  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.
