2.3 E-B Analogy
23
density. This is because the polarization charge always shields in such a way as to
weaken the internal electric field. The electric field that is produced by the true electric
charge is called the electric flux density and represented by D. The relationship
between D and E is given by
E =
1
0
(D − P).
(2.41)
Since P is proportional to E in most cases, there is a proportional relationship between
E and D, which is expressed as
D = E,
(2.42)
where is the dielectric constant.
Only magnetic materials are treated as substances that show magnetic behavior
in the usual electromagnetism. Conductors are non-magnetic materials and are basically the same as vacuum in terms of their magnetic behavior. The sources of the
magnetism are current and magnetic moment as mentioned above. The magnetic field
produced by the magnetic moment in magnetic material is called the magnetization
and is represented by M. In classic electromagnetism the magnetization is formally
described using the virtual magnetizing current, which can be treated in a similar
way to the current. The relationship to the magnetizing current density i m is given
by
∇ × M = i m .
(2.43)
The magnetic field produced only by the current is called the magnetic field and is
represented by H. Its relationship to the magnetic flux density B is
B = μ 0 (H + M).
(2.44)
Since M is proportional to B in most cases, there is a proportional relationship
between B and H, which is expressed as
H =
1
μ
B,
(2.45)
where μ is the magnetic permeability. The fact that the magnetizing current does
not shield most magnetic materials is a characteristic difference from the electrical
phenomena. Hence, the sign is different between (2.40) and (2.43).
As discussed above, there is a difference between electricity and magnetism with
respect to the component materials. That is, while conductors with electric charge and
dielectric materials with polarization charge are treated in electricity, only magnetic
materials with magnetizing current are treated in magnetism. It is proposed here to
23
density. This is because the polarization charge always shields in such a way as to
weaken the internal electric field. The electric field that is produced by the true electric
charge is called the electric flux density and represented by D. The relationship
between D and E is given by
E =
1
0
(D − P).
(2.41)
Since P is proportional to E in most cases, there is a proportional relationship between
E and D, which is expressed as
D = E,
(2.42)
where is the dielectric constant.
Only magnetic materials are treated as substances that show magnetic behavior
in the usual electromagnetism. Conductors are non-magnetic materials and are basically the same as vacuum in terms of their magnetic behavior. The sources of the
magnetism are current and magnetic moment as mentioned above. The magnetic field
produced by the magnetic moment in magnetic material is called the magnetization
and is represented by M. In classic electromagnetism the magnetization is formally
described using the virtual magnetizing current, which can be treated in a similar
way to the current. The relationship to the magnetizing current density i m is given
by
∇ × M = i m .
(2.43)
The magnetic field produced only by the current is called the magnetic field and is
represented by H. Its relationship to the magnetic flux density B is
B = μ 0 (H + M).
(2.44)
Since M is proportional to B in most cases, there is a proportional relationship
between B and H, which is expressed as
H =
1
μ
B,
(2.45)
where μ is the magnetic permeability. The fact that the magnetizing current does
not shield most magnetic materials is a characteristic difference from the electrical
phenomena. Hence, the sign is different between (2.40) and (2.43).
As discussed above, there is a difference between electricity and magnetism with
respect to the component materials. That is, while conductors with electric charge and
dielectric materials with polarization charge are treated in electricity, only magnetic
materials with magnetizing current are treated in magnetism. It is proposed here to