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Index notation for vector id's

  1. Feb 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Prove vector identity [tex]\nabla[/tex] x[tex]\nabla\phi[/tex] = 0 using index notation.

    2. Relevant equations

    [tex]\nabla[/tex] x A = Ejrt[tex]\partial[/tex]rAt

    3. The attempt at a solution
    I'm treating this as [tex]\nabla[/tex]x A, where A = del [tex]\Phi[/tex] = Etpq[tex]\partial[/tex]p[tex]\Phi[/tex]q

    putting A back in the equation:

    = EjrtEtpq[tex]\partial[/tex]r[tex]\partial[/tex]p[tex]\Phi[/tex]q

    =EtrjEtpq[tex]\partial[/tex]r[tex]\partial[/tex]p[tex]\Phi[/tex]q

    =([tex]\partial[/tex]jp[tex]\partial[/tex]rq - [tex]\partial[/tex]jq[tex]\partial[/tex]rp)[tex]\partial[/tex]r[tex]\partial[/tex]p[tex]\Phi[/tex]q

    It's here that I'm stuck. I know it should be simple after this, and somehow I need to get zero, but I'm completely stuck. Maybe I messed up somewhere?
     
  2. jcsd
  3. Feb 18, 2009 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi flame_m13! :smile:

    (have a del: ∇ and a curly d: ∂ :wink:)
    Nooo … (∇φ)p = ∂pφ :wink:
     
  4. Feb 18, 2009 #3
    thanks. i have skill at making things unnecessarily complicated. :)
     
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