Chapter 8:Magnetic Properties

Example 8.1, Page number 8.3

In [1]:
#Variable declaration
M = 1.4        #value of magnetic field when filled with iron
H = 6.5*10**-4 #value of magnetic field in the interior

#Calculations
x = M/H
ur = 1+x

#Result
print "Relative permeability of iron is",round(ur,2),"(Calculation mistake in textbook)"

Relative permeability of iron is 2154.85 (Calculation mistake in textbook)

Example 8.2, Page number 8.3

In [2]:
#Variable declaration
M = 3300    #value of magnetic filed(amp/m) 
H = 220     #strength of magnetic filed(amp/m)

#Calculations
x = (M/H)+1

#Result
print "Relative permeability of iron is",round(x,2)

Relative permeability of iron is 16.0

Example 8.3, Page number 8.4

In [4]:
from math import pi

#Variable declaration
H = 10**6        #magnetic field intensity(amp/m)
x = 1.5*10**-3   #susceptibility
Uo = 4*pi*10**-7 

#Calculations
M = x*H       #magnetization of material
B = Uo*(M+H)  #flux density

#Result
print "Magnetization =",round((M/1E+3),1),"*10^3 A/m"
print "Flux density =",round(B,3),"T"

Magnetization = 1.5 *10^3 A/m
Flux density = 1.259 T

Example 8.4, Page number 8.4

In [5]:
from math import pi

#Variable declaration
H = 10**4        #magnetic field intensity(amp/m)
x = 3.7*10**-3   #susceptibility
Uo = 4*pi*10**-7 

#Calculations
M = x*H       #magnetization of material
B = Uo*(M+H)  #flux density

#Result
print "Magnetization =",M,"A/m"
print "Flux density =",round(B,4),"wb/m^2"

Magnetization = 37.0 A/m
Flux density = 0.0126 wb/m^2

Example 8.5, Page number 8.14

In [6]:
from math import pi

#Variable declaration
I = 500*10**-3  #current(A)
d = 10*10**-2   #diameter of loop(m)

#Calculations
r = d/2         #radius(m)
A = 2*pi*r**2   #area(m^2)
Um = I*A

#Result
print "Magnetic moment =",round((Um/1E-3),3),"*10^-3 A-m^2"

Magnetic moment = 7.854 *10^-3 A-m^2

Example 8.6, Page number 8.18

In [7]:
#Variable declaration
r = 5.29*10**-11  #radius of the orbit(m)
B = 2             #field strength(Tesla)
e = 1.602*10**-19 #charge of an electron(C)
m = 9.108*10**-31 #mass of an electron(kg)

#Calculation
Uind = (e**2*r**2*B)/(4*m)

#Result
print "Change in magnetic moment =",round((Uind/1E-29),3),"*10^-29 A-m^2"

Change in magnetic moment = 3.943 *10^-29 A-m^2

Example 8.7, Page number 8.22

In [8]:
#Varaible declaration
T1 = 350         #temperature(K)
x1 = 2.8*10**-4  #susceptibility at T1
T2 = 300         #temperature(K)

#Calculation
x2 = (x1*T1)/T2

#Result
print "Susceptibility at 300k is",round((x2/1E-4),3),"*10^-4"

Susceptibility at 300k is 3.267 *10^-4

Example 8.8, Page number 8.27

In [10]:
from math import pi 

#Variable declaration
den = 8906          #density of nickel(kg/m^3)
N = 6.025*10**26    #Avogadro's number
Ma = 58.7           #atomic weight
Bs = 0.65           #magnetic induction(wb/m^2)
Uo = 4*pi*10**-7

#Calculations
n = (den*N)/Ma      #no. of nickel atoms per m^3

#Since x is very large, B = n*Uo*Um
Um = Bs/(n*Uo))

#Result
print "Magnetic moment =",Um,"A-m^2"

Magnetic moment = 5.65850692635e-24 A-m^2

Example 8.9, Page number 8.28

In [34]:
import math

#Variable declaration
H = 2         #magnetic filed intensity(wb/m^2)
U = 9.4*10**-24
k = 1.38*10**-23

#Calculations
'''
n = c*no*exp(-Eg/kT)   #no. of electrons
where Eg = -U*H
For parallel orientation,Eg = -U*H
For antiparallel orientation, Eg = U*H
therefore,
np = c*no*exp(U*H/kT)  ---(1)
na = c*no*exp(-U*H/kT) ---(2)
Dividing (1) by (2), we get,'''

T = (2*U*H)/(math.log(2)*k)

#Result
print "T=",round(T,1),"K"

T= 3.9 K

Example 8.10, Page number 8.29

In [41]:
from math import pi

#Variable declaration
Uo = 4*pi*10**-7
Ma = 157.26       #atomic weight og gadolinium
den = 7.8*10**3   #density(kg/m^3)
N = 6.025*10**26  #Avogadro's number
x = 7.1           #Bohr magnetron per atom
Um = 9.27*10**-24

#Calculations
n = (den*N)/Ma    #no. of atoms in 1 kg
n1 = n*10**-3     #no. of atoms in 1 gm
M = n1*x*Um         #magnetic moment per gram(a-m^2)

Bs = n*Uo*Um      #saturization magnetization

#Result
print "Magnetic moment per gram =",round(M,3),"Am^2"
print "Saturization magnetization =",round(Bs,3),"Wb/m^2(Calculation mistake in textbok)"

Magnetic moment per gram = 1966.851 Am^2
Saturization magnetization = 0.348 Wb/m^2(Calculation mistake in textbok)