# Maxwell stress tensor in different coordinate system

1. Sep 12, 2013

### dapias09

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?

2. Sep 13, 2013

### Andy Resnick

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.

3. Sep 13, 2013

### dapias09

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. Sep 15, 2013

### clem

It would hold in any orthogonal coordinate system, because there are no derivatives involved.

5. Sep 15, 2013

### dapias09

Ok, thank you clem.