Four Poynting Theorems

Abstract

The Poynting vector is an invaluable tool for analysing electromagnetic problems. However, even a rigorous stress-energy tensor approach can still leave us with the question: is it best defined as $\Vec{E} \cross \Vec{H}$ or as $\Vec{D} \cross \Vec{B}$? Typical electromagnetic treatments provide yet another perspective: they regard $\Vec{E} \cross \Vec{B}$ as the appropriate definition, because $\Vec{E}$ and $\Vec{B}$ are taken to be the fundamental electromagnetic fields. The astute reader will even notice the fourth possible combination of fields: i.e. $\Vec{D} \cross \Vec{H}$. Faced with this diverse selection, we have decided to treat each possible flux vector on its merits, deriving its associated energy continuity equation but applying minimal restrictions to the allowed host media. We then discuss each form, and how it represents the response of the medium. Finally, we derive a propagation equation for each flux vector using a directional fields approach; a useful result which enables further interpretation of each flux and its interaction with the medium.

8 pages. Updated slightly from EJP version

References in corpus (4)

• Correct Definition of the Poynting Vector in Electrically and Magnetically Polarizable Medium Reveals that Negative Refraction is Impossible
• Theory of directional pulse propagation
• Limits of the uni-directional pulse propagation approximation
• Comment on "Casimir Force Acting on Magnetostatic Bodies Embedded in Media"

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