30
3 Effects of the Introduction of Superconductivity into Electromagnetism
and (3.1) lead to
ρ = 0,
(3.3)
which requires that there is no electric charge inside the conductor. Hence, if electric
charge exists in a conductor, it stays only on the surface of the conductor. From (3.1)
the electric potential of a conductor is
φ = const.
(3.4)
That is, conductor has equi-electric potential. When electric charge is distributed
with density σ on the surface of a conductor, the electric field in the vicinity of the
surface is perpendicular to the surface and its value is given by
E =
σ
ε 0
.
(3.5)
On the other hand, (2.30) and (3.2) lead to
i = 0,
(3.6)
which requires that there is no current inside the superconductor. Hence, if current
flows in a superconductor, it flows only on the surface of the superconductor. From
(3.2) the vector potential of superconductor is
A = const.,
(3.7)
except in the case where the superconductor is not simply connected and a magnetic
flux penetrates a space surrounded by the superconductor such as with a solenoid
coil. Thus, superconductor has equi-vector potential in most cases. When current
flows on the surface of the superconductor with surface density τ , the magnetic flux
density in the vicinity of the surface is parallel to the surface and its value is given
by
B = μ 0 τ.
(3.8)
It will be easily understood from the above example that there is an analogy
between the electric phenomena in a conductor and the magnetic phenomena in
a superconductor. Figure 3.1 shows the electric field lines produced by the electric charge on the surface of a conductor and the magnetic flux lines produced
by the current on the surface of a superconductor. The difference comes from the
different features of the respective fields, i.e., the electric field with divergence and
the magnetic flux density with rotation.
3 Effects of the Introduction of Superconductivity into Electromagnetism
and (3.1) lead to
ρ = 0,
(3.3)
which requires that there is no electric charge inside the conductor. Hence, if electric
charge exists in a conductor, it stays only on the surface of the conductor. From (3.1)
the electric potential of a conductor is
φ = const.
(3.4)
That is, conductor has equi-electric potential. When electric charge is distributed
with density σ on the surface of a conductor, the electric field in the vicinity of the
surface is perpendicular to the surface and its value is given by
E =
σ
ε 0
.
(3.5)
On the other hand, (2.30) and (3.2) lead to
i = 0,
(3.6)
which requires that there is no current inside the superconductor. Hence, if current
flows in a superconductor, it flows only on the surface of the superconductor. From
(3.2) the vector potential of superconductor is
A = const.,
(3.7)
except in the case where the superconductor is not simply connected and a magnetic
flux penetrates a space surrounded by the superconductor such as with a solenoid
coil. Thus, superconductor has equi-vector potential in most cases. When current
flows on the surface of the superconductor with surface density τ , the magnetic flux
density in the vicinity of the surface is parallel to the surface and its value is given
by
B = μ 0 τ.
(3.8)
It will be easily understood from the above example that there is an analogy
between the electric phenomena in a conductor and the magnetic phenomena in
a superconductor. Figure 3.1 shows the electric field lines produced by the electric charge on the surface of a conductor and the magnetic flux lines produced
by the current on the surface of a superconductor. The difference comes from the
different features of the respective fields, i.e., the electric field with divergence and
the magnetic flux density with rotation.