in an analogous fashion to relative permittivity. When both magnetic and electric properties vary, relative permittiv-ity is usually expressed as Ke to avoid confusion.

The presence of a magnetic field induces the individual dipole moment to change orientation and line up with the applied field. In some materials the alignment is in the same direction as the applied field, whereas in other materials the alignment maybe anti-parallel to the applied field. These two types of behavior referred to as paramagnetism and diamagnetism. Generally these responses are very weak and give rise to small variations in magnetic permeability. Typical values of magnetic susceptibility are less than 10-5.

In some situations, however, the magnetic moments can be aligned in large sections (called domains) of the crystal structure of a material. The moment ofdomains can be changed by the molecules in the crystal structure behaving in a sympathetic fashion and moving from one domain to another. Such materials are known as ferromagnetic materi-als.

In ferromagnetic materials, the polarization can be quite large and high values of Kmin the range of tens or even hun-dreds may be observed in materials such as iron, cobalt, and nickel. With ferromagnetic materials, the behavior is more complex in that the dipole moments when moved, or aligned, remain aligned. This is known as permanent magnetization. In such materials the permeability is very high and the dynamic behavior of the material complex. Such materials seldom form a large volume fraction of soilsand rocks but their presence in small amounts can be the dominant factor determining bulk permeability.

Behavior can be very complex. The behavior of dipolemoment density is controlled by how domains move, grow and change orientation which can be field dependent, frequency dependent and temperature dependent. The subjects are well beyond the scope of these notes.