381(3): Spin Connections of the Static Magnetic Field

This note uses the particular solutions of the ECE antisymmetry law given in Note 381(2) to show that ECE2 theory gives a rigorously self consistent solution of the problem of the static magnetic field, described by the well known whirlpool vector potential in a plane, equation (9). The spin connections are omega sub X = – 1/X and omega sub Y = – 1/Y. The electric field strength E and scalar spin connection are zero. The net electric charge density and current density are zero. It can be seen that the static magnetic field in ECE2 is twice the static magnetic flux density in the standard model, in which the spin connection four vector is zero. This note also applies to the static gravitomagnetic field, whose spin connections are the same. Using this particular solution method it is possible to work out the general solution for the three components of A and the four components of the spin connection method. If A is graphed, it will be a swirling vector potential in XY, while B is in Z. The general antisymmetry law in the XY plane is Eq. (4), with particular solutions (5) to (7). One can use this simple method to engineer any magnetic flux density from model spin connections. This example is one in ECE2 magnetostatics and magnetogravitostatics. One can repeat the exercise for ECE2 electrostatics and ECE2 gravitostatics.


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