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Einstein-Notation: rot(rot(A))

  1. Feb 20, 2013 #1
    1. The problem statement, all variables and given/known data
    Write [tex]\nabla \times (\nabla \times \vec A)[/tex] in Einstein-Notation, whereas [tex]\vec A[/tex] is the vector potential of the magnetic field.



    2. Relevant equations
    [tex](\vec a \times \vec b)=\varepsilon_{ijk} a_j b_k[/tex]




    3. The attempt at a solution
    [tex]\nabla \times (\nabla \times \vec A)=\varepsilon_{ijk} \partial_j(\varepsilon_{lmn}\partial_m A_n)_k[/tex]

    What to do with [tex](\varepsilon_{lmn}\partial_m A_n)_k[/tex] though?

    Thank you for your help!
     
  2. jcsd
  3. Feb 20, 2013 #2

    CompuChip

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    Science Advisor
    Homework Helper

    On the right hand side, there is summation over j and k, but i is a free index which only occurs once. What you really meant to write, then, is

    [tex](\vec a \times \vec b)_i=\varepsilon_{ijk} a_j b_k[/tex]
     
  4. Feb 21, 2013 #3
    In index notation it reads
    εijkjklmlum)
    after it you can use an identity
    εkijεklmilδjmimδjl
    (I hope this is not complete solution.if it is then delete this)
     
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