# A modern representation of the flow of electromagnetic power and energy using the Poynting's vector and a generalized Poynting's theorem

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## Abstract

A comprehensive and rigorous description of instantaneous balance of electromagnetic power defined as the derivative of energy with respect to time is offered by the Poynting's theorem. Such theorem is expressed as the sum of a series of volume integrals representing the volume densities of densities of different components of electromagnetic power and the power flow through the general surface surrounding the entire domain in which the Poynting's vector expresses the instantaneous power leaving the domain (the positive normal is the outward normal to the enclosing surface). The original feature of the present approach is the introduction in the electromagnetic power balance and conservation of the electromechanical energy conversion by the use of the flux derivatives of the fields [D with vector arrow] and [B with vector arrow]. For the moving points (rotors) involved in electromechanical energy conversion, the surface of integration is driven together with them and [permittivity] and [permeatility] remain substantially constant--(a point in movement maintains its properties as [formula]). Then the balance of energy (and power) can be written at each infinitesimal time interval for the electromagnetic energy in which case the elementary mechanical work is produced by mechanical forces of electromagnetic origin. The thermal energy accounts for the Joule (and hysteresis) losses in the system. A treatment of the flow of electromagnetic energy is given for a complete of illustrative relationship in time and frequency domain.