Poynting vectors density

To see this, let us introduce some definitions first. The Poynting vector G represents energy flux density (units esu2cm-3 s-1 = ergcm2s 1). It is a capability of the electromagnetic field to perform work defined as... 

This equation simply states that variations of energy density at a given spacetime point are due to transport along the Poynting vector plus transport along electric field. Clearly, when J = 0 all transport is along g [62, Eq. 43, p. 10]. 

The refracted intensity is r = (1 - R), however, this is not just fl. Since this radiation component is now travelling in a different medium, the energy density has to be taken into account. From considering the Poynting vector it follows... 

The constant A can be expressed in terms of the power flux density namely the z component of the Poynting vector is... 

The flux density of an electromagnetic wave is described by the Poynting vector. For the case of the plane wave field one obtains for the time average in the direction of propagation... 

The time-varying Poynting vector, which represents the directional energy flux density of the electromagnetic field, is thus given by... 

The intensity, or power density, S has magnitude and direction determined by the time-averaged Poynting vector. Thus we deduce from Eq. (35-lb) that... 

This is the Poynting theorem S is the Poynting vector. The first two terms in Eq. (1.2.4) represent rate of change of the magnetic and electric energy densities... 

The Poynting vector has a dual role for it can be shown that the electromagnetic radiation fields transport momentum as well as energy, and tliat the momentum density is given by R/c. This relationship is most easily derived by making use of the idea tliat radiation consists of photons of energy hu whose momentum in vacuo is tioi/c, which follows from the quantum theory of radiation (Problem 2.7). 

It was shown in Section 2.8.3 that the energy transferred by an electromagnetic wave is proportional to the square of the wave amplitude E. Without proof, we state that the energy density carried by a wave is defined by the vector product [E B] = S vector S being referred to as the Poynting vector. 

Poynting s vector theorem can be derived from Maxwell s equations as a consequence of power conservation. It shows that the time-averaged power produced by a distribution of currents with density J within volume is given by[l]... 

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