# Chapter 14 : Magnetic Properties and Materials¶

### Example 14.1 pageno : 358¶

In [1]:
# Variables
x = 1500.;			#susceptibility
h = 2400.;			#mafnetic field in A/m

# Calculations
u_r = 1+x;
m = x*h;			    #in A/m
u_0 = 4*3.14*10**-7;
b = u_0*u_r*h;			#in T

# Results
print "relative permeability  =  ",u_r
print "Intensity of magnetisation (in A/m)",m
print "Remanance (in T)  =  ",b

relative permeability  =   1501.0
Intensity of magnetisation (in A/m) 3600000.0
Remanance (in T)  =   4.5246144


### Example 14.2 page no : 368¶

In [1]:
# Variables
w = 80. + 80;			#width of loop in A/m from graph
h = 0.15 + .15;			#height of loop in Wb/sqm

# Calculations
a = w*h;			    #area of the loop in J

# Results
print "Hysteresis energy loss per unit volume of magnetic material during one cycle (in J)  =  %d J"%a

Hysteresis energy loss per unit volume of magnetic material during one cycle (in J)  =  48 J


### Example 14.3 pageno : 370¶

In [2]:
# Variables
a = 600.;			#loop area in J/sqm
f = 50.;			#in Hz
v = 0.01			#volume in cu. m

# Calculations
w = a*f*v;			#in W

# Results
print "Power loss due to Hysteresis (in W)  =  %.f watt"%w

Power loss due to Hysteresis (in W)  =  300 watt


### Example 14.4 pageno : 370¶

In [1]:
# Variables
w_h1 = 300.;           # hysteresis loss
b_1 = 0.9;             # max. flux density

y = b_1**1.7;
b_2 = 1.1;             #raised flux density(Wb/m^2)
x = b_2**1.7;
f1 = 50*10**-7;        #frequency(Hz)
f2 = 40*10**-7;        #frequency(Hz)

# Calculations
w_h2 = (w_h1*x*f2)/(y*f1);

# Results
print "Loss at 40 Hz (in W)  =  %.f W"%w_h2


Loss at 40 Hz (in W)  =  338 W


### Example 14.5 pageno : 376¶

In [2]:
# Variables
m = 6000.;             # megnetization
u_r = 200000.;         # relative permeability

# Calculations
x = u_r-1;
h = m/x;
u_0 = 4*3.14*10**-7;
b = u_0*u_r*h;

# Results
print "Magnetic strength (in T)  =  %.5f tesla"%b

Magnetic strength (in T)  =  0.00754 tesla


### Example 14.6 pageno : 376¶

In [10]:
# Variables
b = 9.27*10**-24;			#Bohr Magneton in A/sqm
m = 0.6*b;

# Calculations
a = 0.35*10**-9;
n = 4.;			#FCC
m_g = n*m/a**3;			#in A/m

# Results
print "Saturation Magnetisation (in A/m)  = %.2e A/m"%m_g

Saturation Magnetisation (in A/m)  = 5.19e+05 A/m


### Example 14.9 page no : 381¶

In [11]:
# Variables
f = 50.;			#in Hz
L = 100.;			#Eddy current loss in transformer in W
f1 = 60.;			#in Hz
f2 = 100;			#in Hz

# Calculations
w_e = L*(f1/f)**2;			#in W
w_ee = L*(f2/f)**2;			#in W

# Results
print "Eddy current loss at 60 Hz (in W)  =  %.1f W"%w_e
print "Eddy current loss at 100 Hz (in W)  =  %.1f W"%w_ee

Eddy current loss at 60 Hz (in W)  =  144.0 W
Eddy current loss at 100 Hz (in W)  =  400.0 W


### Example 14.13 pageno : 382¶

In [12]:
# Variables
l = .25;			#in m
n = 400.;			#turns
i = 15.;			#in A

# Calculations
u_0 = 1.257*10**-6;			#in H/m
h = n*i/l;			#in AT/m
u_r = 1;			#relative permeability
b = u_0*u_r*h;			#in wB/sqm

# Results
print "Magnetic field strength (in AT/m)  =  %.1f AT/m"%h
print "Flux density (in Wb/sq m)  =  %.2f Wb/m**2"%b

Magnetic field strength (in AT/m)  =  24000.0 AT/m
Flux density (in Wb/sq m)  =  0.03 Wb/m**2