arXiv:2611.05606v1 Announce Type: new Abstract: Considering the ideal limit where the speed of light is infinite, or more precisely where the permittivity and permeability of the vaccuum are both zero, we construct a new type of electromagnetic circuit that we name an EM-loop circuit. These consist of wires having very high permittivity (E-wires) and wires having very high permeability (M-wires). These are threaded together by coils, the E-wire loops and M-wire loops. Some of the loops are terminal loops, pierced by an applied magnetic flux (for E-wire loops) or an applied displacement field (for M-wire loops) that are outside the vacuum since it does not support these fields. The response is the net flux of displacement field through a cross section of each E-wire terminal loop and the net magnetic flux through a cross section of each terminal M-wire loop. To calculate this response, the fields at the internal loops (those that are not terminal loops) are eliminated from the equations.It turns out that the response is governed by a new class of function pairs - dual Herglotz functions. Superpositions of a special class of EM-loop circuits, termed fundamental, allow us to realize any pair of dual Herglotz functions. Thus, we have obtained a complete characterization of the response functions of EM-loop circuits.
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