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NEOCLASSICAL THEORY OF INTERACTION 57

magnetic field, the orbital and spin magnetic moments of myriads of electrons or group of such
electrons are typically randomly distributed and randomly oriented within matter, as shown in
2.2.7b. As a result, the average magnetic field in the material in the macroscopic sense is zero.
The exception is some ferromagnetic materials, like iron, which can produce continuous
magnetic fields. Note that the North Pole (N in short) of a magnet is that pole which is attracted
to the geographic North Pole. Therefore, the North Pole of a magnet will repel the north seeking
pole of a magnetic compass shown in Figure 2.2.7d.
The magnetic polarization phenomenon is more complicated than an electric one and its
description almost entirely based on quantum effects. Fortunately, a working understanding of
the magnetic behavior of materials can be acquired using the idea of magnetic moments. The
magnetic dipole model as a tiny bar magnet is shown in Figure 2.2.7d or small carrying-current
loops presented in Figure 2.2.7a. It is the simplest model but still gives an excellent description
of many magnetic effects depending on the dynamics of the movement of electrons. As it has
been demonstrated in Section 2.1.2 of this chapter, the external magnetic field B exerts the
torque or rotating force on existing magnetic moments coercing them to align in parallel to the
applied magnetic field as Figure 2.2.7e demonstrates. If so, we can repeat word for word our
discussion in section 2.2.2 just replacing the term of the electric dipole by a magnetic dipole.
Omitting the details let us write down the final equations for isotropic magnetic medium

= +
0
= � (2.22)
0
=
0
Here M is the vector of magnetic polarization defined as a limit
2
= lim ∑ ∆ Δ [ ∙ m ] (2.23)
⁄

Δ→0
is the dimensionless and in most cases positive parameter called the magnetic susceptibility,

= 1 + is the dimensionless parameter called the relative magnetic constant of material.

But there are some differences in magnitudes and coefficients. Except the case of diamagnetic
material, the additional field induced by the magnetic moments aggravates (see Figure 2.2.7e)
the external magnetic field. Therefore, the total internal inductance field in material is
= + = + (2.24)
0 0
Then the vector of magnetic polarization defined by the external magnetic force is
= (2.25)
0

and the intensified internal field is
= (1 + ) (2.26)

0
As well, we can define the vector of magnetic field strength in material like (2.14)
= = ⁄⁄ 0 0 (2.27)
0
that depends on the applied external fields and entirely independent of the magnetic polarization
effect. That illustrates the apparent similarity between the vectors H and D (both is independent
of material constants) by the same way as between the vectors B and E (both define EM forces
and depends on intrinsic material magnetic and electric moments, respectively).