# example 8.1;page no:331¶

In [1]:
#cal of Magnetic field
#intiation of all variables
#Given that
H_c_0=  0.0306# Critical Field in tesla
T_c = 3.7 # Critical temperature in kelvin
T = 2 # Temperature in kelvin
print("Example 8.1,page no:331")
H_c = H_c_0*(1-(T/T_c)**2) # Calculation of critical field
print("Magnetic Field at K in tesla:"),round(H_c,4)
print("Standard formula used H_c = H_c_0*(1-(T/T_c)^2).")

Example 8.1,page no:331
Magnetic Field at K in tesla: 0.0217
Standard formula used H_c = H_c_0*(1-(T/T_c)^2).


## example 8.2;page no:331¶

In [2]:
#cal of Magnetic field
#intiation of all variables
#Given that
H_c=  3.3e4 # # Magnetic field in A/m
T_c = 7.2 # Critical temperature in kelvin
T = 5 # Temperature in kelvin
print("Example 8.2,page no:331")
H_c_0 = H_c*(1-(T/T_c)**2)**(-1) # Calculation of critical field
print("Magnetic Field at K in A/m:"),round(H_c_0,4)
print("Standard formula used H_c = H_c_0*(1-(T/T_c)^2).")

Example 8.2,page no:331
Magnetic Field at K in A/m: 63737.7049
Standard formula used H_c = H_c_0*(1-(T/T_c)^2).


# example 8.3;page no:332¶

In [3]:
#cal of Required temperature
#intiation of all variables
#Given that
import math
H_c_0= 1 # Let
H_c= 0.1 * H_c_0 # Magnetic field in A/m
T_c = 7.2 # Critical temperature in kelvin
print("Example 8.3,page no:332")
T = T_c*math.sqrt(1- (H_c/H_c_0)) # Calculation of Temperature
print("Required temperature in K:"),round(T,2)
print("Standard formula used H_c = H_c_0*(1-(T/T_c)^2).")

Example 8.3,page no:332
Required temperature in K: 6.83
Standard formula used H_c = H_c_0*(1-(T/T_c)^2).


## example 8.4;page no:332¶

In [4]:
#cal of magnetic field
#intiation of all variables
#Given that
H_c_0=  0.0803# Critical Field in tesla
T_c = 7.2 # Critical temperature in kelvin
T = 4.2 # Temperature in kelvin
print("Example 8.4,page no:332")
H_c = H_c_0*(1-(T/T_c)**2) # Calculation of critical field
print("Magnetic Field at  K in tesla:"),round(H_c,4)
print("Standard formula used H_c = H_c_0*(1-(T/T_c)^2).")
# Answer in book is 0.0548 tesla

Example 8.4,page no:332
Magnetic Field at  K in tesla: 0.053
Standard formula used H_c = H_c_0*(1-(T/T_c)^2).


## example 8.5;page no:333¶

In [5]:
#cal of Required temperature
#intiation of all variables
#Given that
import math
H_c_0= 1.5e5# Critical field in A/m
H_c= 1.05e5 # Magnetic field in A/m
T_c = 9.2 # Critical temperature in kelvin
print ("Example 8.5,page no:333")
T = T_c*math.sqrt(1- (H_c/H_c_0)) # Calculation of Temperature
print("Required temperature in K:"),round(T,2)
print("Standard formula used H_c = H_c_0*(1-(T/T_c)^2).")

Example 8.5,page no:333
Required temperature in K: 5.04
Standard formula used H_c = H_c_0*(1-(T/T_c)^2).


## example 8.6;page no:333¶

In [6]:
#cal of Required temperature
#intiation of all variables
#Given that
import math
H_c_0= 2e5# Critical field in A/m
H_c= 1e5 # Magnetic field in A/m
T_c = 8 # Critical temperature  in kelvin
print("Example 8.6,page no:333")
T = T_c/math.sqrt(1- (H_c/H_c_0)) # Calculation of Temperature
print("Required temperature in K:"),round(T,1)
print("Standard formula used H_c = H_c_0*(1-(T/T_c)^2).")

Example 8.6,page no:333
Required temperature in K: 11.3
Standard formula used H_c = H_c_0*(1-(T/T_c)^2).


## example 8.7;page no:334¶

In [7]:
#cal of Required temperature
#intiation of all variables
#Given that
import math
H_c_0= 8e5# Critical field in A/m
H_c= 4e4 # Magnetic field in A/m
T_c = 7.26 # Critical temperature in kelvin
print("Example 8.7,page no:334")
T = T_c*math.sqrt(1- (H_c/H_c_0)) # Calculation of Temperature
print("Required temperature in K:"),round(T,2)
print("Standard formula used H_c = H_c_0*(1-(T/T_c)^2).")

Example 8.7,page no:334
Required temperature in K: 7.08
Standard formula used H_c = H_c_0*(1-(T/T_c)^2).


## example 8.8;page no:335¶

In [8]:
#cal of Critical field
#intiation of all variables
#Given that
import math
T1 = 14. # Temp in K
T2 = 13. # Temp in K
T = 4.2 # Temp in K
Hc_T1 = 0.176 # Critical field at Temp T1
Hc_T2 = 0.528 # Critical field at Temp T2
print("Example 8.8,page no:335")
T_c = math.sqrt((T1**2*(Hc_T2/Hc_T1)- T2**2) /(Hc_T2/Hc_T1 - 1)) # Calculation of transition temperature
t_c = (T_c*10)/10 # Rounding off two two decimal places
Hc_0 = Hc_T1/(1-(T1/t_c)**2) # Calculation of critical field
Hc_T = Hc_0*(1-(T/t_c)**2) # Calculation of critical field
print("Transition temperature in K:"),round(t_c,1)
print("Critical field at K in T:"),round(T,1),round(Hc_0,3)
print("Critical field at 0 K is T:")
print("Standard formula used Hc_T = H_c_0*(1-(T/T_c)^2)="),round(Hc_T,2)
# Answer in book is 2.588 T for 0 K and 2.37 for 4.2 K

Example 8.8,page no:335
Transition temperature in K: 14.5
Critical field at K in T: 4.2 2.731
Critical field at 0 K is T:
Standard formula used Hc_T = H_c_0*(1-(T/T_c)^2)= 2.5


## example 8.9;page no:343¶

In [9]:
#cal of Penetration depth
#intiation of all variables
#Given that
import math
m_0 = 9.1e-31 # Mass of electron in kg
mu_0 = 12.56e-7# SI
e = 1.6e-19 # Charge on electron in coulomb
eta_s = 1e28 # superelectron density in  no. per cube
T_1 = 0. # First temp in kelvin
T_2 = 1. # Second temp in kelvin
T_c = 3. # Critical temp in kelvin
print("Example 8.9,page no:343")
lamda_0 = math.sqrt(m_0/(mu_0*eta_s*e**2))# Calculation of penetration depth at 0K
lamda_t = lamda_0/math.sqrt(1-(T_2/T_c)**4) # Calculation of penetration depth at 2K
print("Penetration depth at K in angestrom:"),round(lamda_0*1e10,0)
print("Penetration depth at  K in angestrom:"),round(lamda_t*1e10,2)
print("Standard formula used lambda_0 = sqrt(m_0/(mu_0*eta_s*e**2)).")

Example 8.9,page no:343
Penetration depth at K in angestrom: 532.0
Penetration depth at  K in angestrom: 535.31
Standard formula used lambda_0 = sqrt(m_0/(mu_0*eta_s*e**2)).


## example 8.10;page no:344¶

In [10]:
#cal of Penetration depth
#intiation of all variables
#Given that
import math
T_1 = 3.5 # Temperature in kelvin
T_c = 4.153 # Critical temp in kelvin
lamda_t = 750 # Penetration depth at T_1 in angstrom
print("Example 8.10,page no:344")
lamda_0 = lamda_t*math.sqrt(1-(T_1/T_c)**4) # Calculation of penetration depth at 3.5K
print("Penetration depth at 0 K in angstrom:"),round(lamda_0,2)
print("Standard formula used lamda_0 = lamda_t*sqrt(1-(T_1/T_c)**4).")

Example 8.10,page no:344
Penetration depth at 0 K in angstrom: 527.96
Standard formula used lamda_0 = lamda_t*sqrt(1-(T_1/T_c)**4).