Lorentz force law in invariant formulation under Galilean transformations

This paper proposes a generalized formulation of the Lorentz force law that achieves full invariance under Galilean transformations within inertial reference frames. Traditionally, the Lorentz force is considered non-invariant under Galilean relativity, a discrepancy that historically led to the development of Special Relativity. We demonstrate that by redefining the velocity of the charged particle as the relative (reciprocal) velocity between the particle and the magnetic field source, a frame-independent expression is obtained for all inertial observers. Under this formulation, the standard Lorentz force law is shown to be a special case occurring only when the magnetic field source is considered at rest within the laboratory reference frame. This approach restores physical symmetry to the interaction and provides a consistent Galilean description of electromagnetic forces. The implications for fundamental physics and the role of relative motion are discussed.