Poyntings theorem in the time domain

Poynting s theorem can be derived based on the first two Maxwell s equations (8.1) and (8.2)  

Note that the dot product E has the dimensions of energy per unit volume per unit time. Scalar multiplying the first Maxwell s equation (8.87) by E, we find 

Subtracting ecpiation (8.89) from (8.90) and using the vector identity H-VxE-E VxH = V-(ExH), 

Expression (8.92) represents a differential form of Poynting s theorem. 

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Energy conservation follows from Maxwell s equations. The vector identity V (a X 6) = 6 (V X a) - a (V X 6) yields the Poynting theorem in the time domain ... 

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