Maxwell stress tensor in different coordinate system

  • #1
Hi guys,

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

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
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
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
It would hold in any orthogonal coordinate system, because there are no derivatives involved.
  • Like
Likes 1 person
  • #5
Ok, thank you clem.

Suggested for: Maxwell stress tensor in different coordinate system