Chapter 7
Concluding Remarks
Abstract In this chapter the contents from Chaps. 2–6 are briefly summarized,
and the status of electromagnetic phenomena in superconductors is overviewed in
the context of the current electromagnetic theory. Superconductors also have high
potential for applications in various fields because of their characteristic features
such as non-dissipative current and non-linear quantum phenomena. We focus on
their applications in the medical, environmental, and energy fields. Finally, it should
be emphasized that various electromagnetic phenomena in superconductors, whether
reversible or irreversible, are concerned with the flux pinning. The possibilities and
direction of progress of this science, which will extend over electromagnetism and
irreversible thermodynamics in the future, are discussed.
7.1 Summary
Electromagnetism is a science that describes only the electromagnetic properties of
substances without knowledge of the fundamental mechanisms of solid state physics
that play dominant roles. For example, a conductor is defined as a substance in which
the electric field is zero when an external electric field is applied, independently of
our knowledge of the free electron theory in solids. Superconductors can also be
defined as a substance in which the magnetic flux density is zero when an external
magnetic field is applied. In this case there is no problem in such a definition. It
makes even the present E-B analogy more perfect. Although superconductivity was
not yet discovered when Maxwell’s theory was completed, it is included in the
comprehensive theory as if it was known. As was shown in Sect. 3.2, it can be
proved by Maxwell’s theory that the electrical resistivity of a material that shows
B = 0 must be zero. Thus, it was, in principle, possible to predict the superconductor
in the 19th century, even though it might be an imaginary substance.
The phenomenon that adds a new page to electromagnetism is the longitudinal
magnetic field effect. In this phenomenon the force-free state with non-zero magnetic
helicity (A · B = 0) is realized. The static state with non-zero magnetic helicity
appears only in superconductors. The magnetic structure has a characteristic distortion called the force-free distortion in this state, and a general driving force is expected
© 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_7
155
Concluding Remarks
Abstract In this chapter the contents from Chaps. 2–6 are briefly summarized,
and the status of electromagnetic phenomena in superconductors is overviewed in
the context of the current electromagnetic theory. Superconductors also have high
potential for applications in various fields because of their characteristic features
such as non-dissipative current and non-linear quantum phenomena. We focus on
their applications in the medical, environmental, and energy fields. Finally, it should
be emphasized that various electromagnetic phenomena in superconductors, whether
reversible or irreversible, are concerned with the flux pinning. The possibilities and
direction of progress of this science, which will extend over electromagnetism and
irreversible thermodynamics in the future, are discussed.
7.1 Summary
Electromagnetism is a science that describes only the electromagnetic properties of
substances without knowledge of the fundamental mechanisms of solid state physics
that play dominant roles. For example, a conductor is defined as a substance in which
the electric field is zero when an external electric field is applied, independently of
our knowledge of the free electron theory in solids. Superconductors can also be
defined as a substance in which the magnetic flux density is zero when an external
magnetic field is applied. In this case there is no problem in such a definition. It
makes even the present E-B analogy more perfect. Although superconductivity was
not yet discovered when Maxwell’s theory was completed, it is included in the
comprehensive theory as if it was known. As was shown in Sect. 3.2, it can be
proved by Maxwell’s theory that the electrical resistivity of a material that shows
B = 0 must be zero. Thus, it was, in principle, possible to predict the superconductor
in the 19th century, even though it might be an imaginary substance.
The phenomenon that adds a new page to electromagnetism is the longitudinal
magnetic field effect. In this phenomenon the force-free state with non-zero magnetic
helicity (A · B = 0) is realized. The static state with non-zero magnetic helicity
appears only in superconductors. The magnetic structure has a characteristic distortion called the force-free distortion in this state, and a general driving force is expected
© 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_7
155