Two procedures to introduce the familiar retarded potentials of Maxwell’s equations are reviewed.
The first well-known procedure makes use of the Lorenz-gauge potentials of Maxwell’s equations. The
second less-known procedure applies the retarded Helmholtz theorem to Maxwell’s equations. Both
procedures are compared in the context of an undergraduate presentation of electrodynamics. The
covariant form of both procedures is discussed for completeness. As a related discussion, two
procedures to introduce the unfamiliar instantaneous potentials of Maxwell’s equations are also
reviewed. The first procedure applies the standard Helmholtz theorem to Maxwell’s equations and the
second one uses the Coulomb-gauge potentials of Maxwell’s equations. The retarded and instantaneous
forms of the potentials of Maxwell’s equations are briefly commented upon. The retarded Helmholtz
theorem is used to introduce the retarded potentials of Maxwell’s equations with magnetic monopoles.