In deriving the electromagnetic coupled field equations we make the assumption that within the medium the divergence of the electric stress field is zero (), i.e. that there are no ``batteries'' buried in the medium. Making this assumption is equivalent to setting the forcing term in Equation 5 to zero. We note that the magnetic fields and magnetic induction are related by the magnetic permeability (). Since there is no magnetic monopole, divergence of the magnetic field is also zero (div B=0). If we allow electric current to flow, the current density is related to the electric stress field by the conductivity as follows:
(9) |
We can use Maxwell's equation to describe the relation ship between electric and magnetic fields:
(10) | ||
(11) |
The linear law relating electric stress components to components of elastic strain, electric and thermal displacements is now
(12) |
Consequently, in terms of electric displacements, we end up with the coupled electromagnetic field equations
(13) |