Chemistry Reference
In-Depth Information
Superconducting
matrix
(a)
(b)
B
-
M
Normal region
H
c1
H
c2
H
Figure 8.5
(a) Induced magnetisation,
M
, as a function of applied field,
H
, in a Type II
superconductor. Above
H
c1
, there is partial penetration of magnetic flux into
the superconductor. Above
H
=
H
c2
, the superconductor reverts fully to the
normal state. (b) Between
H
c1
and
H
c2
, the magnetic flux penetrates through
thin cylindrical normal regions, each of which encloses a single quantum of
magnetic flux, and is refered to as a flux vortex. (From P. J. Ford and G. A.
Saunders (1997)
Contemporary Physics
38
75 © Taylor & Francis.)
to consider what determines whether a superconductor will be Type I or
Type II, but turn first to seek an explanation of the Meissner effect.
8.5 Electromagnetic momentum and
the London equation
To explain the Meissner effect, we first introduce the concept of
electro-
magnetic momentum
for a classical charged particle. This allows us to deal
more efficiently and elegantly with the motion of particles in an applied
magnetic field,
B
. Because the divergence of the magnetic field is zero,
∇·
A
.
If we consider a particle of mass
M
and charge
q
moving with velocity
v
in the applied field
B
B
=
0, we can always define a vector potential,
A
, such that
B
=∇×
=∇×
A
, then the total momentum,
p
, of the particle
can be defined as
p
=
M
v
+
q
A
(8.6)
where
M
v
is the kinetic momentum, and
q
A
is referred to as the electro-
magnetic momentum.
It can be shown that the total momentum
p
is conserved in the presence
of time-dependent magnetic fields, even when
B
is constant at the position
of the charged particle. The general proof is beyond the scope of this text,
but the conservation of total momentum can be readily demonstrated by
a specific example.
