13: Magnetic properties of solids

Example number 13.1, Page number 256

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

#Variable declaration
chi=-4.2*10**-6;    #magnetic susceptibility
H=1.2*10**5;    #magnetic field(A/m)
mew0=4*math.pi*10**-7;   #permitivity of free space(H/m)

#Calculation
M=chi*H;    #magnetisation(A/m)
B=mew0*(H+M);   #flux density(T)
mewr=(M/H)+1;   #relative permeability

#Result
print "magnetisation is",M,"A/m"
print "flux density is",round(B,3),"T"
print "relative permeability is",round(mewr,6)

magnetisation is -0.504 A/m
flux density is 0.151 T
relative permeability is 0.999996

Example number 13.2, Page number 258

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

#Variable declaration
Z=2;   #atomic number
mew0=4*math.pi*10**-7;   #permitivity of free space(H/m)
e=1.6*10**-19;   #conversion factor from J to eV
m=9.1*10**-31;    #mass of electron(kg)
N=28*10**26;   #number of atoms(per m**3)
r=0.6*10**-10;   #mean radius(m)

#Calculation
chi=-mew0*Z*e**2*N*r**2/(6*m);   #diamagnetic susceptibility

#Result
print "diamagnetic susceptibility is",round(chi*10**8,3),"*10**-8"

diamagnetic susceptibility is -11.878 *10**-8

Example number 13.3, Page number 259

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

#Variable declaration
n=2;
a=2.55*10**-10;   #lattice constant(m)
chi=5.6*10**-6;   #susceptibility
Z=1;
mew0=4*math.pi*10**-7;   #permitivity of free space(H/m)
e=1.6*10**-19;   #conversion factor from J to eV
m=9.1*10**-31;    #mass of electron(kg)

#Calculation
N=n/(a**3);    #number of electrons per unit volume(per m**3)
rbar=math.sqrt(chi*6*m/(mew0*Z*e**2*N));    #radius of atom(m)

#Result
print "radius of atom is",round(rbar*10**10,3),"angstrom"

radius of atom is 0.888 angstrom

Example number 13.4, Page number 260

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

#Variable declaration
mew0=4*math.pi*10**-7;   #permitivity of free space(H/m)
k=1.38*10**-23;   #boltzmann constant(J/K)
T=300;     #temperature(K)
N=6.5*10**25;   #number of atoms(per m**3)
mew=9.27*10**-24;    

#Calculation
chi=mew0*N*mew**2/(3*k*T);    #susceptibility

#Result
print "susceptibility is",round(chi*10**7,2),"*10**-7"

susceptibility is 5.65 *10**-7

Example number 13.5, Page number 260

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration
rho=4370;    #density(kg/m**3)
NA=6.02*10**26;   #avagadro number(k/mole)
M=168.5;    #molecular weight(kg/kmol)
mew0=4*math.pi*10**-7;   #permitivity of free space(H/m)
k=1.38*10**-23;   #boltzmann constant(J/K)
T=300;     #temperature(K)
H=2*10**5;   #electric field(A/m)
mew=2*9.27*10**-24; 

#Calculation
N=rho*NA/M;   
chi=mew0*N*mew**2/(3*k*T);    #susceptibility
M=chi*H;   #magnetisation(A/m)

#Result
print "susceptibility is",round(chi*10**4,4),"*10**-4"
print "magnetisation is",round(M,3),"A/m"
print "answer varies due to rounding off errors"

susceptibility is 5.4298 *10**-4
magnetisation is 108.596 A/m
answer varies due to rounding off errors