A.1 Field Quantities and Constitutive Parameters

The basic electromagnetic field quantities in the meter-kilogram-second (MKS) system are

= electric field intensity, V/m

= electric flux density, or displacement vector, C/m ²

= magnetic field intensity, A/m

= magnetic flux density, Wb/m ² or T

= volume current density, A/m ²

All of these quantities can be a function of time and space. For instance, in the Cartesian coordinate system, ( x , y, z, t ).

The constitutive parameters relate the intensities to the densities:

where ? = ? ₀ ? _r is the permittivity and = _{0 r} the permeability of the medium. The quantities with the subscript r are relative values with respect to the values of free space. Another important property of a medium is its conductivity. A general form of Ohm s law is = ? . All the constitutive parameters can be complex quantities.

A.2 Maxwell s Equations

Maxwell s equations, along with the boundary conditions, completely describe the behavior of electromagnetic fields in a region of space. The four equations in differential and integral forms are as follows.

1. Faraday s law:

   
   

2. Ampere s circuital law:

   
   

3. Gauss s law:

   
   

4. No isolated magnetic charge:

   
   

In the preceding formulas, V represents a volume of the medium enclosed by a surface S, and ? _v is the volume charge density in Coulombs per cubic meter. The differential line, surface, and volume...