Page 78 - Maxwell House

58 Chapter 2

Finally, notice that for magnetic materials are quite natural to be anisotropic, and their magnetic
constant can be described by the tensor similar to (2.19). Besides, the magnetic moment much
easier than electric moment reaches the saturation that provokes nonlinearity effect like
hysteresis, for example. More information about magnetic polarization effects will be discussed
late.

2.2.6 Phenomena of Electric Conductance

In the previous discussions, we implicitly suggested that all electrons in materials are mutually
coupled and cannot migrate freely. That is not quite right because even in best insulators not
speaking about metals or semiconductors the free or valence electrons form an electron “cloud”
or gas around the peripheries of the material atoms and are free to move. They move chaotically,
and their average velocity through the material is equal or close to zero. In other words, the
average macroscopic current defined by random electron movements is typically negligible.
The situation changes entirely in the presence of external electrical fields. While the electrons
continue their random
movement, they under
exertion of Coulomb’s force
acquire a drift
velocity proportional to

the electric field strength.
Since electrons are
negatively charged they
move in the direction to
positive charge, i.e. the drift
velocity is opposite to
electric field direction as
shown in Figure 2.2.8. Then
Figure 2.2.8 Drift velocity and current direction in the
conductive material the volume density of

such electric current is
according to (1.6) proportional to charge drift velocity and can be written in equivalent forms

= − = (2.28)

taking part in drift, and the minus is required because electrons carry negative charge while the
current was defined as a flux of positive charges.

Here the factor is called the material volume conductivity and measured in
−1
−1
−2
[(A ∙ m ) (V ∙ m ) = R −1 ∙ m −1 = S ∙ m ], is the mean volume density of charges. In
⁄

solid materials, the electrical conductivity is determined mainly by the response of electrons to
external electric fields. The electrical conductivity among some other parameters depends on
cloud electron concentration, electron charge e, and mass . We will consider the nature of

conductivity at length later in this chapter.
The magnitude of conductivity can vary quite widely, from the infinity for superconductors
7
−1
−1
and 6.3 ∙ 10 [S ∙ m ] for such good conductors as silver to 10 −25 [S ∙ m ] for good electrical
insulators such as Teflon. In analogy with (2.19) we can define the mediums with anisotropic
conductivity as