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Kroneker delta

  1. May 14, 2016 #1
    1. The problem statement, all variables and given/known data
    I need to prove B.(Gradient . B) - B X(Gradient X B)=Del{i} [B{i}B{j} -1/2 (kroneker delta {ij} B^2]

    where I have used . as the dot product, {} as subscript. Thank you!

    2. Relevant equations

    3. The attempt at a solution

    I have attempted the solution but am not sure how it is possible to keep a kroneker delta on the right hand side.
    Last edited by a moderator: May 14, 2016
  2. jcsd
  3. May 14, 2016 #2

    Charles Link

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    I can not read your complete statement above, but this looks like it comes from a standard vector identity: (where ## A ## and ## B ## are both equal to ## B ##).
    ## \nabla (A \cdot B)=(A \cdot \nabla) B +(B \cdot \nabla) A+A \times \nabla \times B+B \times \nabla \times A ##
  4. May 14, 2016 #3
    I have uploaded the page from Jackson it is equation (6.119) I am trying to prove, however I must use Levi Cevita notation.

    Attached Files:

  5. May 14, 2016 #4

    Charles Link

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    On the left side of the equation in your OP, they are only taking one component. You may be able to use the identity I presented to simplify the ## B \times \nabla \times B ## term.
  6. May 14, 2016 #5


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