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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/m 2 ); kg/s 3 in base SI units.
In electrodynamics, Poynting's theorem is a statement of conservation of energy for electromagnetic fields developed by British physicist John Henry Poynting. [1] It states that in a given volume, the stored energy changes at a rate given by the work done on the charges within the volume, minus the rate at which energy leaves the volume.
Building on the concept of the Poynting vector, which describes the flow of energy in a transverse electromagnetic wave as the vector product of its electric and magnetic fields (E × H), Heaviside sought to extend this by treating the transfer of energy due to the electric current in a conductor in a similar manner. In doing so he reversed the ...
For waves in a birefringent (doubly-refractive) crystal, under the old definition, one must also specify whether the direction of propagation means the ray direction (Poynting vector) or the wave-normal direction, because these directions generally differ and are both perpendicular to the magnetic vector (Fig. 1).
Notice the cyclic permutation of indices in this equation: α → β → γ → α from each term to the next. Another covariant electromagnetic object is the electromagnetic stress-energy tensor, a covariant rank-2 tensor which includes the Poynting vector, Maxwell stress tensor, and electromagnetic energy density.
The Poynting vector for a wave is a vector whose component in any direction is the irradiance (power per unit area) of that wave on a surface perpendicular to that direction. For a plane sinusoidal wave the Poynting vector is 1 / 2 Re{ E × H ∗ } , where E and H are due only to the wave in question, and the asterisk denotes ...
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
In three dimensions, the derivative has a special structure allowing the introduction of a cross product: = + = + from which it is easily seen that Gauss's law is the scalar part, the Ampère–Maxwell law is the vector part, Faraday's law is the pseudovector part, and Gauss's law for magnetism is the pseudoscalar part of the equation.