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Homework Help: Calculus - vector potentials

  1. Feb 18, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    Please take a look at:


    What do they mean by that hint?

    3. The attempt at a solution
    First I want to find the divergence of the three vectors.

    Second, for the vectors which have a divergence equal to zero, I want to find the vector A so the rotation of A = B. But this is the part I am in doubt about - can you help?

    Sincerely, Niles.
  2. jcsd
  3. Feb 18, 2008 #2

    Tom Mattson

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    Staff Emeritus
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    Gold Member

    For static fields, the vector potential [itex]\vec{A}[/itex] is parallel to the current density [itex]\vec{J}[/itex]. And, Ampere's law says that [itex]\vec{\nabla}\times\vec{B}[/itex] is parallel to the current density as well, under the same condition. Since the vector potential and the curl of the magnetic field are both parallel to the same vector, they are parallel to each other.

    Here's a hint: If [itex]\vec{A}[/itex] is parallel to [itex]\vec{\nabla}\times\vec{B}[/itex], then [itex]\vec{A}=k\vec{\nabla}\times\vec{B}[/itex] for some [itex]k[/itex].
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