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Poynting's Theorem in Forms

  1. Apr 17, 2010 #1
    In this PDF file, through some guess work, I propose a p-form equivalent of Poynting's Theorem and derive his expression in the tensor calculus--oops, I mean, vector calc. It happened to work.

    https://dl.dropbox.com/u/6215524/Post%20of%20Notes%20on%20Poyntings%20Theorem.pdf" [Broken]

    Pointing's equation of energy continuity appears as the temporal component of a 1-form.

    G*dG + F*dF = FK–GJ, ​

    F is the Faraday tensor with lower indices, and G=*F, the Hodge dual of F. J and K are the covariant charge/current density 4-vector duals; electric and magentic. Though derived in pseudo Riemann normal coordinates, it is true under general coordinate transforms.

    In afterthought I think the p-form equations as well as Poynting's Theorem are at root physically meaningless, via the hidden invocation of magnetic and electric currents in propagating electromagnetic fields.

    Comments welcome.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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