386(5): Complete Magnetostatic Solution

This solution emerges from the assumption (1), a special case of the last note. This assumption is solved simultaneously with the antisymmetrry law (6) to (8) to give the three spin connection components uniquely, Eqs. (18) to (20). The well known current in a circular loop is used as an illustration. The algebra can be worked out with computer algebra and graphed as usual. The exact solution is Eq. (26) in terms of the complete elliptic integrals K and E with argument (27). The translation from spherical to Cartesian is given in Eqs. (32) and (33). An approximate solution is given in Eqs. (34) to (36), and the dipole solution far from the current loop is given in Eqs. (40) to (42). In each case antisymmetry is conserved and the spin connections can be computed and graphed. In this case the algebra can get complicated but that is no problem. This general method can also be used for electrostatics and probably also for electrodynamics.

a386thpapernotes5.pdf

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