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      Grouping the first two, middle two, and last two terms of the right-hand side reformulates this relation as

      (2.61)

      which, using again , becomes

      (2.62)

      Finally, grouping the first two terms of the right-hand side of this relation yields

(2.63)

Similarly, the term in (2.57) becomes

(2.64)

Substituting now (2.63) and (2.64) into (2.57) finally yields the bianisotropic Poynting theorem:

(2.65)

      where is the energy density, is the Poynting vector, and and are the impressed source power densities, and and are the induced polarization power densities, respectively, which are defined by

      (2.66a)

      (2.66b)

      (2.66c)

(2.66d)

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