14: Magnetic Properties of Materials

Example number 14.1, Page number 306

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

#Variable declaration
N = 6.02*10**23;      #Avogadro's number(per mole)
A = 56;      #Atomic weight of the substance(g/mole)
d = 7.9;     #Density of the substance(g/cm**3)
m_B = 9.27*10**-24;     #Bohr's Magneton(J/T)

#Calculation
m = 2.2*m_B;       #Magnetic moment of substance(J/T)
n = d*N/A ;      #Number of atoms per unit volume of the substance(per cm**3)
n = n*10**6;     #Number of atoms per unit volume of the substance(per m**3)
M = n*m;         #Spontaneous magnetisation of the substance(A/m)
M = M/10**6;
M = math.ceil(M*10**3)/10**3;     #rounding off the value of M to 3 decimals

#Result
print "The spontaneous magnetisation of the substance is",M,"*10**6 A/m"

The spontaneous magnetisation of the substance is 1.732 *10**6 A/m

Example number 14.2, Page number 307

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

#Variable declaration
H = 200;        #Field strength to which the ferromagnetic material is subjected(A/m)
M = 3100;       #Magnetisation of the ferromagnetic material(A/m)

#Calculation
chi = M/H;      #Magnetic susceptibility
mew_r = 1 + chi;    #Relative permeability of ferromagnetic material

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

The relative permeability of ferromagnetic material is 16.5

Example number 14.3, Page number 307

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

#Variable declaration
H = 300;        #Field strength to which the ferromagnetic material is subjected(A/m)
M = 4400;       #Magnetisation of the ferromagnetic material(A/m)

#Calculation
chi = M/H;      #Magnetic susceptibility
mew_r = 1 + chi;    #Relative permeability of ferromagnetic material
mew_r = math.ceil(mew_r*100)/100;     #rounding off the value of mew_r to 2 decimals

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

The relative permeability of ferromagnetic material is 15.67

Example number 14.4, Page number 307

In [8]:
#importing modules
import math

#Variable declaration
mew_0 = 4*math.pi*10**-7;       #Magnetic permeability of free space(Tm/A)
H = 10000;         #Field strength to which the diamagnetic material is subjected(A/m)
chi = -0.4*10**-5;       #Magnetic susceptibility

#Calculation
M = chi*H;        #Magnetisation of the diamagnetic material(A/m)
B = mew_0*(H + M);      #Magnetic flux density of diamagnetic material(T)
B = math.ceil(B*10**4)/10**4;     #rounding off the value of B to 4 decimals

#Result
print "The magnetisation of diamagnetic material is",M, "A/m"
print "The magnetic flux density of diamagnetic material is",B, "T"

The magnetisation of diamagnetic material is -0.04 A/m
The magnetic flux density of diamagnetic material is 0.0126 T

Example number 14.5, Page number 307

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

#Variable declaration
mew_0 = 4*math.pi*10**-7;      #Magnetic permeability of free space(Tm/A)
H = 1.2*10**5;      #Field strength to which the diamagnetic material is subjected(A/m)
chi = -4.2*10**-6;      #Magnetic susceptibility

#Calculation
M = chi*H;      #Magnetisation of the diamagnetic material(A/m)
B = mew_0*(H + M);     #Magnetic flux density of diamagnetic material(T)
B = math.ceil(B*10**3)/10**3;     #rounding off the value of B to 3 decimals
mew_r = M/H + 1;       #The relative permeability of diamagnetic material
mew_r = math.ceil(mew_r*10**6)/10**6;     #rounding off the value of mew_r to 6 decimals

#Result
print "The magnetisation of diamagnetic material is",M, "A/m"
print "The magnetic flux density of diamagnetic material is",B, "T"
print "The relative permeability of diamagnetic material is",mew_r

The magnetisation of diamagnetic material is -0.504 A/m
The magnetic flux density of diamagnetic material is 0.151 T
The relative permeability of diamagnetic material is 0.999996

Example number 14.6, Page number 308

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
chi = 5.6*10**-6;      #Magnetic susceptibility of diamagnetic material
m = 9.1*10**-31;      #Mass of an electron(kg)
mew_0 = 4*math.pi*10**-7;      #Magnetic permeability of free space(Tm/A)
Z = 1;      #Atomic number
e = 1.6*10**-19;     #Electronic charge(C)
a = 2.53;     #Lattice parameter of bcc structure(A)

#Calculation
a = a*10**-10;    #Lattice parameter of bcc structure(m)
N = 2/a**3;       #The number of electrons per unit volume(per metre cube)
r = math.sqrt(chi*6*m/(mew_0*Z*e**2*N));    #Mean radius of body centered cubic structure(m)
r = r*10**10;      #Mean radius of body centered cubic structure(A)
r = math.ceil(r*100)/100;     #rounding off the value of r to 2 decimals

#Result
print "The mean radius of body centered cubic structure is",r, "A"

The mean radius of body centered cubic structure is 0.88 A

Example number 14.7, Page number 308

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

#Variable declaration
mew_0 = 4*math.pi*10**-7;     #Magnetic permeability of free space(Tm/A)
N_A = 6.02*10**26;       #Avogadro's number(per kmol)
rho = 4370;       #Density of paramegnetic salt(kg/metre cube)
M = 168.5;      #Molecular weight of paramagnetic salt(g/mol)
T = 27;     #Temperature of paramagnetic salt(C)
H = 2*10**5;     #Field strength to which the  paramagnetic salt is subjected(A/m)
mew_B = 9.27*10**-24;      #Bohr's magneton(Am**2)
p = 2;          #Number of Bohr magnetons per molecule
k = 1.38*10**-23;      #Boltzmann constant(J/K)

#Calculation
T = T+273;     #Temperature of paramagnetic salt(K)
N = rho*N_A/M;       #Total density of atoms in the paramagnetic salt(per meter cube)
chi_para = mew_0*N*p**2*mew_B**2/(3*k*T);      #Magnetic susceptibility of paramagnetic salt
chi_para = chi_para*10**4;
chi_para = math.ceil(chi_para*10**2)/10**2;     #rounding off the value of chi_para to 2 decimals
M = chi*H;       #Magnetisation of paramagnetic salt(A/m)
M = math.ceil(M*10)/10;     #rounding off the value of M to 1 decimal

#Result
print "The magnetic susceptibility of paramagnetic salt is",chi_para,"*10**-4"
print "The magnetisation of paramagnetic salt is",M, "A/m"

#answer for magnetisation is not given in the textbook

The magnetic susceptibility of paramagnetic salt is 5.43 *10**-4
The magnetisation of paramagnetic salt is 1.2 A/m
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