16: Superconductivity

Example number 1, Page number 384

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

#Variable declaration    
HcT=3.3*10**4;        #critical magnetic field(A/m)
T=5;                  #temperature(K)
Tc=7.2;               #critical temperature(K)

#Calculations
Hc0=HcT/(1-(T/Tc)**2);      #magnetic field(A/m)

#Result
print "magnetic field is",round(Hc0/10**4,2),"*10**4 A/m"

critical magnetic field is 6.37 *10**4 A/m

Example number 2, Page number 384

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration    
HcT=4*10**4;        #critical magnetic field(A/m)
Tc=7.26;            #critical temperature(K)
Hc0=8*10**5;        #magnetic field(A/m)

#Calculations
T=Tc*math.sqrt(1-(HcT/Hc0));     #temperature(K)

#Result
print "temperature is",round(T,2),"K"

temperature is 7.08 K

Example number 3, Page number 384

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

#Variable declaration    
Hc0=1;              #assume
HcT=0.1*Hc0;        #critical magnetic field(A/m)
Tc=7.2;            #critical temperature(K)

#Calculations
T=Tc*math.sqrt(1-(HcT/Hc0));     #temperature(K)

#Result
print "temperature is",round(T,2),"K"

temperature is 6.83 K

Example number 4, Page number 385

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration    
Hc0=0.0306;            #magnetic field(Tesla)
T=2;                  #temperature(K)
Tc=3.7;               #critical temperature(K)

#Calculations
HcT=Hc0*(1-(T/Tc)**2);        #critical magnetic field(tesla)

#Result
print "critical magnetic field is",round(HcT,4),"tesla"

critical magnetic field is 0.0217 tesla

Example number 5, Page number 385

In [24]:
#importing modules
import math
from __future__ import division

#Variable declaration    
HcT=1*10**4;        #critical magnetic field(A/m)
T=8;                #temperature(K)
Hc0=2*10**5;        #magnetic field(A/m)

#Calculations
Tc=T/math.sqrt(1-(HcT/Hc0));     #transition temperature(K)

#Result
print "transition temperature is",round(Tc,2),"K"
print "answer given in the book is wrong"

transition temperature is 8.21 K
answer given in the book is wrong

Example number 6, Page number 385

In [29]:
#importing modules
import math
from __future__ import division

#Variable declaration    
Hc1=1.4*10**5;        #critical magnetic field(A/m)
Hc2=4.2*10**5;        #critical magnetic field(A/m)
T1=14;                #temperature(K)
T2=13;                #temperature(K)
T3=4.2;               #temperature(K)

#Calculations
Tc=round(math.sqrt(((Hc1*T2**2)-(Hc2*T1**2))/(Hc1-Hc2)),1);        #transition temperature(K)
H0=Hc1/(1-(T1/Tc)**2);                #critical field at 0K(A/m)
Hc=H0*(1-(T3/Tc)**2);                 #critical field at 4.2K(A/m)

#Result
print "transition temperature is",Tc,"K"
print "critical field at 0K is",round(H0/10**5,2),"*10**5 A/m"
print "critical field at 4.2K is",round(Hc/10**5,1),"*10**5 A/m"

transition temperature is 14.5 K
critical field at 0K is 20.66 *10**5 A/m
critical field at 4.2K is 18.9 *10**5 A/m

Example number 7, Page number 390

In [31]:
#importing modules
import math
from __future__ import division

#Variable declaration    
r=(10**-3)/2;       #radius(m)
Hc=7.9*10**3;       #critical field(A/m)

#Calculations
Ic=2*math.pi*r*Hc;     #critical current(amp)

#Result
print "critical current is",round(Ic,3),"amp"

critical current is 24.819 amp

Example number 8, Page number 390

In [37]:
#importing modules
import math
from __future__ import division

#Variable declaration    
Hc0=6.5*10**4;            #magnetic field(Tesla)
T=4.2;                  #temperature(K)
Tc=7.18;               #critical temperature(K)
r=(10**-3)/2;       #radius(m)

#Calculations
HcT=Hc0*(1-(T/Tc)**2);        #critical magnetic field(tesla)
Ic=2*math.pi*r*HcT;     #critical current(amp)
A=math.pi*r**2;         #area(m**2)
Jc=Ic/A;                #current density(A/m**2)

#Result
print "critical magnetic field is",round(HcT/10**4,3),"*10**4 A/m"
print "critical current is",round(Ic,1),"amp"
print "current density is",round(Jc/10**8,2),"*10**8 A/m**2"

critical magnetic field is 4.276 *10**4 A/m
critical current is 134.3 amp
current density is 1.71 *10**8 A/m**2