Inhomogeneous Wave Equation, Liénard-Wiechert Potentials, and Hertzian Dipole in Weber Electrodynamics

<p>Aiming to bypass the equation of the Lorentz force, this study analyzes Maxwell's equations from the perspective of a receiver at rest. This approach is necessary because experimental results suggest that the general validity of the Lorentz force is questionable in non-stationary cases. Calculations in the receiver's rest frame are complicated, and thus, rarely performed. However, after a Lorentz boost, the resulting force should be identical to the force obtained when the problem is considered in the rest frame of the transmitter with the Lorentz force applied, as is commonly done. Yet, this is not the case. Instead, Maxwell's equations lead to Weber electrodynamics. The present article demonstrates this result by deriving and solving the inhomogeneous wave equation from Maxwell's equations. Subsequently, it is shown that the resulting force is a relativistic generalization of the Weber force. Furthermore, the Hertzian dipole, i.e., a simple antenna, is mathematically investigated and discussed from the viewpoint of Weber electrodynamics for the first time.</p>