Inhomogeneous Wave Equation, Liénard-Wiechert Potentials, and Hertzian
Dipole in Weber Electrodynamics
- Steffen Kühn
Abstract
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.