# Chapter 2 : Magnetic Circuits¶

## Example 2.1 Page No : 2.3¶

In [1]:
import math

# Variables
N = 200.;				#turns
c = 600.;				#mm(circumference)
A = 500.;				#m**2(Cross section area)
I = 4.;				#A(Current through coil)

# Calculations and Results
H = I*N/(c*10**-3);				#A/m(Magnetic field strength)
print "(a) Magnetic field strength(A/m) : %.2f"%H
mu0 = 4*math.pi*10**-7;				#constant
FD = mu0*H*10**6;				#micro T(Flux density)
print "(b) Flux density(micro T) : %.2f"%FD
Ft = FD*A*10**-6;				#micro Wb(Total flux)
print "(c) Total flux(micro Wb) : %.2f"%Ft
#Answer in the book is wrong.

(a) Magnetic field strength(A/m) : 1333.33
(b) Flux density(micro T) : 1675.52
(c) Total flux(micro Wb) : 0.84


## Example 2.2 Page No : 2.4¶

In [2]:
import math

# Variables
fi = 0.015;				#Wb(flux)
ag = 2.5;				#mm(airgap)
Ae = 200;				#cm**2(Effective area)

# Calculations
FD = fi/(Ae*10**-4);				#T(Flux density)
mu0 = 4*math.pi*10**-7;				#constant
H = FD/mu0;				#A/m(Magnetic field strength)
mmf = H*ag*10**-3;				#A(magnetomotive force required)

# Results
print "Magnetomotive force required(A) : %.2f"%mmf

#Answer in the book is not accurate.

Magnetomotive force required(A) : 1492.08


## Example 2.3 Page No : 2.7¶

In [3]:
import math

# Variables
A = 500.;				#mm**2(Cross sectional area)
c = 400.;				#mm(circumference)
N = 200.;				#turns
fi = 800.;				#micro Wb(flux)

# Calculations and Results
B = fi*10**-6/(A*10**-6);				#T(Flux density)
mu0 = 4*math.pi*10**-7;				#constant
mur = 380.;				#relative permeability
S = (c/1000)/(mur*mu0*A*10**-6);				#A/Wb(Relucmath.tance)
print "(a) Relucmath.tance of the ring(A/Wb) :%.2e"%S
mmf = fi*10**-6*S;				#A
Im = mmf/N;				#A(Magnetizing current)

print "(b) Required magnetizing current(A) :%.2f"%Im

(a) Relucmath.tance of the ring(A/Wb) :1.68e+06
(b) Required magnetizing current(A) :6.70


## Example 2.4 Page No : 2.8¶

In [4]:
import math

# Variables
la = 80.;				#mm
Aa = 50.;				#mm**2(Cross sectional area)
lb = 60.;				#mm
Ab = 90.;				#mm**2(Cross sectional area)
lc = 0.5;				#mm(airgap)
Ac = 150.;				#mm**2(Cross sectional area)
N = 4000.;				#turns
Bc = 0.30;				#T(Flux density in airgap)

# Calculations
mu0 = 4*math.pi*10**-7;				#constant
mur = 1300;				#relative permeability
fi = Bc*Ac*10**-6;				#Wb(flux)
Fa = fi*la*10**-3/(mu0*mur*Aa*10**-6);				#At
Fb = fi*lb*10**-3/(mu0*mur*Ab*10**-6);				#At
Fc = fi*lc*10**-3/(mu0*1*Ac*10**-6);				#At
F = Fa+Fb+Fc;				#At
I = F/N*1000;				#mA

# Results
print "Coil current(mA) : %.2f"%I

Coil current(mA) : 45.45


## Example 2.5 Page No : 2.12¶

In [5]:
# Variables
L = 0.5;				#H
deltaI = 2-5;				#A
deltaT = 0.05;				#sec

# Calculations
dIBYdT = deltaI/deltaT;				#A/s
emf = L*dIBYdT;				#V

# Results
print "emf induced(V) : %.2f"%emf

emf induced(V) : -30.00


## Example 2.6 Page No : 2.14¶

In [7]:
# Variables
N = 300;				#turns
L = 10.;				#mH
I = 5;				#A

# Calculations and Results
fi = L*10**-3/N*I*10**6;				#micro Wb
print "(a) Flux produced(micro Wb) : %.f"%fi
#on reverse the current
delta_fi = 2*fi;				#micro Wb
#(as it goes to zero and increase to same value in reverse direction)
deltaT = 8*10**-3;				#seconds
dfiBYdT = delta_fi*10**-6/deltaT;				#Wb/s
emf = N*dfiBYdT;				#V(Average emf induced)
print "(b) Average emf induced(V) : %.2f"%emf

(a) Flux produced(micro Wb) : 167
(b) Average emf induced(V) : 12.50


## Example 2.7 Page No : 2.16¶

In [9]:
# Variables
c = 400.;				#mm(circumference)
A = 500.;				#mm**2(Cross sectional area)
N = 200.;				#turns

# Calculations and Results
#Part (a)
I = 2;				#A
H = N*I/(c*10**-3);				#A/m
B = 1.13;				#T(Corresponding Flux density)
fi = B*A*10**-6;				#Wb(total flux)
L = N*fi/I*1000;				#mH
print "(a) Inductance of coil(mH) : %.2f"%L

#Part (a)
I = 10;				#A
H = N*I/(c*10**-3);				#A/m
B = 1.63;				#T(Corresponding Flux density)
fi = B*A*10**-6;				#Wb(total flux)
L = N*fi/I*1000;				#mH
print "(b) Inductance of coil(mH) : %.2f"%L

(a) Inductance of coil(mH) : 56.50
(b) Inductance of coil(mH) : 16.30


## Example 2.8 Page No : 2.16¶

In [8]:
import math

# Variables
c = 400;				#mm(circumference)
A = 500;				#mm**2(Cross sectional area)
N = 200;				#turns

# Calculations
mu0 = 4*math.pi*10**-7;				#constant
L = mu0*A*10**-6*(N**2)/(c*10**-3)*10**6;				#micro H

# Results
print "Inductance(micro H) : %.2f"%L

Inductance(micro H) : 62.83


## Example 2.10 Page No : 2.23¶

In [9]:
import math

# Variables
A = 800;				#mm**2(Cross sectional area)
N1 = 500;				#turns
N2 = 700;				#turns
mur = 1200;				#relative permeability

# Calculations and Results
mu0 = 4*math.pi*10**-7;				#constant
S = 2*math.pi*r*10**-3/(mu0*mur*A*10**-6);				#H
L1 = N1**2/S;				#H
print "Self Inductance of coil 1(H) : %.2f"%L1

L2 = N2**2/S;				#H
print "Self Inductance of coil 2(H) : %.2f"%L2

k = 1;				#constant
M = k*math.sqrt(L1*L2);				#H
print "Mutual Inductance(H) : %.2f"%M

Self Inductance of coil 1(H) : 0.28
Self Inductance of coil 2(H) : 0.55
Mutual Inductance(H) : 0.40