Electromagnetism coupled with continuum mechanics

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HomogenousCow
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Are there any textbooks on something like this, a self consistent treatment of classical electromagnetism (relavistic is fine too) where the field equations are solved alongside with the matter fields.
 
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Yeah, it's the best to use Landau Lifgarbagez. One of the very best treatments of classical and quantum transport theory is vol. X (Kinetics). There is a lot about em. plasmas!