Poynting vector

In physics, the Poynting vector represents the directional energy flux (the energy transfer per unit area per unit time) of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m2). It is named after its discoverer John Henry Poynting who first derived it in 1884.:132 Oliver Heaviside also discovered it independently. In physics, the Poynting vector represents the directional energy flux (the energy transfer per unit area per unit time) of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m2). It is named after its discoverer John Henry Poynting who first derived it in 1884.:132 Oliver Heaviside also discovered it independently. In Poynting's original paper and in many textbooks, the Poynting vector is defined as where bold letters represent vectors and This expression is often called the Abraham form. The Poynting vector is usually denoted by S or N. In the 'microscopic' version of Maxwell's equations, this definition must be replaced by a definition in terms of the electric field E and the magnetic field B (it is described later in the article). It is also possible to combine the electric displacement field D with the magnetic field B to get the Minkowski form of the Poynting vector, or use D and H to construct yet another version. The choice has been controversial: Pfeifer et al. summarize and to a certain extent resolve the century-long dispute between proponents of the Abraham and Minkowski forms (see Abraham–Minkowski controversy). The Poynting vector represents the particular case of an energy flux vector for electromagnetic energy. However, any type of energy has its direction of movement in space, as well as its density, so energy flux vectors can be defined for other types of energy as well, e.g., for mechanical energy. The Umov–Poynting vector discovered by Nikolay Umov in 1874 describes energy flux in liquid and elastic media in a completely generalized view. The Poynting vector appears in Poynting's theorem (see that article for the derivation), an energy-conservation law: where Jf is the current density of free charges and u is the electromagnetic energy density for linear, nondispersive materials, given by