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) |

1/13/1998