Maxwell stress tensor in different coordinate system

  • Thread starter dapias09
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  • #1
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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
 

Answers and Replies

  • #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.
 
  • #3
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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
 
  • #4
Meir Achuz
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It would hold in any orthogonal coordinate system, because there are no derivatives involved.
 
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  • #5
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Ok, thank you clem.
 

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