Maxwell stress tensor in different coordinate system

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Discussion Overview

The discussion revolves around the applicability of the Maxwell stress-energy tensor in different coordinate systems, specifically whether its expression is valid in Cartesian coordinates or can be generalized to any orthogonal coordinate system. The inquiry includes both theoretical aspects and potential implications for various coordinate representations.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the correctness of an answer from a previous thread regarding the Maxwell stress tensor's expression in different coordinate systems.
  • Another participant states that the Maxwell stress-energy tensor can be expressed in a coordinate-free form, suggesting it is applicable in any coordinate system.
  • A participant seeks clarification on whether a specific expression for the tensor can be used with indices from various coordinate systems, including both Cartesian and spherical coordinates.
  • It is proposed that the expression for the tensor holds in any orthogonal coordinate system, as it does not involve derivatives.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the Maxwell stress tensor's expression across coordinate systems. While some suggest it is universally applicable, others seek clarification on specific cases, indicating that the discussion remains unresolved.

Contextual Notes

The discussion does not resolve the assumptions regarding the validity of the tensor's expression in non-Cartesian systems, nor does it clarify the implications of using different coordinate systems.

dapias09
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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
 
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The Maxwell stress-energy tensor can be written in a co-ordinate free form:

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

So any coordinate system may be used.
 
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
 
It would hold in any orthogonal coordinate system, because there are no derivatives involved.
 
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Ok, thank you clem.
 

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