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Basic vector calculus

  1. Jan 6, 2008 #1
    I'm having a hard time proving that if [tex]A=k \frac{m\times r}{(r\cdot r)^{3/2}}[/tex] (the vectorpotential of a magnetic dipole with moment [tex]m[/tex]), then:

    [tex]B=\nabla\times A=k\frac{3e_r(e_r\cdot m) -m}{(r\cdot r)^{3/2}}[/tex]

    without writing the whole thing in components, which becomes long, messy and ugly.
    What's the elegant way of proving the magnetic induction [tex]B[/tex] in vectorial form from the vector potential [tex]A[/tex]?
     
  2. jcsd
  3. Jan 7, 2008 #2
    I've attached a page from my vector notes. There you see the basic equations to treat these kind of problems. There first part I found in a book which one can check by components.

    In the second part I derived some particular results from the general equations. Feel free to check them, as I haven't done that yet.

    There you also find your case.
     

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