Electromagnetism and relativity

Abstract

In this chapter we show first that the magnetic field B arises naturally from a Lorentz transformation of the electric force in Coulomb’s law and so we can investigate the electric and magnetic fields of rapidly moving charges. Then by introducing a vector potential A subject to the Lorentz gauge condition we find a remarkable similarity between the equations of electrostatics, expressed in terms of the scalars ϕ (potential) and p, and the equations of magnetostatics in terms of the vectors A and j. Finally we show, using a four-dimensional notation, that it is possible to reduce Maxwell’s four equations to just one equation which expresses directly the invariance of electromagnetism under the Lorentz transformation.