On limiting velocity with Weber-like potentials

Abstract

This work analyses the problem of a charge moving perpendicularly to the plates of a charged capacitor. The results obtained from the current theoretical framework (Maxwell–Lorentz electromagnetism and special relativity theory) are compared with the results obtained from Weber’s electrodynamic potential, with the Phipps’s potential and a new potential proposed here. The aim of this comparison is to analyse the causes of the inability of these Weber-like potentials to predict the existence of a limiting velocity for this problem, as special relativity theory does indeed predict and many experimental results confirm. To overcome this incapacity, the need to employ an effective potential to solve the capacitor problem is shown. In the adoption of this strategy, it is shown that the potential proposed here reproduces the same relativistic result. Finally, the origin and possible interpretation of the aforementioned effective potential are analysed.