Poynting

Poynting may refer to John Henry Poynting, a British physicist (1852–1914) who made foundational contributions to the theory of electromagnetism. He introduced the concept of electromagnetic energy flux and established what is now known as Poynting's theorem and the Poynting vector, which describe how electromagnetic energy propagates and is conserved.

The Poynting vector, denoted S, describes the rate of energy transfer per unit area carried by an electromagnetic field. It is defined as S = E × H, where E is the electric field and H is the magnetic field. In vacuum, this reduces to S = (1/μ0) E × B, since B = μ0H. The magnitude of S gives the power crossing a unit area, and its direction indicates the direction of energy flow. The electromagnetic energy density is u = (ε0 E^2 + B^2/μ0)/2, and the local energy balance is expressed by the Poynting theorem: ∂u/∂t + ∇·S = -J·E, where J is the current density.

In practice, the concept is widely used to analyze power flow in antennas, waveguides, and optical fields. In materials, the relation extends with D and B and the corresponding constitutive relations, but the same energy-conservation framework applies. The Poynting vector thus provides a concise description of how electromagnetic energy moves and interacts with matter, forming a central element of classical electromagnetism.