9: Superconductivity

Example number 9.1, Page number 9.3

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
Tc = 3.7      #critical temperature(K)
Hc_0 = 0.0306    #critical field(T)
T = 2     #temperature(K)

#Calculation
Hc_2 = Hc_0*(1-(T/Tc)**2)     #critical field(T)
Hc_2 = math.ceil(Hc_2*10**5)/10**5   #rounding off to 5 decimals

#Result
print "critical field at 2K is",Hc_2,"T"

critical field at 2K is 0.02166 T

Example number 9.2, Page number 9.5

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration
T = 4.2     #temperature(K)
d = 1       #diameter(mm)
Tc = 7.18    #critical temperature(K)
H0 = 6.5*10**4     #critical field(A/m)

#Calculation
d = d*10**-3     #diameter(m)
Hc = H0*(1-((T/Tc)**2))    #critical field at 2K(A/m)
ic = math.pi*d*round(Hc);     #critical current(A)
ic = math.ceil(ic*10**2)/10**2;   #rounding off to 2 decimals

#Result
print "critical current for lead is",ic,"A"
print "answer given in the book differs due to rounding off errors"

critical current for lead is 134.34 A
answer given in the book is wrong

Example number 9.3, Page number 9.13

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda_T = 750    #penetration depth of mercury(Armstrong)
T = 3.5    #temperature(K)
Tc = 4.12    #critical temperarure(K)

#Calculation
lamda_0 = lamda_T*((1-(T/Tc)**4))**(1/2)     #penetration depth(Armstrong)

#Result
print "penetration depth at 0K is",int(lamda_0),"armstrong"

penetration depth at 0K is 519 armstrong

Example number 9.4, Page number 9.13

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
T1 = 3     #temperature(K)
T2 = 7.1    #temperature(K)
lamda_T1 = 396    #penetration depth(armstrong)
lamda_T2 = 1730    #penetration depth(armstrong)

#Calculation
A = (((lamda_T2/lamda_T1)**2)*T2**4) - T1**4
B = ((lamda_T2/lamda_T1)**2)-1
Tc = (A/B)**(1/4)      #critical temperature(K)
Tc = math.ceil(Tc*10**4)/10**4;   #rounding off to 4 decimals

#Result
print "critical temperature for lead is",Tc,"K"

critical temperature for lead is 7.1932 K