Sign of Maxwell's stress tensor

[sweet springs]

Why Maxwell's stress tensor has minus sign to the corresponding components of electromagnetic momentum energy tensor ?

From WP ---

,

where

,
is the Poynting vector,

is the Maxwell stress tensor, and c is the speed of light.
----

 

[ShayanJ]

You can find a derivation here.

 

[sweet springs]

Thanks. From there

$$-\mathbf{f} = \epsilon_0 \mu_0 \frac{\partial \mathbf{S}}{\partial t}\, + \nabla \cdot \mathbf{(-\sigma)}$$

where f is the force per unit volume of material, so -f should be the force per unit volume of e.m. field.

Rather than $\mathbf{T^{ij}}=\mathbf{-\sigma}^{ij}$, $\mathbf{\sigma^{ij}}$ first, I prefer T first, defined from T,
$\mathbf{\sigma^{ij}} =\mathbf{-T^{ij}}$.

 

[sweet springs]

I found Laudau Lifshitz call -$\sigma^{ij}$ Maxwell's stress tensor in (33.3) at
https://archive.org/stream/TheClassicalTheoryOfFields/LandauLifshitz-TheClassicalTheoryOfFields#page/n93/mode/2up

 

[stedwards]

,

On which wikipedia page did you find this?

 

[sweet springs]

I referred to https://en.wikipedia.org/wiki/Electromagnetic_stress–energy_tensor. Thanks.