64
4 Fundamental Electromagnetic Properties of Superconductors
Fig. 4.8 Nonuniform
component of the electric
field inside and outside the
normal core
the nonuniform component of the electric field, which is given by the first terms of
(4.42) and (4.43), is shown in Fig. 4.8.
Here we estimate the macroscopic power loss density due to the obtained electric
field. The power loss density is averaged over a space sufficiently larger than λ or
the flux line spacing and can be regarded as a quantity that varies gradually in space.
Most of the power loss is caused by the intensified electric field inside the normal
core, i.e., the first term in (4.43). The power loss in a unit length of flux line is given
by
P
= πξ
2 e
2
ρ n
=
φ
2
0 v
2
4πξ 2 ρ n
,
(4.44)
where ρ n is the normal resistivity. Equation (4.44) gives the power loss under the
macroscopic electric field of (4.41). Since the power loss is expressed as
P
=
φ 0
B
·
E
2
ρ f
(4.45)
in terms of the effective resistivity ρ f in the flux flow state, we have
ρ f =
B
μ 0 H c2
ρ n ,
(4.46)