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Maxwell stress tensor in different coordinate system

  1. Sep 12, 2013 #1
    Hi guys,

    I would like to know if the answer given to this thread is correct

    https://www.physicsforums.com/showthread.php?t=457405

    I got the same doubt, is the expression for the tensor given in cartesian coordinates or is it general to any orthogonal coordinate system?

    Thanks in advance
     
  2. jcsd
  3. Sep 13, 2013 #2

    Andy Resnick

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    The Maxwell stress-energy tensor can be written in a co-ordinate free form:

    4πT[itex]^{ij}[/itex] = F[itex]^{ik}[/itex]F[itex]^{j}_{k}[/itex]-1/4 η[itex]^{ij}[/itex]F[itex]_{ab}[/itex]F[itex]^{ab}[/itex]

    So any coordinate system may be used.
     
  4. Sep 13, 2013 #3
    Hi Andy, thanks for your answer.

    Well, my punctual question is, can I type

    $$ T_{ij} = (E_iE_j - \frac{1}{2}\delta_{ij}E^2) + (B_iB_j - \frac{1}{2}\delta_{ij}B^2)$$

    with the dummy indices equal to $x$, $y$, $z$ as well as $r$, $\theta$, $\phi$ , or the indices of any other coordinate system.

    I don't know if the expression given is valid only for cartesian coordinates
     
  5. Sep 15, 2013 #4

    clem

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    It would hold in any orthogonal coordinate system, because there are no derivatives involved.
     
  6. Sep 15, 2013 #5
    Ok, thank you clem.
     
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