Chapter4:MAGNETIC PROPERTIES OF MATERIALS

Eg1:pg-153

In [1]:
import math
phi_B=2.4e-5  #magnetic flux in weber
A=0.2         #cross-sectional area in cm**2
H=1600        #magnetising field in A/m
mu_o=4*round(math.pi,2)*1e-7 #absolute permeability of air in N/A**2
B=phi_B/(A*1e-4)
mu=B/H
Xm=mu/mu_o-1
print"Magnetic permeability of iron bar is ","{:.1e}".format(mu),"N/A**2"
print"Magnetic susceptibility of iron bar is ",round(Xm,2)

Magnetic permeability of iron bar is  7.5e-04 N/A**2
Magnetic susceptibility of iron bar is  596.13

Eg2:pg-154

In [2]:
import math
Xm=948e-11      #magnetic susceptibility of a medium
pi=1            #let
mu_o=4*pi*1e-7  #absolute permeability of air in H/m
mu_r=1+Xm
mu=int(mu_r)*mu_o
print"Relative Permeability is =",mu_r,"=",int(mu_r),"or >",int(mu_r)
print" Relative permeability is slightly greater than one."
print"Permeability is = %s*pi H/m"%mu #answer in book is 4*(pi)*1e-7 H/m

Relative Permeability is = 1.00000000948 = 1 or > 1
 Relative permeability is slightly greater than one.
Permeability is = 4e-07*pi H/m

Eg3:pg-154

In [3]:
import math
mu_r=1200 #relative permeability of iron rod
n=5       #number of turns per cm
i=0.5     #current in ampere
V=1e-3    #volume of iron rod in m**3
I=(mu_r-1)*(n*1e2)*i
M=I*V
print"Magnetic moment is ","{:.0e}".format(M),"Am**2"

Magnetic moment is  3e+02 Am**2

Eg4:pg-155

In [4]:
import math
mu_r=100  #relative permeability of iron rod
n=300     #number of turns per meter
i=0.5     #current in ampere
D=10      #diameter of iron rod in mm
r=D/2     #radius of iron rod in mm
l=2       #length of iron rod in meter
I=(mu_r-1)*n*i
V=round(math.pi,2)*(r*1e-3)**2*l
M=I*V
print"Magnetic moment is ",round(M,3),"Am**2"
#answer in book is wrong as the value of l is taken wrong in calcultion.          

Magnetic moment is  2.331 Am**2

Eg5:pg-163

In [5]:
import math
n=1e29        #number of atoms per unit volume in atoms/m**3
Pm=1.8e-23    #magnetic moment of one atom in A-m**2
K=1.38e-23    #Boltzmann's constant in J/K
T=300         #temperature in Kelvin
mu_o=4*round(math.pi,2)*10**-7 #absolute permeability of air in N/A**2
B=0.1         #magnetic flux density in weber/m**2
A=1           #cross-section area in cm**2
l=10          #length of iron bar in cm
Xm=mu_o*n*Pm**2/(3*K*T) #magnetic susceptibility of iron bar
P_m=Pm**2*B/(3*K*T)     #mean dipole moment of an iron atom in A-m**2
V=(A*1e-4)*(l*1e-2)     #volume of iron bar in m**3
n_o_a=V*n               
dm=n_o_a*P_m            #dipole moment of the iron bar 
I=Pm*n                  
m=I*V
print"Magnetic Susceptibility is ","{:.3e}".format(Xm)
print"Dipole moment is ","{:.3e}".format(dm),"Am**2"
print"Magnetisation is ","{:.1e}".format(I),"A/m"
print"Magnetic moment is ",int(m),"Am**2"#this answer is wrong in book

Magnetic Susceptibility is  3.277e-03
Dipole moment is  2.609e-03 Am**2
Magnetisation is  1.8e+06 A/m
Magnetic moment is  18 Am**2

Eg6:pg-169

In [6]:
import math
H=5e3  #Coercivity of bar magnet in ampere/m 
l=10   #length of solenoid in cm
n=50   #number of turns in solenoid
i=H*(l*1e-2)/n
print"Current is ",int(i),"amp"

Current is  10 amp

Eg8:pg-170

In [7]:
import math
a=250    #area of B-H loop in J/m**3
f=50     #frequency of a.c. in Hz
m=9.0    #mass of iron core in Kg
p=7500   #density of iron in Kg/m**3
V=m/p
n=50*60*60
E=n*V*a
print"Hysteresis loss of energy E per hour is ","{:.1e}".format(E),"J"

Hysteresis loss of energy E per hour is  5.4e+04 J

Eg10:pg-170

In [8]:
import math
A=0.785e-4   #cross-sectional area of rowland ring in m**2
Ri=5.0       #inner radius in cm
Ro=6.0       #outer radius in cm
N=400        #number of turns of wire
Bo=2e-4      #magnetic flux density in weber/m**2
mu_o=4*math.pi*10**-7 #absolute permeability of air in N/A**2
Ns=50        #number of turns in secondary coil
R=8.0        #resistance in ohm
B1=800*Bo    #magnetic flux density in weber/m**2
l=2*math.pi*(Ri+Ro)*1e-2/2
i=Bo*l/(mu_o*N)
q=Ns*B1*A/R
print"Required Current is ",i,"amp"
print"Charge passed is ",q,"coulomb"

Required Current is  0.1375 amp
Charge passed is  7.85e-05 coulomb

Eg11:pg-171

In [9]:
import math
mu_r=400 #relative permeability of iron ring
r=0.1    #mean radius of iron ring in meter
A=5e-4   #cross-sectional area of iron ring in m**2
n=1000   #number of turns of wire
i=4      #current in ampere
mu_o=4*math.pi*10**-7  #absolute permeability of air in N/A**2
B=mu_o*mu_r*n*i/(2*math.pi*r)
phi=B*A 
print"Flux in the ring is ","{:.2e}".format(phi),"weber"
n_o=500  #number of turns in secondary coil per meter
R=10     #resistance in ohm
q=2*n_o*A*B/R
print"Electricity discharged through the secondary coil is ",q,"coulomb"

Flux in the ring is  1.60e-03 weber
Electricity discharged through the secondary coil is  0.16 coulomb

Eg12:pg-171

In [10]:
import math
m=12    #weight of the iron core in Kg
p=7.5   #density of iron core in gm/cc
f=50    #frequency in cycles/sec
a=3000  #area of hysteresis loop in ergs/cm**3 (unit is misprinted in question in book)
V=(m*1e3)/p
n=f*60*60
E=n*V*a
print"Hourly loss of energy is ",E,"erg"

Hourly loss of energy is  8.64e+11 erg

Eg13:pg-172

In [12]:
import math
a=0.5   #area of B-H loop in cm**2
H=1e3   #value of 1 cm on X-axis in A/m
B=1     #value of 1 cm on Y-axis in Tesla
V=1e-3  #volume of specimen in m**3
n=50    #frequency of a.c. in Hz
area=a*H*B #area of B-H loop in J/m**3 (this is misprinted in solution in book)
p=n*V*area
print"Hysteresis power loss is ",int(p),"Watt"

Hysteresis power loss is  25 Watt