Electromagnetic power flow and its expression—poynting vector and Nukiyama vector

Abstract

AbstractUsually, the Poynting vector is considered to be a vector field expressing the power flow. However, in many textbooks on electromagnetics the following statements are given which cause confusion: (a) since an arbitrary vector field with zero divergence can be added without violating the energy conservation law, the Poynting vector is not a unique expression for the power flow; and (b) the Poynting vector has nonzero value near a charged magnet. Since it cannot be accepted that a power flow exists in such a space, the Poynting vector may not represent a power flow.Such statements which cause confusion come from the education in which the relativistic aspects of electromagnetic theory have not been considered seriously. This paper is intended to contribute to the electromagnetic education and presents: (a) a clear explanation for the fact that the electromagnetic theory is essentially relativistic; (b) an explanation why the Nukiyama vector does not replace the Poynting vector; (c) general conditions to be satisfied by a vector which can be added to the Poynting vector; and (d) the basis on which we take the Poynting vector as the only expression for the power flow density.