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The Poynting vector appears in Poynting's theorem (see that article for the derivation), an energy-conservation law: =, where J f is the current density of free charges and u is the electromagnetic energy density for linear, nondispersive materials, given by = (+), where
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 ...
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.
However, because black-body radiation increases rapidly with temperature (as the fourth power of temperature, given by the Stefan–Boltzmann law), radiation pressure due to the temperature of a very hot object (or due to incoming black-body radiation from similarly hot surroundings) can become significant. This is important in stellar interiors.
But, for given amplitude (as noted above), the component of the Poynting vector in the y direction is proportional to the geometric factor cos θ and inversely proportional to the wave impedance Z. Applying these corrections to each wave, we obtain two ratios multiplying the square of the amplitude transmission coefficient:
In this way, the above equation will be the law of conservation of momentum in classical electrodynamics; where the Poynting vector has been introduced =. in the above relation for conservation of momentum, ∇ ⋅ σ {\displaystyle {\boldsymbol {\nabla }}\cdot {\boldsymbol {\sigma }}} is the momentum flux density and plays a role similar to S ...
Geyser, now 22 years old, filed her latest petition in October. Bohren decided to grant her release after a day-long hearing Thursday, finding that she had maximized her treatment options at the ...
For the special case of = , this gives a re-statement of conservation of energy or Poynting's theorem (since here we have assumed lossless materials, unlike above): The time-average rate of work done by the current (given by the real part of ) is equal to the time-average outward flux of power (the integral of the Poynting vector). By the same ...