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I Correct relation is F^{ij} = - epsilon^{ijk} B^k.

  1. May 6, 2017 #1
    When I tried to derive this relation I got the wrong sign. Please check the pic and tell me my mistakes.
     

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  2. jcsd
  3. May 7, 2017 #2

    haushofer

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    What is correct probably depends on your conventions, which you don't give.
     
  4. May 7, 2017 #3

    vanhees71

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    If you use the west-coast convention you have ##\partial^l=-\partial_l##, and thus
    $$B^i=-\epsilon_{ijk} \partial_j A^k.$$
    Note that
    $$\partial_j=\frac{\partial}{\partial x^j}.$$
     
  5. May 8, 2017 #4
    Thank you for your response. I am using metric [tex] diag(1,-1) [/tex] and the expression you gave [tex] B^i = - \epsilon_{ijk} \partial_j A^k [/tex] contains also [tex] A^i = - A_i [/tex], so I think it does not make any difference. Could you do it for me in complete and explicit steps?
     
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