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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.
Electromagnetism and continuum mechanics are two branches of physics that are closely related. Electromagnetism deals with the study of electric and magnetic fields, while continuum mechanics deals with the behavior of materials under stress and strain. The relationship between the two lies in the fact that electric and magnetic fields can cause stresses and strains in materials, and vice versa.
In continuum mechanics, electric and magnetic fields can exert forces on materials, causing them to deform or change their properties. This interaction is described by Maxwell's equations in electromagnetism and the equations of motion in continuum mechanics.
One practical application of this coupling is in the design and analysis of electronic devices, such as transistors, that utilize the properties of materials under the influence of electric and magnetic fields. Another application is in the study of geophysical processes, where electromagnetism can be used to probe the properties of materials deep within the Earth's crust.
In order to study the coupling between electromagnetism and continuum mechanics, mathematical models are used. These models involve the use of partial differential equations, such as Maxwell's equations and the equations of motion, to describe the behavior of electric and magnetic fields and materials under stress and strain.
Some current research areas in this field include the development of new materials with specific electromagnetic properties, such as those used in metamaterials and photonic crystals. Another area of research is the study of the effects of electromagnetic fields on biological systems, such as in the field of bioelectromagnetics.