Is the Maxwell stress tensor a true stress?

  • #1
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Should it be added to the Cauchy stress to calculate a "total stress", or it doesn't have such a physical interpretation as a surface force(EM field force is usually considered more of a "body force")?
Certainly when the MST was first derived before aether theories were made superfluous by Einstein, it might make sense to think of the MST as a physical true stress, I think now it is rather considered a mathematical device to ease calculations of EM forces at a point.
There seems to be situations in wich the magnetization of the material is not strictly linear(i. e. ferrofluids) and demand the use of an non-symmetric MST where it leads to incorrect results.
Maybe this is an issue more related with the different view of engineers and field theoretic physicists on EM problems(fluid and solid mechanics versus classical EM field in vacuum).
 

Answers and Replies

  • #2
Jano L.
Gold Member
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Your question is hard to answer. It seems too general to me - could you could formulate definite situation (liquid, solid?) and what is your definition of "total stress" ?

Feynman's remark from his lectures (vol. II, sec. 10-5):

Feynman said:
What does happen in a solid? This is a very difficult problem which has not
been solved, because it is, in a sense, indeterminate. If you put charges inside a
dielectric solid, there are many kinds of pressures and strains. You cannot deal
with virtual work without including also the mechanical energy required to com-
press the solid, and it is a difficult matter, generally speaking, to make a unique
distinction between the electrical forces and the mechanical forces due to the solid
material itself
. Fortunately, no one ever really needs to know the answer to the
question proposed. He may sometimes want to know how much strain there is
going to be in a solid, and that can be worked out. But it is much more complicated
than the simple result we got for liquids.
 
  • #3
Andy Resnick
Science Advisor
Education Advisor
Insights Author
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Should it be added to the Cauchy stress to calculate a "total stress", or it doesn't have such a physical interpretation as a surface force(EM field force is usually considered more of a "body force")? <snip>
Electromechanical systems (piezoelectricity, acousto-optics, magnetohydrodynamics, etc.) incorporate both electromagnetic and "mechanical" stress terms.
 

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