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Existence of Vector Potential

  1. Apr 4, 2014 #1
    1. The problem statement, all variables and given/known data
    Given that the divergence of a vector C = 0, show that there exists a vector A such that C = curl A.

    2. Relevant equations
    See above.

    3. The attempt at a solution
    No clue. Can this be proved with introductory vector calculus? That's all I know, including many of the vector-calculus identities. I don't know anything about differential topology, Poincare's Lemma, etc.

    I assume that somehow A has to be constructed, but that's as far as I get.

    Thank you.
  2. jcsd
  3. Apr 4, 2014 #2
    What is .(xA)?
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