Chapter 10:Superconductivity

Example 10.1 , Page no:313

In [1]:
import math
from __future__ import division

#given
Tc=7.2; #in K (critical temperature)
T=5; #in K (given temperature)
H0=6.5E3; #in A/m (critical magnetic field at 0K)

#calculate
Hc=H0*(1-(T/Tc)**2); #calculation of magnitude of critical magnetic field

#result
print"The magnitude of critical magnetic field is Hc=",round(Hc,2),"A/m";

The magnitude of critical magnetic field is Hc= 3365.35 A/m

Example 10.2 , Page no:313

In [2]:
import math
from __future__ import division

#given
r=0.02; #in m (radius of ring)
Hc=2E3; #in A/m (critical magnetic field at 5K)
pi=3.14; #value of pi used in the solutiion

#calculate
Ic=2*pi*r*Hc; #calculation of critical current value

#result
print"The critical current value is Ic=",Ic,"A";

The critical current value is Ic= 251.2 A

Example 10.3 , Page no:313

In [3]:
import math
from __future__ import division

#given
M1=199.5; #in amu (isotropic mass at 5K)
T1=5; #in K (first critical temperature)
T2=5.1; #in K (second critical temperature)
#calculate
#since Tc=C*(1/sqrt(M)
#therefore T1*sqrt(M1)=T2*sqrt(M2)
#therefore we have M2=(T1/T2)^2*M1
M2=(T1/T2)**2*M1; #calculation of isotropic mass at 5.1K

#result
print"The isotropic mass at 5.1K is M2=",round(M2,3),"a.m.u.";

The isotropic mass at 5.1K is M2= 191.753 a.m.u.

Example 10.4 , Page no:314

In [4]:
import math
from __future__ import division

#given
T=6; #in K (given temperature)
Hc=5E3; #in A/m (critical magnetic field at 5K)
H0=2E4; #in A/m (critical magnetic field at 0K)

#calculate
#since Hc=H0*(1-(T/Tc)^2)
#therefor we have Tc=T/sqrt(1-(Hc/H)^2)
Tc=T/math.sqrt(1-(Hc/H0)); #calculation of transition temperature

#result
print"The transition temperature is Tc=",round(Tc,3),"K";
print "NOTE: The answer in the textbook is wrong" 

The transition temperature is Tc= 6.928 K
NOTE: The answer in the textbook is wrong

Example 10.5 , Page no:314

In [5]:
import math
from __future__ import division

#given
T=5; #in K (given temperature)
d=3; #in mm (diameter of the wire)
Tc=8; #in K (critical temperature for Pb)
H0=5E4; #in A/m (critical magnetic field at 0K)
pi=3.14; #value of pi used in the solution

#calculate
Hc=H0*(1-(T/Tc)**2); #calculation of critical magnetic field at 5K
r=(d*1E-3)/2; #calculation of radius in m
Ic=2*pi*r*Hc; #calculation of critical current at 5K

#result
print"The critical magnetic field at 5K is Hc=",'%.3E'%Hc,"A/m";
print"The critical current at 5K is Ic=",round(Ic,4),"A";
print "   (roundoff error)"

The critical magnetic field at 5K is Hc= 3.047E+04 A/m
The critical current at 5K is Ic= 287.0156 A
   (roundoff error)

Example 10.6 , Page no:314

In [6]:
import math
from __future__ import division

#given
V=8.50; #in micro V (voltage across Josephson junction )
e=1.6E-19; #in C (charge of electron)
h=6.626E-34; #in J/s (Planck’s constant)

#calculate
V=V*1E-6; #changing unit from V to microVolt
v1=2*e*V/h; #calculation of frequency of EM waves

#result
print"The frequency of EM waves is v=",'%.3E'%v1,"Hz";
print "NOTE: The answer in the textbook is wrong" 

The frequency of EM waves is v= 4.105E+09 Hz
NOTE: The answer in the textbook is wrong

Example 10.7 , Page no:315

In [7]:
import math
from __future__ import division

#given
M1=200.59; #in amu (average atomic mass  at 4.153K)
Tc1=4.153; #in K (first critical temperature)
M2=204; #in amu (average atomic mass of isotopes)

#calculate
#since Tc=C*(1/sqrt(M)
#therefore T1*sqrt(M1)=T2*sqrt(M2)
#therefore we have Tc2=Tc1*sqrt(M1/M2)
Tc2=Tc1*math.sqrt(M1/M2); #calculation of transition temperature of the isotopes

#result
print"The transition temperature of the isotopes is  Tc2=",round(Tc2,3),"K";

The transition temperature of the isotopes is  Tc2= 4.118 K