Electromagnetic deduction of the power in electric circuits

The classical electromagnetic deduction of the power in electric circuits resorts to the Poynting's theorem. However this theorem relies on an assumption regarding the expression of locally stored electromagnetic energy. This assumption allows for alternative expressions of the power required to build the electromagnetic field, which are proposed and exploited in specific analyses. An alternative formulation is presented here based on the Slepian's vector, directly derived form the Maxwell's equations, that fits particularly to circuits, as it provides an easy and straightforward confirmation the power expression through circuit elements.