Four Poynting Theorems
P. Kinsler, A. Favaro, M.W. McCall
Blackett Laboratory,
Imperial College London,
Prince Consort Road,
London SW7 2AZ,
United Kingdom.
Eur. J. Phys. 30, 983, (2009).
http://www.iop.org/EJ/abstract/0143-0807/30/5/007/
doi: 10.1088/0143-0807/30/5/007
http://arxiv.org/abs/0908.1721
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.
(Alt Keywords: Poynting Theorum, Poynting flux)