Conservation of energy and the Poynting vector

The Poynting theorem expresses the conservation of energy in electromagnetism. If one takes the scalar product of Eq. (1.1.1) with E and of Eq. (1.1.2) with H, and adds the results one finds 

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 

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