Consider the integral of the inwardly directed normal component of the Poynting vector over a surface S bounding a volume V of a linear, isotropic, homogeneous, conducting medium. Show that this quantity can be identified with the sum of the rate of change of the electromagnetic energy and the power dissipated when there is a free current density J within V. You may assume that electric and magnetic energy densities are (1/2)E.D and (1/2)B.H respectively (aside: how might these definitions be justified?) Could you please show me how to prove this?
What you are being asked to prove here is energy conservation.
The Poynting vector gives the power density (power per unit area) of an electromagnetic wave and points in the direction for which this ...
This solution provides guidelines on how to show that the Poynting vector can be identified with the sum of the rate of change of electromagnetic energy and the power dissipated when there is free current density.