The Lorentz force

Abstract This chapter studies Maxwell theory by defining the electromagnetic potential and field as well as the force exerted by an external field on a particle carrying an electric charge. In Maxwell theory, the fundamental mathematical quantity representing electromagnetic phenomena is a field of covariant vectors (or a field of 1-forms), the electromagnetic potential, with components Aμ(Xν) in a given inertial frame with Minkowski coordinates Xν. A quantity derived from the potential plays a central role because it is this quantity rather than the potential itself which directly represents observable phenomena. In addition, this chapter integrates the equation of motion for the cases of uniform rectilinear and circular motion. It follows the four-dimensional approach, which, being more efficient and transparent, can also give the main results in 3-vector notation.