Chapter7:SUPERCONDUCTIVITY

Eg1:pg-272

In [1]:
import math
Tc=3.7      #critical temperature in K
Hc_0=0.0306 #critical magnetic field in Tesla at 0K
T=2         #temperature in K
Hc=Hc_0*(1-(T/Tc)**2)
print"Critical field at 2 K is ",round(Hc,4),"Tesla"

Critical field at 2 K is  0.0217 Tesla

Eg2:pg-272

In [2]:
import math
Tc=7.2     #transition temperature in K
T=5        #temperature in K
Hc_T=3.3e4 #critical magnetic field at 5K in A/m
Hc_0=Hc_T/(1-(T/Tc)**2)
print"Maximum value of H at 0 K is ","{:.2e}".format(Hc_0),"A/m"

Maximum value of H at 0 K is  6.37e+04 A/m

Eg3:pg-273

In [4]:
import math
Tc=7.2  #critical temperature in K
Hc_0=1  #let,critical magnetic field at 0K
Hc_T=0.1*Hc_0 #critical magnetic field at T Kelvin
T=math.sqrt(1-Hc_T/Hc_0)*Tc
print"Temperature is ",round(T,2),"K"

Temperature is  6.83 K

Eg4:pg-273

In [5]:
import math
T=4.2        #temperature in K
Hc_0=0.0803  #critical magnetic field at 0K in Wb/m**2
Tc=7.2       #critical temperature for Pb in K
Hc_T=Hc_0*(1-(T/Tc)**2)
print"Critical field at 4.2 K is ",round(Hc_T,5),"Tesla"#answer is wrong in book

Critical field at 4.2 K is  0.05298 Tesla

Eg5:pg-273

In [6]:
import math
Hc_T=105e3 #critical magnetic field at T Kelvin in A/m
Hc_0=150e3 #critical magnetic field at 0K in A/m
Tc=9.2     #critical temperature in K
T=math.sqrt(1-Hc_T/Hc_0)*Tc
print"Temperature is ",round(T,2),"K"

Temperature is  5.04 K

Eg6:pg-274

In [7]:
import math
Hc_T=1e5  #critical magnetic field at 8K in A/m
T=8       #temperature in K
Hc_0=2e5  #critical magnetic field at 0K in A/m
Tc=T/math.sqrt(1-Hc_T/Hc_0)
print"Transition temperature is ",round(Tc,1),"K"

Transition temperature is  11.3 K

Eg7:pg-274

In [9]:
import math
Tc=7.26   #critical temperature in K
Hc_0=8e5  #critical magnetic field at 0K in A/m
Hc_T=4e4  #critical magnetic field at T kelvin in A/m
T=math.sqrt(1-Hc_T/Hc_0)*Tc
print"T =",round(T,2),"K","\nThe temperature of the metal should be held below",round(T,2),"K" 

T = 7.08 K 
The temperature of the metal should be held below 7.08 K

Eg8:pg-275

In [10]:
import math
T1=14       #temperature in K
T2=12       #temperature in K
T=4.2       #temperature in K
Hc_T1=0.176 #critical magnetic field at temperature T1
Hc_T2=0.528 #critical magnetic field at temperature T2
Tc=math.sqrt((Hc_T2*T1**2-Hc_T1*T2**2)/(Hc_T2-Hc_T1))
Tc=int(Tc*10)/10. #rounding off
Hc_0=Hc_T1/(1-(T1/Tc)**2)
Hc_T=Hc_0*(1-(T/Tc)**2)
print"Transition temperature is ",Tc,"K"
print"Critical field at 0 K is ",round(Hc_0,3),"Tesla"
print"Critical field at 4.2 K is ",round(Hc_T,2),"Tesla"
#answers in book are wrong because value of T2 is taken as 13K in calculation which is wrong.

Transition temperature is  14.8 K
Critical field at 0 K is  1.673 Tesla
Critical field at 4.2 K is  1.54 Tesla

Eg9:pg-275

In [11]:
import math
D=1.0      #diameter of Pb wire in mm
Bc=0.0548  #in Tesla
mu_0=4*math.pi*1e-7 #absolute permeability of air in N/A**2
Ic=math.pi*D*1e-3*Bc/mu_0
print"Current is ",int(Ic),"amp"

Current is  137 amp

Eg10:pg-276

In [12]:
import math
Hc_0=6.5e3   #critical magnetic field at 0K in A/m
Tc=7.18      #critical temperature in K
Hc_T=4.5e3   #critical magnetic field at T Kelvin in A/m
T=math.sqrt(1-Hc_T/Hc_0)*Tc
print"Temperature is ",round(T,2),"K"
D=2          #diameter of the lead wire in mm
r=D/2          
Ic=2*math.pi*r*1e-3*Hc_T
Jc=Ic/(math.pi*(r*1e-3)**2)
print"Critical current density is ","{:.1e}".format(Jc),"A/m**2"

Temperature is  3.98 K
Critical current density is  9.0e+06 A/m**2

Eg11:pg-281

In [13]:
import math
T=3.5       #temperature in K
lamda_T=750 #penetration depth of Hg at 3.5K in Angstrom
Tc=4.153    #critical temperature in K
lamda_0=lamda_T*math.sqrt(round(1-(T/Tc)**4,3))
print"Penetration depth at 0 K is",round(lamda_0,1),"Angstrom"#answer is wrong in book because of calculation mistake  

Penetration depth at 0 K is 528.2 Angstrom

Eg12:pg-281

In [15]:
import math
m=9.1e-31     #mass of electron kg
mu_0=12.56e-7 #absolute permeability of air in N/A**2
e=1.6e-19     #charge of electron in coulomb
ns=1e28       #number of super electrons per meter cube
lamda_0=math.sqrt(m/(mu_0*ns*e**2))
lamda_0=round(lamda_0,9)*1e10
print"Penetration depth at 0 K is ",int(lamda_0),"Angstrom"
Tc=3          #critical temperature in K
T=1.          #temperature in K
lamda_T=lamda_0/math.sqrt(1-(T/Tc)**4)
print"Penetration depth at 1 K is ",int(lamda_T),"Angstrom"
#in book lamda(at 3K) is printed,which is wrong. Correct notation is lamda(at 1K)

Penetration depth at 0 K is  530 Angstrom
Penetration depth at 1 K is  533 Angstrom

Eg13:pg-286

In [16]:
import math
Tc=9.25     #critical temperature in K
T=0         #temperature in K
Kb=1.38e-23 #Boltzmann's constant in J/K
Eg=3.53*Kb*Tc/(1.6e-19)
h=6.63e-34  #planck constant joule-sec
c=3e8       #speed of light in m/sec
print"Energy gap Eg is ",round(Eg*1e3,2),"meV"
lamda_min=h*c/round(Eg*1.6e-19,23)
print"Minimum photon wavelength is ","{:.2e}".format(lamda_min),"m"
print"  This wavelength lie in the far-infrared region of electromagnetic radiations."
v=round(Eg*1.6e-19,23)/h
print"Frequency needed is ","{:.2e}".format(v),"s**-1"

Energy gap Eg is  2.82 meV
Minimum photon wavelength is  4.42e-04 m
  This wavelength lie in the far-infrared region of electromagnetic radiations.
Frequency needed is  6.79e+11 s**-1

Eg14:pg-286

In [18]:
import math
M=200.59  #average atomic mass of Hg in amu
m=204     #mass of isotope in amu
T=4.153   #temperature in K
t=4.118   #temperature in K
dM=m-M
dTc=t-T
alpha=-(M*dTc/(dM*T))
print"Isotope effect coefficient is ",round(alpha,3)

Isotope effect coefficient is  0.496