Define the Poynting vector. Starting from Maxwell's equations, derive the Poynting theorem and explain its physical interpretation in terms of energy conservation in electromagnetic fields.
The Poynting vector is a fundamental concept in classical electrodynamics that represents the directional energy flux, or power per unit area, of an electromagnetic field. It is denoted by S and mathematically defined as S = E × H, where E is the electric field vector and H is the magnetic field vector. The Poynting vector points in the direction in which electromagnetic energy is flowing and its magnitude gives the rate at which energy passes through a unit area perpendicular to that direction. To derive the Poynting theorem, _______ ________ ___ __________ _____ ___ __________ ______ _________ ________ __________ __________.
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