Equivalence between Work-Energy Theorem (WET) and Poynting’s Theorem (PT)

Focusing on scattering problem, the mathematical expressions and physical interpretations of the entire-structure-oriented work-energy theorem (ES-WET) and some different forms of Poynting’s theorem (PT) are simply reviewed. Using Maxwell’s equations and volume equivalence principle, the equivalence between the ES-WET and PT is proved rigorously. The equivalence provides a clear physical explanation why the external impressed and environmental fields are treated as a whole–incident field–in the scatterer-oriented characteristic mode theory. In addition, the equivalence between the partial-structure-oriented work-energy theorem (PS-WET, which governs the working process of lumped-port structures) and PT can also be proved similarly. Thus, it can be concluded that work-energy theorem (WET, which is the collective name of the ES-WET and PS-WET) and PT are equivalent to each other.