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The time-averaged power flow (according to the instantaneous Poynting vector averaged over a full cycle, for instance) is then given by the real part of S m. The imaginary part is usually ignored, however, it signifies "reactive power" such as the interference due to a standing wave or the near field of an antenna.
Poynting vector: S, N = ... = time averaged poynting vector; I = irradiance; I 0 = intensity of source; P 0 = power of point source; Ω = solid angle;
where: is the rate of change of the energy density in the volume. ∇•S is the energy flow out of the volume, given by the divergence of the Poynting vector S. J•E is the rate at which the fields do work on charges in the volume (J is the current density corresponding to the motion of charge, E is the electric field, and • is the dot product).
At a given point in space, in a steady-state field, the vector flux density, a radiometric quantity, is equal to the time-averaged Poynting vector, [8] an electromagnetic field quantity. [4] [7] Within the vector approach to the definition, however, there are several specialized sub-definitions.
The result is a gradual spiral of dust grains into the Sun. Over long periods of time, this effect cleans out much of the dust in the Solar System. While rather small in comparison to other forces, the radiation pressure force is inexorable. Over long periods of time, the net effect of the force is substantial.
where = [] is the time averaged Poynting vector. If W a > 0 {\displaystyle W_{\text{a}}>0} energy is absorbed within the sphere, otherwise energy is being created within the sphere. We will not consider this case here.
The direction of power flow for both nondispersive and dispersive media is determined by the time-averaged Poynting vector. Negative refraction was shown to be possible for multiple frequency signals by explicit calculation of the Poynting vector in the LHM. [45]
The resulting vector has the units of ... then the time-averaged energy density ... The intensity should then be defined as the magnitude of the Poynting vector. [1]