385(2): Conservation of Antisymmetry for the Electric Dipole Field Strength

The methodology developed in Note 385(1) is applied to the electric dipole field strength (7) in electrostatics. The spin connections can be worked out and graphed with computer algebra using Eqs. (9) and (10), and in the absence of a magnetic flux density B, automatically conserve antisymmetry. In general, the latter is conserved for any electric field strength E in ECE2 electrostatics in the absence of B, and with the assumptions (2) and (4) that A has no time dependence and that the scalar spin connection is universal:
omega sub 0 = – c / r.
In the special case where the electric dipole moment p is aligned in the Z axis, the electric field strength is given in Cartesian components by Eq. (26), and the vector potential by Eq. (27). So the spin connections can be worked out and graphed from Eqs. (10) and (27). They will have a very interesting graphical structure and will all conserve ECE2 antisymmetry. The calculation can be repeated for the electric n pole field, e.g. quadrupole, octopole, hexadecapole and so on. Any electric field strength of electrostatics will conserve antisymmetry under the conditions (2) and (4). The next not will apply this same methodology to magnetostatics.


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