THEORETICAL PUBLICATIONS

This article extends the Electromagnetic (EM) field's Energy-Momentum tensor by adding the missing momentum flux terms. The conservation equations are consequently changed, and as a result the missing electromagnetic terms of inertia forces,  centrifugal, Coriolis and shear  forces emerge.  All the new quantities and the extended quantities are defined as proper covariant tensors. The new definitions of the physical quantities and the extended conservation equations, enable to resolve  known problems in classic electrodynamics. Three known problems were chosen to prove the validity of the extended equations and new definitions. The first problem  is the 4/3 problem, the second problem  is the lack of centrifugal forces when a static  EM momentum density exists on the theta direction and the third is the  problem of  radiation reaction known as the Abraham-Lorentz force. The extended EM motion  equations become essential only  when very strong EM fields are present or when the inertial terms can not be neglected, otherwise, as in most classical cases in labs, Maxwell's equations are a very good  approximation, this is probably why these inertia terms were missed by Maxwell and other classical electrodynamics researchers. The extended motion equations are Non-linear, which means the EM fields can influence  themselves or other EM fields, for example a light passing through a strong magnetic field should be bend, this situation is relevant when a light passes  a  Magnetar's magnetic field. Lastly, the Lagrangian of the extended equation is defined and compared to other two extended nonlinear Lagrangians, the Euler- Heisenberg and Born-Infeld.