Retardation and relativity: The case of a moving line charge

The electric and magnetic fields of a line charge of finite length uniformly moving along its axis are derived by using retarded field integrals and also by using transformation equations of the special relativity theory. Both derivations yield the same field equations, although the derivation methods are drastically different. In particular, whereas transformation equations generally associated with Lorentz length contraction are crucial for the relativistic derivation, Lorentz contraction is not used in the retarded field derivation. On the other hand, although the retarded field derivation is based on the idea that retardation in the propagation of electromagnetic effects is a fundamental electromagnetic phenomenon, the relativistic derivation does not take retardation into account. An examination of the two solutions indicates that the field equations obtained classically and relativistically are identical because retardation is implicit in relativistic transformations.