7: Magnetic Properties

Example number 7.1, Page number 7.3

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

#Variable declaration
M = 1.4      #field(T)
H = 6.5*10**-4      #magnetic field(T)

#Calculation
chi = M/H      #susceptibility
mew_r = 1+chi       #relative permeability

#Result
print "relative permeability of iron is",round(mew_r)
print "answer given in the book is wrong"

relative permeability of iron is 2155.0
answer given in the book is wrong

Example number 7.2, Page number 7.3

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

#Variable declaration
M = 3300     #magnetisation(amp/m)
H = 220      #field strength(amp/m)

#Calculation
mew_r = (M/H)+1      #relative permeability

#Result
print "relative permeability of material is",mew_r

relative permeability of material is 16.0

Example number 7.3, Page number 7.4

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

#Variable declaration
H = 10**6      #magnetic field intensity(amp/m)
chi = 1.5*10**-3     #susceptibility

#Calculation
mew0 = 4*math.pi*10**-7
M = chi*H      #magnetisation(A/m)
B = mew0*(M+H)      #flux density(T)
M = M*10**-3
B = math.ceil(B*10**3)/10**3   #rounding off to 3 decimals

#Result
print "magnetisation of material is",M,"*10**3 A/m"
print "flux density is",B,"T"
print "answer for flux density B given in the book is wrong"

magnetisation of material is 1.5 *10**3 A/m
flux density is 1.259 T
answer for flux density B given in the book is wrong

Example number 7.4, Page number 7.5

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

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

#Calculation
mew0 = 4*math.pi*10**-7
M = chi*H      #magnetisation(A/m)
B = mew0*(M+H)      #flux density(Wb/m**2)
B = math.ceil(B*10**5)/10**5   #rounding off to 5 decimals

#Result
print "magnetisation of material is",M,"A/m"
print "flux density is",B,"Wb/m**2"

magnetisation of material is 37.0 A/m
flux density is 0.01262 Wb/m**2

Example number 7.5, Page number 7.14

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

#Variable declaration
I = 500     #current(mA)
d = 10     #diameter(cm)

#Calculation
I = I*10**-3     #current(A)
r = d/2    #radius(cm)
r = r*10**-2    #radius(m)
A = 2*math.pi*r**2   #area(m**2)
mew_m = I*A     #magnetic moment(Am**2)
mew_m = mew_m*10**3
mew_m = math.ceil(mew_m*10**3)/10**3   #rounding off to 3 decimals

#Result
print "magnetic moment associated with the loop is",mew_m,"*10**-3 Am**2"
print "answer given in the book is wrong in the 3rd decimal"

magnetic moment associated with the loop is 7.854 *10**-3 Am**2
answer given in the book is wrong in the 3rd decimal

Example number 7.6, Page number 7.19

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
r = 5.29*10**-11    #radius of orbit(m)
B = 2     #field applied(T)
e = 1.602*10**-19     #charge of electron(coulomb)
m = 9.108*10**-31    #mass of electron(kg)

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

#Result
print "change in magnetic moment is",round(mew_ind/1e-29,3),"*10^-29 Am**2"

change in magnetic moment is 3.943 *10^-29 Am**2

Example number 7.7, Page number 7.22

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
chi_1 = 2.8*10**-4     #susceptibility
T1 = 350      #temperature(K)
T2 = 300      #temperature(K)

#Calculation
#chi = C/T where C is curie constant
chi_2 = chi_1*T1/T2     #susceptibility at 300 K
chi_2 = chi_2*10**4
chi_2 = math.ceil(chi_2*10**3)/10**3   #rounding off to 3 decimals

#Result
print "susceptibility at 300 K is",chi_2,"*10**-4"

susceptibility at 300 K is 3.267 *10**-4

Example number 7.8, Page number 7.28

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
d = 8906     #density(kg/m**3)
n = 6.025*10**26     #avagadro number
AW = 58.7     #atomic weight
Bs = 0.65     #magnetic induction(Wb/m**2)
mewB = 9.27*10**-24 

#Calculation
N = d*n/AW     #number of atoms(per m**3)
mew0 = 4*math.pi*10**-7
mew_m = Bs/(N*mew0)      #magnetic moment(Am**2)
mew_m = mew_m/mewB       #magnetic moment(mewB)
mew_m = math.ceil(mew_m*10**3)/10**3   #rounding off to 3 decimals

#Result
print "the magnetic moment of Ni is",mew_m,"mewB"

the magnetic moment of Ni is 0.611 mewB

Example number 7.9, Page number 7.29

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration
H = 2     #magnetic field(Wb/m**2)
mew = 9.4*10**-24
k = 1.38*10**-23

#Calculation
#np = C*n0*math.exp(mew*H/(k*T))
#na = C*n0*math.exp(-mew*H/(k*T))
#np/na = exp(mew*H/(k*T))/exp(-mew*H/(k*T)) = exp(2*mew*H/(k*T))
#given np/na = 2. therefore exp(2*mew*H/(k*T)) = 2
T = 2*mew*H/(k*math.log(2))    #temperature(K)
T = math.ceil(T*10**2)/10**2   #rounding off to 2 decimals

#Result
print "temperature is",T,"K"

temperature is 3.94 K

Example number 7.10, Page number 7.30

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
AW = 157.26      #atomic weight
d = 7.8*10**3     #density(kg/m**3)
A = 6.025*10**26     #avagadro number
mew0 = 4*math.pi*10**-7
N = d*A/AW      #number of atoms 1 kg contains
g = N/10**3      #number of atoms 1 g contains
mew_B = 7.1      #bohr magneton
mew_m = 9.27*10**-24
mew_mg = g*mew_B*mew_m     #magnetic moment per gram(Am**2)
mew_mg = math.ceil(mew_mg*10**3)/10**3   #rounding off to 3 decimals
print "magnetic moment per gram is",mew_mg,"Am**2"
Bs = N*mew0*mew_m      #saturation magnetisation(Wb/m**2)
Bs = math.ceil(Bs*10**4)/10**4   #rounding off to 4 decimals
print "saturation magnetisation is",Bs,"Wb/m**2"
print "answers given in the book are wrong"

magnetic moment per gram is 1966.852 Am**2
saturation magnetisation is 0.3482 Wb/m**2
answers given in the book are wrong