Maxwellian and cavity electromagnetic fields within continuous sources

Maxwellian and cavity electromagnetic fields are derived within a continuous source distribution of volume current or electric and magnetic polarization densities by direct, rigorous differentiation of the vector potential. The derivation, which uses only operations of vector calculus, reveals naturally the contributions from interior and exterior source regions. Results are obtained for static and arbitrarily time‐varying fields as well as for time‐harmonic fields.