The relativistic connection between harmonic bidimensional electrostatic and magnetostatic fields

The antecedent of this contribution is [1], which constructed the harmonic bidimensional expansions for electrostatic and magnetostatic potentials, produced by a straight line with uniform charge current distributions, respectively, in Cartesian, cylindrical circular, elliptic parabolic coordinates. For successive geometries, sources are confined respective cylinders containing source line, plus induced two grounded flat, elliptical plates; potentials continuous at cylinder vanish plates. In case, electric intensity field evaluated as negative gradient potential; magnetic induction rotational axial potential. Both potential force fields bidimensional, equipotential surfaces orthogonal. normal components show discontinuity, according to Gauss’s law measure surface distribution; contrast, tangential due conservative character force. its solenoidad character; discontinuity Ampere’s linear intensity. Figures 1-4 illustrate equipotentials on left lines right; right, exhibiting also their orthogonalities. differences between multipoles recognized, but we can still ask if there connection them. answer given here terms Lorentz transformations four-vector sources, antisymmetric four-tensor.