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We are concerned in this section with establishing the basic material upon which the subsequent sections of the chapter depend. Thus we must establish the Maxwell field equations and the wave potentials in the unitary system to be utilized (mks)follow this with solutions of the wave equation pertinent to some of the later development. This abbreviated summary of electromagnetic fundamentals then permits us to follow the subsequent presentations of specific problems in electromagnetic theory; the problems chosen are essential to our comprehension of the electrical methods.


Electrical conductivity is the movement of electrical charge from one location to another. Because the charge may be carried by ions or electrons, whose mobilities vary from material to material, there is a full spectrum of conductivities ranging from highly conducting metals to nearly perfect insulators, as illustrated in Figure 1

Electrical conductivity can be derived from the relation where n is the number of charge carriers in a material, e is the charge carried by eachu is the mobility of the carriers. The mobility is defined as the drift velocity per unit electric field. Since the charge carriers may be ions or electrons (or “holes” as we shall see later), we classify conduction in solids as ioncc or electroncc within the range 1 to 10s mho/m. Below this range of conductivity, materials may be semiconductors or insulators. For porous media, such as rocks at the earth’s surface, conductors extend into the range normally covered by solid semiconductors.

Ionic conductivity involves the ordered movement of ions in an electrolyte upon application of an external electric field. In the absence of an electric field, the ions move randomly as a result of thermal agitation and collisions with other ions and atoms. Since both cations and anions are present in an electrolyte, the conductivity can be expressed as where the numbers and mobilities of the positive and negative ions are indicated by superscript signs. A temperature increase results in a conductivity increase since the mobility of both ion species is

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