Sign of Maxwell's stress tensor

In summary, Maxwell's stress tensor has a minus sign because it represents the force per unit volume of the electromagnetic field, which is opposite in direction to the force per unit volume of material. This is derived from the Poynting vector and the Maxwell stress tensor, and is further explained in Laudau Lifshitz's work. The notation -σij is also used to represent Maxwell's stress tensor on Wikipedia.
  • #1
sweet springs
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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
,

where
imgtex.png
,
is the Poynting vector,
imgtex.png

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

Related to Sign of Maxwell's stress tensor

1. What is the Sign of Maxwell's stress tensor?

The sign of Maxwell's stress tensor is a mathematical quantity used in the study of electromagnetism. It describes the distribution of forces and stresses within an electromagnetic field.

2. How is the sign of Maxwell's stress tensor determined?

The sign of Maxwell's stress tensor is determined by calculating the stresses and forces acting on a unit area within an electromagnetic field. This calculation takes into account the electric and magnetic fields, as well as the permittivity and permeability of the medium.

3. Why is the sign of Maxwell's stress tensor important?

The sign of Maxwell's stress tensor is important because it helps us understand the behavior of electromagnetic fields and how they interact with matter. It is also used in the development of theories and models for electromagnetism.

4. What does a positive sign of Maxwell's stress tensor indicate?

A positive sign of Maxwell's stress tensor indicates that the electromagnetic field is exerting a force in the direction of increasing energy density. This can result in the compression or expansion of the medium in which the field is present.

5. How does the sign of Maxwell's stress tensor relate to the direction of electromagnetic waves?

The sign of Maxwell's stress tensor is related to the direction of electromagnetic waves through the Poynting vector, which describes the direction and magnitude of energy flow in an electromagnetic field. A positive sign of the stress tensor indicates that the Poynting vector is pointing in the same direction as the wave propagation, while a negative sign indicates the opposite.

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