# Chapter 16 : Superconductivity and Superconductors¶

### Example 16.1 page no : 431¶

In [1]:
# Variables
b = 0;
#m = -h
#m = x*h
# =  = >> -h = x*h

# Calculations
x = -1;			#from above realtions
ur = x+1;			#relative permeability

# Results
print "Susceptibility of superconductor  =  ",x
print "Relative permeability of superconductor  =  ",ur

Susceptibility of superconductor  =   -1
Relative permeability of superconductor  =   0


### Example 16.2 pageno : 434¶

In [4]:
# Variables
ho = 0.0803;			#in A/m
t1 = 3.;    			#in K
t2 = 10.;	    		#in k
tc = 7.17;		    	#in K

# Calculations
hc1 = ho*(1-(t1/tc)**2);
hc2 = ho*(1-(t2/tc)**2);

# Results
print "Critical field at 3K (in A/m)  =  %f A/m"%hc1
print "Critical field at 10K (in A/m)  =  %.4f A/m"%hc2

Critical field at 3K (in A/m)  =  0.066242 A/m
Critical field at 10K (in A/m)  =  -0.0759 A/m


### Example 16.3 pageno : 434¶

In [5]:
# Calculations
r = 1.*10**-3;			#in m
hc = 7.9*10**3;			#in A/m
ic = 2.*3.14*r*hc;			#in m

# Results
print "Critical current in superconducting state (in A)  =  %.2f A"%ic

Critical current in superconducting state (in A)  =  49.61 A


### Example 16.4 pageno : 441¶

In [13]:
# Variables
p = 11.4*10**3;			#in kg/m**3
aw = 207.2;			#in kg/kg-mol
v = 1200.;			#in m/s

# Calculations
e = 1.6*10**-19;			#charge in C
m = 9.1*10**-31;			#mass of electron in kg
mo = 4*3.14*10**-7;			#in H/m
ne = 2*p*na/aw;			#in per m**3
ied = ne*e*v;			#in A/m**2
dp = (m/(mo*(6.62*10**28)*(e**2)))**(1./2);
dp1 = round(dp*10**10,-1);

# Results
print "Electron density (in per m**3)  =  %.2e electron/m**3"%ne
print "Current density (in A/m**2)  =  %.2e A/m**2"%ied
print "Depth of penetration (in angstorm)  =  %.1f A"%dp1

Electron density (in per m**3)  =  6.63e+29 electron/m**3
Current density (in A/m**2)  =  1.27e+14 A/m**2
Depth of penetration (in angstorm)  =  210.0 A


### Example 16.9 page no : 446¶

In [14]:
# Variables
ho = 65.*10**3;			#in A/m
tc = 7.18;			#in K
t = 4.2;			#in K
r = 0.5*10**-3;			#in m

# Calculations
hc = ho*(1-(t/tc)**2);			#in A/m
ic = 2*3.14*r*hc;   			#in A
a = 3.14*r**2;		        	#area in m**2
j = ic/a;			            #in A/m**2

# Results
print "current density (in A/m**2)  =  %.2e A/m**2"%j

current density (in A/m**2)  =  1.71e+08 A/m**2


### Example 16.10 page no : 446¶

In [16]:
import math

# Variables
hc1 = 21.;			#in A/m
hc2 = 10.;			#in A/m
tc = 7.;			#in K
t = 14.;			#in K
h = hc1/hc2;

# Calculations
#Determining critical temperature
tc1 = math.sqrt(3626./11);			#by quadratic eqn in the example
ho = hc1/(1-(tc**2/tc1**2));
t = 4.2;			#in k
hc = ho*(1-(t/tc1)**2);

# Results
print "Critical field at 0 K (in A/m)  =  %.2f A/m"%ho
print "Critical field At 4.2 k (in A/m)  =  %.3f A/m"%hc

Critical field at 0 K (in A/m)  =  24.67 A/m
Critical field At 4.2 k (in A/m)  =  23.347 A/m


### Example 16.11 page no : 447¶

In [4]:
import math

# part (b)
# Variables
m = 39.6                    # materials
Tc = 7.19                   # K

# Calculation
dp = math.sqrt(m**2 * (1 - 3**4/Tc**4))

# Results
print "Depth of penetration at absolute zero dp(0) = %.3f nm"%dp

Depth of penetration at absolute zero dp(0) = 38.995 nm