The physics of the moving charge in em field is the foundation to understand the most known knowledge that we have reached so far: the interaction of light and matter. Look around us, name a thing that is not made of light and matter! ##The EoM## First of all, let us briefly discuss the motion of charges in em field without acceleration. The easiest way to determine the EoM of a moving charge in em field is from the principle of the last action (please read [1]), which leads to the easiest understanding of Lagrangian and Hamiltonian equation. This part I...