Chapter 2
Basic Electromagnetism
Abstract In this chapter we summarize the essential principles associated with electrostatic and magnetic phenomena caused by electric charges and currents, respectively, based on the E-B analogy. These are necessary to understand the usefulness of
introducing superconductivity into electromagnetism, which will be done in Chap. 3.
Poynting’s vector, which will be used to discuss the flow of energy in other chapters,
is also described. It is recommended that readers who have not studied electromagnetism for many years read this chapter before proceeding to the next chapter. Since
this chapter is compactly summarized, it will be actively utilized further on.
2.1 Electrostatic Phenomena
Here we treat electrostatic phenomena that do not change with time. The source
that causes various kinds of electric phenomena is electric charge, and there are two
kinds of electric charge. One is the electric charge that flows in a conductor and can
be transferred elsewhere, which is also called true electric charge, and the other is
polarization charge that is locally bound around a nucleus in a dielectric material and
cannot be transferred outside. The densities of these electric charges are denoted by
ρ and ρ p , respectively. The electrical distortion that these electric charges cause in
a space is electric field. It is represented by a vector E. When electric charge Q is
placed in this space, the following force is exerted on the charge:
F = QE.
(2.1)
This force is called the Coulomb force. When the true electric charge is distributed
with density ρ at position r
in a region V, the electric field at position r that is caused
by the charge is given by
E(r) =
1
4ππ 0
V
ρ
r
r − r
|r − r |
3
dV
,
(2.2)
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
T. Matsushita, Superconductivity and Electromagnetism, Springer Series
in Solid-State Sciences 195, https://doi.org/10.1007/978-3-030-67568-4_2
11
Basic Electromagnetism
Abstract In this chapter we summarize the essential principles associated with electrostatic and magnetic phenomena caused by electric charges and currents, respectively, based on the E-B analogy. These are necessary to understand the usefulness of
introducing superconductivity into electromagnetism, which will be done in Chap. 3.
Poynting’s vector, which will be used to discuss the flow of energy in other chapters,
is also described. It is recommended that readers who have not studied electromagnetism for many years read this chapter before proceeding to the next chapter. Since
this chapter is compactly summarized, it will be actively utilized further on.
2.1 Electrostatic Phenomena
Here we treat electrostatic phenomena that do not change with time. The source
that causes various kinds of electric phenomena is electric charge, and there are two
kinds of electric charge. One is the electric charge that flows in a conductor and can
be transferred elsewhere, which is also called true electric charge, and the other is
polarization charge that is locally bound around a nucleus in a dielectric material and
cannot be transferred outside. The densities of these electric charges are denoted by
ρ and ρ p , respectively. The electrical distortion that these electric charges cause in
a space is electric field. It is represented by a vector E. When electric charge Q is
placed in this space, the following force is exerted on the charge:
F = QE.
(2.1)
This force is called the Coulomb force. When the true electric charge is distributed
with density ρ at position r
in a region V, the electric field at position r that is caused
by the charge is given by
E(r) =
1
4ππ 0
V
ρ
r
r − r
|r − r |
3
dV
,
(2.2)
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
T. Matsushita, Superconductivity and Electromagnetism, Springer Series
in Solid-State Sciences 195, https://doi.org/10.1007/978-3-030-67568-4_2
11