# Capter 19: Magnetic Materials¶

## Example 19.1, page no-541¶

In [1]:
#Relative permiability and magnetic force

import math
#Variable Declaration
M=2300.0                            # Magnetization
B=0.00314                           # Flux density

#Calculation
mu=4*math.pi*10**-7
H=(B/mu)-M
mur=(M/H)+1

#Result
print('The magnetic force H is %.4f A/m and the relative permeability mu_r is %.5f'%(H,mur))

The magnetic force H is 198.7326 A/m and the relative permeability mu_r is 12.57334


## Example 19.2, page no-542¶

In [2]:
# magnetisation and flux density

import math
#Variable Declaration
H=10**4                                   # Magnetic field intensity
sus=3.7*10**-3                            # Susceptibility
mu=4*math.pi*10**-7                       # permeability of free space

#Calculation
M=sus*H
B=mu*(M+H)

#Result
print('The magnetisation in the material is %.0f A/m and flux density in the material is %.2f * 10^-2 Wb.m^-2'%(M,B*10**2))

The magnetisation in the material is 37 A/m and flux density in the material is 1.26 * 10^-2 Wb.m^-2


## Example 19.3, page no-542¶

In [9]:
#Flux density in a material

import math
#variable declaration
H=10**4                      # Magnetic field intensity
sus=-0.8*10**-5              # susceptibility of copper
mu=4*math.pi*10**-7          # permeability of free space

#Calculations
M=sus*H
B=mu*(M+H)

#Result
print('The flux density in the material is %.2f * 10^-2 Wb.m^-2'%(B*10**2))

# Magnetic field intensity: value given in the book is 10^6 but calculations are done with 10^4

The flux density in the material is 1.26 * 10^-2 Wb.m^-2


## Example 19.4, page no-543¶

In [15]:
#Permeability

import math
# Variable declarations
H=1800.0                   # Magnetic field intensity
fi=3*10**-5                # Magnetic flux
A=0.2*10**-4               # Area of cross-section

#Calculations
B=fi/A
mu=B/H

#Result
print('\nThe magnetic flux is %.1f Wb/m^2\nThe permeability is %.3f*10^-4 H/m'%(B,mu*10**4))

The magnetic flux is 1.5 Wb/m^2
The permeability is 8.333*10^-4 H/m


## Example 19.5, page no-544¶

In [17]:
# Magnetic moment of Nickel

import math
#variable declaration
B=0.65                           # Magnetic inductionof Nickel
r=8906                           # Density of Nickel
M=58.7                           # Atomic weight
mu=4*math.pi*10**-7              # Permeability of free space
k=9.27*10**-24                   # 1 Bohr Magnetron

#Calculations
N=r*avg/M
mu_m=B/(N*mu)
mu_m=mu_m/k

#Result
print("The magnetic moment of nickel atom is %.2f Bohr magneton"%mu_m)

The magnetic moment of nickel atom is 0.61 Bohr magneton


## Example 19.6, page no-545¶

In [18]:
# Average magnetization contributed per atom

import math
# Variable declaration
a=2.5*10**-10                  # interatomic spacing
M=1.8*10**6                    # MAgnetization
e=1.6*10**-19                  # charge of an electron

#Calculations
n=2/a**3
m=9.1*10**-31
h=6.625*10**-34
ma=M/n
beta1=e*h/(4*math.pi*m)

#Result
print("The average magnetisation contributed per atom = %.3f Bohr Magneton"%(ma/beta1))

The average magnetisation contributed per atom = 1.517 Bohr Magneton


## Example 19.7, page no-545¶

In [19]:
# Tempoerature using classical statistics

import math
#Variable declarations
mu=9.4*10**-24                   # Permeability
H=2                              # MAgnetic field intensity
k=1.38*10**-23                   # Bolzmann's constant

#Calculations
T=2*mu*H/(k*math.log(2))

#Result
print("The temperature of the system T is %.1f K"%T)

The temperature of the system T is 3.9 K


## Example 19.8, page no-547¶

In [48]:
# Saturation magnetic field of Gd atom

import math
#Variable declaration
ba=7.1                           # Bohr magnetron per atom
aw=1.8*10**6                     # Atomic weight of Gd
d=7.8*10**3                      # Density of Gd
M=157.26                         # Atomic number of Gd
k=9.27*10**-24                   # 1 Bohr magnetron
mu=4*math.pi*10**-7              # permeability of free space

#Calculations
N=d*avg/M
mm=N*ba*k
B=N*mu*k*7.1

#Result
print("\nThe saturation magnetic field of Gd atom is %.2f Wb/m^2"%B)

The saturation magnetic field of Gd atom is 2.47 Wb/m^2


## Example 19.9, page no-547¶

In [55]:
#saturation magnetisation

import math
# variable ddeclaration
bet=9.27*10**-24                    # 1 Bohr magnetron
V=0.839*10**-9                      # unit cell edge length

#Calculations
M=32*bet/V**3

#Result
print("The saturation magnetisation is %.3f *10^5 A/m"%(M*10**-5))
# Answer in the book is given as 5.023 x 10^-5

The saturation magnetisation is 5.023 *10^5 A/m


## Example 19.10, page no-548¶

In [57]:
# Saturation flux density

import math
#variable declaration
d=8900                       # Density of Ni
wt=58.71                     # Atomic weight
bet=9.27*10**-24             # 1 Bohr magnetron
mu=4*math.pi*10**-7              # permeability of free space

#Calculations
mm=0.6*bet
N=d*avg/wt
ms=mm*N
bs=mu*ms

#Result
print("\nThe saturation magnetisation is %.3f *10^5 A/m\nThe saturation flux density is %.3f Wb/m^2"%(ms*10**-5,bs))

The saturation magnetisation is 5.077 *10^5 A/m
The saturation flux density is 0.638 Wb/m^2


## Example 19.11, page no-548¶

In [58]:
# Saturation magnetisation of gadolinium

import math
#variable declaration
awt=157.25                  # Atomic weight
an=64                       # Atomic number
d=7860                      # density
k=9.27*10**-24              # 1 Bohr magnetron

#Calculations
N=d*8*k*avg/awt

# Result
print("The saturation magnetisation of gadolinium is %.2f*10^6 A/m"%(N*10**-6))

The saturation magnetisation of gadolinium is 2.23*10^6 A/m


## Example 19.12, page no-549¶

In [67]:
# Magnetic flux density inside the material

import math
#variable declaration
H=1000                       # Magnetic field strength
sus=-0.3*10**-5              # magnetic susceptibility
mu=4*math.pi*10**-7          # permeability of free space

#calculation
M=sus*H
B=mu*(M+H)
B=math.floor(B*10**6)/10**6

#Result
print("The magnetic flux density inside the material is %.3f T or Wb.m^-2"%(B*10**3))

The magnetic flux density inside the material is 1.256 T or Wb.m^-2