The singularity of the exact electromagnetic fields is derived to include the "source terms" for harmonically oscillating electric (and magnetic) dipoles, so that the fields will be consistent with the full Maxwell equations with a source. It is shown explicitly, as somewhat expected, that the same [delta]-function terms for the case of static dipole fields will have to be included in the dynamic case for this purpose, while the associated magnetic (electric) field will remain unaffected by these singular source terms. (Contains 5 footnotes.)