DERIVATION OF A MODERNIZED WEBER FORCE LAW

A derivation from first principles is given of a modernized form, recently proposed in this journal [Phys. Essays 3, 414 (1990)], of the Weber action-at-a-distance law of force between point electrical charges. The modernization invokes the existence of a limiting relative particle speed in nature. Like Weber's original (1848) law, our result amounts to a Coulomb law describing static interaction, modified at higher orders to describe instant action-at-a-distance through a simple dependence of potential energy on charged-particle relative velocity. Weber's law appears as a low-speed limiting case.