Field Generated by an Irrotational Current

ABSTRACT The field generated by a time‐harmonic pure irrotational current distributed in a finite region of free space is derived analytically. Only an electric field is produced and is nonzero even merely within the finite interior of the current distribution, though the problem space itself is infinite. To consider the obtained field solution nonphysical according to our current physical concepts, however, lacks evidence or reasoning. It satisfies the original first‐order Maxwell's equations (MEs) and the related continuity conditions exactly, hence cannot be rejected mathematically. It is also shown that a conceptual denial of such a different kind of solution based on physical interpretations of other known solutions of the same MEs is logically not acceptable. A direct experiment study is necessary to conclude convincingly whether or not the above solution is physical. The completeness problem of MEs and their consistency with the Lorentz force law and the equation of motion are discussed. Free space MEs are incomplete or underdetermined due to the absence of a curl equation for the current density. If the solution is nonphysical, ME‐based electromagnetic (EM) theory is not self‐consistent. On the other hand, if it is physical, this type of inconsistency within the frame of the ME‐based EM theory disappears, yet it is inconsistent with the Lorentz force law and the equation of motion in this case.