Chemistry Reference
In-Depth Information
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Problems
8.1 We found in Section 8.5 that a charged particle outside a solenoid
experiences a transient electric field
E
and hence a net force
F
q
E
as the current decays in the solenoid. This is initially surprising, as
the magnetic field
B
=
=
0 at all times outside the solenoid, and hence
∇×
0 at all times. Why does the charged particle
nevertheless experience this transient electric field and force?
E
=−
∂
B
/∂
t
=
8.2 Verify by explicit derivation in Cartesian coordinates that
∇×
(
∇×
2
j
. Using this result and the continuity equation for
current density, show that the current density decays inside the plane
surface of a superconductor as
j
)
=∇
(
∇·
j
)
−∇
|
j
|=
j
0
exp
(
−
x
/λ
)
, where
µ
0
j
0
λ
=
L
L
B
0
,
L
is the London penetration depth, and
B
0
is the magnitude of
the magnetic field at the superconductor surface. Show also that the
magnetic flux penetrating the superconductor per unit length is
B
0
λ
L
.
8.3 Combine eqs (8.5) and (8.42) to deduce the temperature dependence
of the difference in entropy,
S
N
λ
, between the normal and
superconducting state of a Type I supe
r
conductor. Show that this
difference is maximised when
T
(
T
)
−
S
sc
(
T
)
/
√
3.
=
T
c
8.4 The heat capacity
C
is related to the entropy
S
by
C
T
. Cal-
culate how the difference in heat capacity between the normal and
superconducting states varies with temperature, and hence calcu-
late the magnitude of the discontinuity in the heat capacity at the
=
T
∂
S
/∂
