# Chapter 16: Magnetic Properties of Materials¶

## Exa 16.1¶

In [2]:
from __future__ import division
import math
# Python Code Ex16.1 Response of Cu to magnetic field: Page-503 (2010)

#Variable declaration

H = 1e+06; # Applied magnetic field in copper, A/m
chi = -0.8e-05; # Magnetic susceptibility of copper
mu_0 = 4*math.pi*1e-07; # Magnetic permeability of free space, henry/metre

#Calculation

M = chi*H; # Intesity of magnetization in copper, A/m
B = mu_0*(H + M); # Magnetic flux density in copper, tesla

#Result

print"\nThe magnetization of copper =",M," A/m"
print"\nThe magnetic flux density of copper =",round(B,2),"T"


The magnetization of copper = -8.0  A/m

The magnetic flux density of copper = 1.26 T


## Exa 16.2¶

In [3]:
from __future__ import division
import math
# Python Code Ex16.2 Diamagnetic susceptibility of copper: Page-512 (2010)

#Variable declaration

e = 1.6e-019;                          # Charge on an electron, C
m = 9.1e-031;                           # Mass of an electron, kg
mu_0 = 4*math.pi*1e-07;   # Magnetic permeability of free space, henry/metre
Z = 1;     # Number of electrons contributing to the magnetic moment
r = 1e-010;                             # Radius of copper atom, m
a = 3.608e-010;                         # Lattice parameter of copper, m
# For FCC lattice of Cu, there are 4 atoms per unit cell
n = 4;                                  # Number of atoms per unit cell

#Calculation

N = n/a**3;        # Number of electrons per unit volume, per metre cube
chi_dia = -mu_0*Z*e**2*N*r**2/(6*m); # Diamagnetic susceptibility of copper

#Result

print"\nThe diamagnetic susceptibility of copper = "
print round(( chi_dia*10**6))*10**-6,

The diamagnetic susceptibility of copper =
-5e-06


## Exa 16.3¶

In [4]:
from __future__ import division
import math
#Python Code Ex16.3 Calculating magnetic induction from
#orientational energy equivalent of thermal energy: Page-514 (2010)

#Variable declaration

k = 1.38e-023;             # Boltzmann constant, joule per mole per kelvin
mu_B = 9.27e-024;                # Bohr's magneton, joule per tesla
T = 300;                                # Thermal energy of specimen, joule

#Calculation

mu_m = 5*mu_B; # Magnetic moment of paramagnetic sample, joule per tesla
# At equilibrium, mu_m*B = k*T, solving for B
# Magentic induction of paramagnetic sample, weber per metre square
B = k*T/mu_m;

#Result

print"\nThe magentic induction of paramagnetic sample ="
print round(B,2)," weber per metre square"


The magentic induction of paramagnetic sample =
89.32  weber per metre square


## Exa 16.4¶

In [5]:
from __future__ import division
import math
# Python Code Ex16.4 Behaviour of paramagnetic salt when placed
#in uniform magnetic field: Page-514 (2010)

#Variable declaration

k = 1.38e-023; # Boltzmann constant, joule per mole per kelvin
T = 300; # Thermal energy of specimen, joule
mu_B = 9.27e-024; # Bohr's magneton, ampere per metre square
mu_0 = 4*math.pi*1e-07; # Magnetic permeability of free space, henry per metre
N = 1e+28;#Concentration of paramagnetic ions in paramagnetic salt,per metre cube
mu_m = mu_B;
H = 1e+06; # Applied magnetic field, A/m

#Calculatin

chi = mu_0*N*mu_m**2/(3*k*T);#Paramagnetic susceptibility of salt at room temp.
M = chi*H; # Intensity of magnetization at room temperature, A/m

#Result

print"\nThe paramagnetic susceptibility of salt at room temperature = "
print round(( chi*10**5),2)*10**-5
print"\nThe intensity of magnetization of salt =",round(M,2)," A/m"

The paramagnetic susceptibility of salt at room temperature =
8.69e-05

The intensity of magnetization of salt = 86.95  A/m