Maxwell stress tensor coordinate system

In summary, the Maxwell Stress Tensor is defined by Griffiths as T_{ij} = \epsilon_0 (E_i E_j - \tfrac{1}{2} \delta_{ij} E^2) + \frac{1}{\mu_0} (B_i B_j - \tfrac{1}{2} \delta_{ij} B^2) and can be used in various coordinate systems such as cylindrical and spherical coordinates. However, the derivatives may need to be adjusted accordingly.
  • #1
elsevers
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Hello,

I am trying to understand the Maxwell Stress Tensor. Specifically, I would like to know if it is coordinate-system dependent (and if so, what the expressions are for the stress tensor in cylindrical and spherical coordinates).

Griffiths gives the definition of the maxwell stress tensor in EQ8.19:
[tex]
T_{ij} = \epsilon_0 (E_i E_j - \tfrac{1}{2} \delta_{ij} E^2) + \frac{1}{\mu_0} (B_i B_j - \tfrac{1}{2} \delta_{ij} B^2)

[/tex]

where Griffiths says i and j can be x, y, z -- now can they also by r, z, phi or r, theta, phi? (or do we require a new definition for the stress tensor to handle cylindrical and spherical coordinates?)

Any comments would be really appreciated! Thanks!
Eric
 
Last edited:
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  • #2
It would work in other orthogonal systems.
Derivatives get changed in the other systems.
 

1. What is the Maxwell stress tensor coordinate system?

The Maxwell stress tensor coordinate system is a mathematical framework used in electromagnetism to describe the distribution of stress and forces within a given region of space. It is a tensor field that contains information about the electromagnetic forces acting on a charged particle or conductor.

2. How is the Maxwell stress tensor coordinate system calculated?

The Maxwell stress tensor is calculated using the electromagnetic field equations, which describe the relationship between electric and magnetic fields and their sources. The tensor is derived from the electromagnetic stress-energy tensor, which contains information about the energy and momentum of the electromagnetic field.

3. What are the main applications of the Maxwell stress tensor coordinate system?

The Maxwell stress tensor coordinate system is used in a variety of applications, including the study of electromagnetic fields in devices such as antennas and electrical circuits. It is also used in the analysis of electromagnetic interactions in materials and the design of electromagnetic devices.

4. How does the Maxwell stress tensor coordinate system relate to other coordinate systems?

The Maxwell stress tensor coordinate system is a tensor field that is independent of any specific coordinate system. However, it can be expressed in terms of different coordinate systems, such as Cartesian or cylindrical coordinates, depending on the specific application or problem being studied.

5. What is the physical significance of the Maxwell stress tensor coordinate system?

The Maxwell stress tensor coordinate system is significant because it provides a mathematical description of the forces and stresses in electromagnetic fields. This allows scientists and engineers to analyze and design complex electromagnetic systems and devices with greater precision and efficiency.

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