A critical analysis of Helmholtz's argument against Weber's electrodynamics

We present Helmholtz's argument against Weber's electrodynamics. It is related with a fixed charged nonconducting spherical shell and a charged particle moving inside it. Then we utilize Weber's electrodynamics plus Schrödinger's expression for gravitational interactions in order to obtain the equation of motion and to study this situation. We show that this approach avoids the problems pointed out by Helmholtz. Moreover, it indicates that the effective inertial mass of the charged particle will depend not only on the electrostatic potential of the shell but also on its velocity. This is a relevant aspect of Weber's theory.