Chapter 17: Superconductivity

Exa 17.1

In [1]:
from __future__ import division
import math
 # Python Code Ex17.1 Variation of critical magnetic field with temp. Page-537



 
#Variable declaration

 
T_c = 3.7;      # Critical temperature of superconducting transition, kelvin
H_c0 = 0.0306;  # Critical magnetic field to destroy superconductivity, tesla
T = 2#Temperature at which critical magnetic field is to be found out, kelvin


#Calculation

H_cT = H_c0*(1-(T/T_c)**2);


#Result

print"\nThe critical magnetic field at",T," K =",round(H_cT,3)," T"
 

The critical magnetic field at 2  K = 0.022  T

Exa 17.2

In [2]:
from __future__ import division
import math
 # Python Code Ex17.2 Variation of critical magnetic field with temperature
# for tin Page-537 (2010)



 
#Variable declaration


T_c = 3.69;       # Critical temperature of superconducting transition, kelvin
# Critical magnetic field intensity to destroy superconductivity 
# at zero kelvin, tesla
B_c0 = 3e+5/(4*math.pi);                    
# Critical magnetic field at temperature T kelvin
B_cT = 2e+5/(4*math.pi);             



#Calculation
       
 # T = 2;Temperature at which critical magnetic field is to be found out, kelvin
 # since B_cT = B_c0*(1-(T/T_c)**2);
 #Critical magnetic field intensity as a function of temperature
 # Solving for T
# Temperature at which critical magnetic field becomes B_cT, kelvin   
T = (1-B_cT/B_c0)**0.5*T_c;              


#Result

print"\nThe temperature at which critical magnetic field becomes "
print round((B_cT*10**-4),2)*10**4," T = ",round(T,2)," K"
 

The temperature at which critical magnetic field becomes 
15900.0  T =  2.13  K

Exa 17.3

In [3]:
from __future__ import division
import math
 # Python Code Ex17.3 Calculating critical current for a lead wire from 
 #critical temperature of lead Page-537 (2010)
 
 
 
 
  
#Variable declaration


 # Critical temperature of superconducting transition for Pb, kelvin
T_c = 7.18;                            
#Critical magnetic field intensity to destroy superconductivity at zero K,A/m
H_c0 = 6.5e+4;                          
# Temperature at which critical magnetic field becomes H_cT, kelvin  
T = 4.2;                                
d = 1e-03;                              # Diameter of lead wire, m




#Calculation

# Critical magnetic field intensity at temperature T kelvin, A/m
H_cT = H_c0*(1-(T/T_c)**2)             
# Critical current through the lead wire, A
I_c = math.pi*d*H_cT;                   


#Result

print"\nThe critical current through the lead wire = ",round(I_c,2)," A"

The critical current through the lead wire =  134.33  A

Exa 17.4

In [4]:
from __future__ import division
import math
 # Python Code Ex17.4 Dependence of London penetration depth 
 #on temperature Page-548 (2010)
 
 
 
 
#Variable declaration


N = 6.02e+023;                         # Avogadro's number
rho = 13.55e+03;                    # Density of mercury, kg per metre cube
M = 200.6e-03;                          # Molecular mass of mercury, kg
lambda_T = 750e-010;   # Penetration depth of mercury at T kelvin, m
T_c = 4.12; # Critical temperature of superconducting transition for Hg, kelvin
T = 3.5;#Temperature at which penetration depth for Hg becomes lambda_T, kelvin   



# Calculation

# Penetration depth of mercury at 0 kelvin, m
lambda_0 = lambda_T*(1-(T/T_c)**4)**(1/2);
n_0 = N*rho/M;   # Normal electron density in mercury, per metre cube
n_s = n_0*(1-(T/T_c)**4);  # Superelectron density in mercury, per metre cube



#Result

print"\nThe penetration depth at 0 K =",round((lambda_0*10**8),2)*10**-8," m"
print"\nThe superconducting electron density ="
print round((n_s*10**-28),2)*10**28,"per metre cube"

 

The penetration depth at 0 K = 5.19e-08  m

The superconducting electron density =
1.95e+28 per metre cube