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Coupled PDEs - all 4 Maxwell's equations?

  1. Feb 23, 2016 #1
    Greetings all,

    Quick question. I know that all 4 Maxwell's equations are said to be first-order, coupled PDEs, where each equation has an unknown field. I see that with Faraday's and Ampere's law, because, E and H appear in each of those equations.

    But Gauss' laws, I'm not seeing that, since they're both equal to electric/magnetic charge densities (or 0 in the case of the magnetic law due to there not being magnetic monopoles).

    So, are Gauss' laws coupled? And do they still have the unknown fields? Sorry I am not seeing this. I just need a quick "reality check" here.

  2. jcsd
  3. Feb 28, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
  4. Feb 28, 2016 #3
    Yes, all 4 Maxwell's equations are coupled. This may be hard to see since they are usually written with notation using 4 different fields, E, B, D and H, plus the current density J. The coupling become more apparent when considering the constituent equations:
    1) D = epsilon * E
    2) B = mu * H
    3) J = sigma * E

    Then all 4 Maxwell's equations can be written in terms of E, H, and the charge density, rho.
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