Poynting vector

In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area per unit time) or power flow of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m2); kg/s3 in base SI units. It is named after its discoverer John Henry Poynting who first derived it in 1884. Nikolay Umov is also credited with formulating the concept. Oliver Heaviside also discovered it independently in the more general form that recognises the freedom of adding the curl of an arbitrary vector field to the definition. The Poynting vector is used throughout electromagnetics in conjunction with Poynting's theorem, the continuity equation expressing conservation of electromagnetic energy, to calculate the power flow in electromagnetic fields. In Poynting's original paper and in most textbooks, the Poynting vector is defined as the cross product where bold letters represent vectors and E is the electric field vector; H is the magnetic field's auxiliary field vector or magnetizing field. This expression is often called the Abraham form and is the most widely used. The Poynting vector is usually denoted by S or N. In simple terms, the Poynting vector S depicts the direction and rate of transfer of energy, that is power, due to electromagnetic fields in a region of space that may or may not be empty. More rigorously, it is the quantity that must be used to make Poynting's theorem valid. Poynting's theorem essentially says that the difference between the electromagnetic energy entering a region and the electromagnetic energy leaving a region must equal the energy converted or dissipated in that region, that is, turned into a different form of energy (often heat). So if one accepts the validity of the Poynting vector description of electromagnetic energy transfer, then Poynting's theorem is simply a statement of the conservation of energy. If electromagnetic energy is not gained from or lost to other forms of energy within some region (e.g.