The Lorentz Force and the Nature of Charge from a Photonic Toroidal Vortex Model

In 1865, Maxwell characterized a magnetic field line as an axis of angular momentum. It is shown why this cannot provide an explanation for the migration of charge and the generation of an emf in a conductor moving perpendicularly through these lines. The Lorentz force deflection is instead derived from the photonic toroidal vortex (PTV) model developed by Clarke (2025). The model defines a mass in terms of optical orbital angular momentum (OAM) with a specific beam waist, and here it is shown how motion towards a magnetic momentum field line with a gradient creates a change in momentum perpendicular to it, resulting in an excess or deficit of action in the mass’s OAM circuit. This is redistributed into motion along the OAM axis. The mean value of these redistributions, averaged over all OAM positions in the PTV rotation, results in the Lorentz force deflection. In the process, a geometrical nature of electric charge is suggested in terms of a combination of OAM and toroidal rotation senses.