Poyntings

Poyntings is a term used to refer to concepts named after John Henry Poynting, an English physicist who lived from 1852 to 1914. The most prominent of these concepts is the Poynting vector, S, which represents the directional energy flux of an electromagnetic field. In SI units, S = (1/μ0) E × B, where E is the electric field and B the magnetic field; in materials, S is often written as E × H. The direction of S indicates the direction in which electromagnetic energy propagates, and its magnitude corresponds to the instantaneous power per unit area carried by the field. The Poynting vector is a fundamental tool for analyzing power flow in antennas, waveguides, optical beams, and other radiative systems.

Poynting's theorem is the related energy conservation statement for electromagnetic fields. It can be written as ∂u/∂t + ∇·S = - J·E, where J is the current density and u is the electromagnetic energy density, defined as u = (ε0 E^2 + B^2/μ0)/2. This theorem links the rate of change of field energy and the divergence of the energy flux to the work done on charges, ensuring total energy conservation when fields interact with matter.

The concepts bearing Poynting’s name have had a lasting impact on physics and engineering. They provide a rigorous framework for understanding how energy and momentum are transported by electromagnetic fields, underpinning practical analyses in classical electrodynamics, photonics, and radio engineering. The term Poyntings, in this sense, covers the vectorial and dynamical tools derived from John Henry Poynting’s foundational work.