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Grad(div(V)) = 0 ?

  1. Nov 23, 2015 #1
    This is closely related to this thread I posted yesterday, but the question is different so I created another thread. There is a vector identity often used when deriving EM waves equation :

    d0e4740eaf9a820b14f267ae70cf9bca.png

    Then the grad(div(V)) part of it is simply dropped, assuming it equals 0. And I wonder why.

    Is it because, since there is no "sources" here (no charges), any divergence is 0 ? Can this be proven more formally ?
     
  2. jcsd
  3. Nov 23, 2015 #2

    Samy_A

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    Isn't it because the identity is used for ##V=E## and ##V=H##, and according to Maxwell's equations (see your Wikipedia link):
    ##\nabla.{E}=0##
    ##\nabla.{H}=0##
    ?
     
  4. Nov 23, 2015 #3

    haushofer

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    Yes, that's the reason.
     
  5. Nov 23, 2015 #4
    Oh ! Of course ! Thank you. Well, I formulated that divergence without charges/sources is 0, that is indeed Gauss's law from Maxwell's in vacuum...There is the obvious formalism I was looking for, I should have seen it. -_-'
     
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