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Sign of Maxwell's stress tensor

  1. Jul 4, 2015 #1
    Why Maxwell's stress tensor has minus sign to the corresponding components of electromagnetic momentum energy tensor ?

    From WP ---
    Bzx%7D%20&%20-%5Csigma_%5Ctext%7Bzy%7D%20&%20-%5Csigma_%5Ctext%7Bzz%7D%20%5Cend%7Bbmatrix%7D$%7D.png ,

    imgtex.png ,
    is the Poynting vector,
    is the Maxwell stress tensor, and c is the speed of light.
  2. jcsd
  3. Jul 4, 2015 #2


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    Gold Member

    You can find a derivation here.
  4. Jul 5, 2015 #3
    Thanks. From there

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

    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 [itex]\mathbf{T^{ij}}=\mathbf{-\sigma}^{ij}[/itex], [itex]\mathbf{\sigma^{ij}}[/itex] first, I prefer T first, defined from T,
    [itex]\mathbf{\sigma^{ij}} =\mathbf{-T^{ij}} [/itex].
  5. Jul 6, 2015 #4
  6. Jul 8, 2015 #5
    Bzx%7D%20&%20-%5Csigma_%5Ctext%7Bzy%7D%20&%20-%5Csigma_%5Ctext%7Bzz%7D%20%5Cend%7Bbmatrix%7D$%7D.png ,

    On which wikipedia page did you find this?
  7. Jul 9, 2015 #6
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