Special Theory of Relativity

6

Covariant Electrodynamics

6.1  INVARIANCE OF MAXWELL’S EQUATIONS UNDER LORENTZ TRANSFORMATION

It is shown in Section 1.4 that the wave equations

are not invariant under Galilian transformation. Our immediate objective is to prove that Lorentz transformations also leave Maxwell–Lorentz equations invariant.

Maxwell–Lorentz equations governing the field created by a given distribution of charge and current are (in Gaussian units in which the field vectors have the same dimensions)

∇· E = 4πρ        (6.5)

 

∇· B = 0        (6.6)

 

where ...