statements like the current desity of the orbitsphere is constant and usually spike and call bullshit due to the impossibility to comb the sphere. Technically correct, but Mills do indeed have a constant current density although not at the south pole and the north pole which is undefined but bounded e.g. nice singularities that doesn't contribute technical problems to the solution of the electric field. Now how to see this? One can tak one point at the sphere that is not the south or the north pole and ask yourself what is the speed vectors e.g. we consider a uniform density of loops with normal density in the uppper half sphere. In order for a loop to pass through the point it has to have the normal pointing to the geodesic or great circle that sits in the plane orthogonal to the vector to the point in question. The intersection with the upper half sphere is for all points but the south and north pole a half circle implying that the magnitude summing all speed vectors e.g. summing all currents through the point is independent of the selected points. Hence constant current density. It is worth pointing out that the actual directions lead to flow loops that are all loops representing the intersection of all horizontal at different altitudes with the sphere. So this point is not too difficult to explain.