Maxwell stress tensor coordinate system

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SUMMARY

The Maxwell Stress Tensor is coordinate-system dependent, as confirmed by the discussion. The expression provided by Griffiths in EQ8.19 applies to Cartesian coordinates (x, y, z) but can be adapted for cylindrical (r, z, φ) and spherical (r, θ, φ) coordinates. However, the derivatives must be adjusted accordingly in these alternative systems. Therefore, a new definition is necessary to accurately express the stress tensor in non-Cartesian coordinates.

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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:
<br /> 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)<br /> <br />

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
 
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It would work in other orthogonal systems.
Derivatives get changed in the other systems.
 
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