Modifications of the Lorentz Force Law Complying with Galilean   Transformations and the Local-Ether Propagation Model
  It is generally expected from intuition that the electromagnetic force exerted on a charged particle should remain unchanged when observed in different reference frames in uniform translational motion. In the special relativity, this invariance is achieved by invoking the Lorentz transformation of space and time. In this investigation an entirely different interpretation of the invariance of force is presented. We propose a new model of the electromagnetic force given in terms of the augmented potentials, which are derived from the electric scalar potential by incorporating a velocity difference between involved particles. The propagation of the potentials is supposed to follow the local-ether model. All of the position vectors, time derivatives, and velocities involved in the proposed potentials and force law are referred specifically to their respective frames. By virtue of this feature, the electromagnetic force is independent of reference frame simply based on Galilean transformations. The proposed model looks quite different from the Lorentz force law, except the electrostatic force. However, under the common low-speed condition where the mobile charged particles forming the current drift very slowly in a neutralizing matrix, it is shown that the proposed model reduces to the Lorentz force law, if the latter is observed in the matrix frame as done tacitly in common practice. 
Ching-Chuan Su