The Connection Between Inertial Forces and the Vector Potential
  . The inertia property of matter is discussed in terms of a type of induction law related to the extended charged particle's own vector potential. Our approach is based on the Lagrangian formalism of canonical momentum writing Newton's second law in terms of the vector potential and a development in terms of obtaining retarded potentials, that allow an intuitive physical interpretation of its main terms. This framework provides a clear physical insight on the physics of inertia. It is shown that the electron mass has a complete electromagnetic origin and the covariant equation obtained solves the "4/3 mass paradox". This provides a deeper insight into the significance of the main terms of the equation of motion. In particular a force term is obtained from the approach based on the continuity equation for momentum that represents a drag force the charged particle feels when in motion relatively to its own vector potential field lines. Thus, the time derivative of the particle's vector potential leads to the acceleration inertia reaction force and is equivalent to the Schott term responsible for the source of the radiation field. We also show that the velocity dependent term of the particle's vector potential is connected with the relativistic increase of mass with velocity and generates a stress force that is the source of electric field lines deformation. This understanding broadens the possibility to manipulate inertial mass and potentially suggests some mechanisms for possible applications to electromagnetic propulsion and the development of advanced space propulsion physics. 
Alexandre A. Martins and Mario J. Pinheiro