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This work reveals previously hidden structural features of Maxwell’s equations that emerge when the Lorentz force is embedded into their flux formulation, exposing motional and rotational contributions to the field of an elementary charge. These modifications extend the field--source relationship to encompass phenomena beyond the standard static Coulomb case. We demonstrate this by deriving the magnetic field of a rotating spherical charge distribution, where magnetic charge appears not as a monopole but as an emergent quantity producing a dipole-like field. The same configuration generates a distinct component opposing the Coulomb field, arising purely from rotation. Building on these results, we formulate a force--flux law analogous to Gauss’s electric flux relation, but with force replacing field. Owing to its units, this law permits direct replacement of electric charge and constants with other charge types---magnetic, gravitational, or inertial---while preserving the force magnitude for a given separation. The result is a compact, nonrelativistic framework that retains Maxwell’s geometric elegance while extending its scope to unified static-field interactions.
Xydous I. 2025. Hidden Geometries in Maxwell’s Equations and a Force–Flux Route to Unified Static Fields. PREPRINTS.RU. https://doi.org/10.24108/preprints-3113890
