8: Magnetic Materials

Example number 8.1, Page number 170

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
r=0.05*10**-9;     #radius(m)
B=1;     #magnetic induction(web/m**2)
e=1.6*10**-19;    #charge(c)
m=9.1*10**-31;    #mass(kg)

#Calculation
d_mew=e**2*r**2*B/(4*m);       #change in magnetic moment(Am**2)

#Result
print "change in magnetic moment is",round(d_mew*10**30,2),"*10**-30 Am**2"
print "answer in the book is wrong"

change in magnetic moment is 17.58 *10**-30 Am**2
answer in the book is wrong

Example number 8.2, Page number 170

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
chi=-0.5*10**-5;       #magnetic susceptibility
H=9.9*10**4;        #magnetic field intensity(amp/m)
mew0=4*math.pi*10**-7;

#Calculation
I=chi*H;      #intensity of magnetisation(amp/m)
B=mew0*H*(1+chi);       #magnetic flux density(wb/m**2)

#Result
print "intensity of magnetisation is",I,"amp/m"
print "magnetic flux density is",round(B,3),"wb/m**2"

intensity of magnetisation is -0.495 amp/m
magnetic flux density is 0.124 wb/m**2

Example number 8.3, Page number 170

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
H=220;        #magnetic field intensity(amp/m)
I=3300;      #magnetisation(amp/m)

#Calculation
mewr=1+(I/H);      #relative permeability

#Result
print "relative permeability is",int(mewr)

relative permeability is 16

Example number 8.4, Page number 171

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
r=6.1*10**-11;     #radius of atom(m)
new=8.8*10**15;    #frequency(revolution/sec)
mew0=4*math.pi*10**-7;
e=1.6*10**-19;    #charge(c)

#Calculation
i=e*new;      #current(amp)
B=mew0*i/(2*r);     #magnetic induction(web/m**2)
mew=i*math.pi*r**2;     #dipole moment(amp m**2)

#Result
print "magnetic induction is",round(B,3),"web/m**2",i
print "dipole moment is",round(mew*10**23,3),"*10**-23 amp m**2"
print "answers in the book are wrong"

magnetic induction is 14.503 web/m**2 0.001408
dipole moment is 1.646 *10**-23 amp m**2
answers in the book are wrong

Example number 8.5, Page number 171

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
Is=1.96*10**6;        #saturation magnetisation(amp/m)
a=3*10**-10;        #cube edge(m)
mewB=9.27*10**-24;   #bohr magneton(amp/m**2)
n=2;       #number of atoms

#Calculation
N=n/(a**3);      
mew_bar=Is/(N*mewB);     #average number of bohr magnetons(bohr magneton/atom)

#Result
print "average number of bohr magnetons is",round(mew_bar,3),"bohr magneton/atom"

average number of bohr magnetons is 2.854 bohr magneton/atom

Example number 8.6, Page number 172

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
I=3000;      #magnetisation(amp/m)
mew0=4*math.pi*10**-7;
B=0.005;     #flux density(weber/m**2)

#Calculation
H=(B/mew0)-I;      #magnetizing force(amp/m)
mewr=(I/H)+1;      #relative permeability

#Result
print "magnetizing force is",round(H,3),"amp/m"
print "relative permeability is",round(mewr,3)
print "answer in the book varies due to rounding off errors"

magnetizing force is 978.874 amp/m
relative permeability is 4.065
answer in the book varies due to rounding off errors

Example number 8.7, Page number 172

In [7]:
#importing modules
import math
from __future__ import division

#Variable declaration
H=1800;      #magnetizing force(amp/m)
chi=3*10**-5;    #magnetic flux(wb)
A=0.2*10**-4;    #area(m**2)

#Calculation
B=chi/A;
mew=B/H;     #permeability(henry/m)

#Result
print "permeability is",round(mew*10**4,3),"*10**-4 henry/m"
print "answer in the book is wrong"

permeability is 8.333 *10**-4 henry/m
answer in the book is wrong

Example number 8.8, Page number 172

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
r=0.04;    #radius(m)
i=1000*10**-3;    #current(mA)
B=10**-3;   #magnetic flux density(wb/m**2)
theta=45;   #angle(degrees)

#Calculation
A=math.pi*r**2;     #area(m**2)
mew=i*A;        #magnetic dipole moment(amp m**2)
theta=theta*math.pi/180;
tow=i*B*math.cos(theta);    #torque(Nm)

#Result
print "magnetic dipole moment is",round(mew*10**3,4),"*10**-3 amp m**2"
print "answer in the book varies due to rounding off errors"
print "torque is",round(tow*10**3,4),"*10**-3 Nm"

magnetic dipole moment is 5.0265 *10**-3 amp m**2
answer in the book varies due to rounding off errors
torque is 0.7071 *10**-3 Nm

Example number 8.9, Page number 173

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
A=100;     #area(m**2)
B=0.01;    #flux density(wb/m**2)
H=40;      #magnetic field(amp/m)
M=7650;    #atomic weight(kg/m**3)

#Calculation
h=A*B*H;    #hysteresis loss per cycle(J/m**3)

#Result
print "hysteresis loss per cycle is",h,"J/m**3"

hysteresis loss per cycle is 40.0 J/m**3

Example number 8.10, Page number 173

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=200;     #hysteresis loss per cycle(J/m**3)
M=7650;    #atomic weight(kg/m**3)
n=100;     #magnetisation cycles per second

#Calculation
hpl=h*n;     #hysteresis power loss per second(watt/m**3)
pl=hpl/M;    #power loss(watt/kg)

#Result
print "hysteresis power loss per second is",hpl,"watt/m**3"
print "power loss is",round(pl,3),"watt/kg"

hysteresis power loss per second is 20000 watt/m**3
power loss is 2.614 watt/kg