# Sign of Maxwell's stress tensor

1. Jul 4, 2015

### 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.
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2. Jul 4, 2015

### ShayanJ

You can find a derivation here.

3. Jul 5, 2015

### 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,
$\mathbf{\sigma^{ij}} =\mathbf{-T^{ij}}$.

4. Jul 6, 2015

5. Jul 8, 2015

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