A note on the uniqueness of the Poynting vector and of the Maxwell tensor

Abstract

Many alternatives to the classical Poynting vector P have been proposed, but they lack a property of locality that makes P special and makes it the right choice to represent the energy flux. We give a geometrical proof of this uniqueness. Similar considerations apply to the Maxwell stress tensor. KEYWORDS energy flux, Maxwell tensor, momentum flux, Poynting vector 1 x elc , and B mag [resp. D elc ]. This way, the constitutive laws are H(x) = B mag (x, B(x)) and E(x) = D elc (x, D(x)) at point x. This excludes nonlocal dependencies, in space or time (as would happen in case of hysteresis), between the four fields, while allowing to deal with anisotropies and nonlinearities. (The linear isotropic case corresponds to mag (x, B) = 1 / 2 (x)|B| 2 and elc (x, D) = 1 / 2 |D| 2 / (x), where Int J Numer Model. 2018;31:e2214.wileyonlinelibrary.com/journal/jnm

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