What is the physical meaning of the Maxwell Stress tensor symmetry?
Answer
No, it's not symmetric. Let me explain:
Say for instance that you only take the magnetic part of the Maxwell stress tensor (let's ignore the electric part). Then you would have the outer product BB + (diagonal tensor). A lot of textbooks usually write it as 1/μBB+ (diagonal tensor), which is wrong and misleading, since it assumes that the material has a linear behavior B=μ∗H.
The right expression is BH+ (diagonal tensor), where B=μ0(M+H) Therefore if M is not colinear with H you will get a non-symmetric tensor. However if M is colinear with H then you will get a symmetric one. This colinearity between M and H holds true when the magnetization can be described by a linear and isotropic relationship ... that is M=some_physical_constant * H.
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