# CHAPTER02:ELECTROMAGNETISM¶

## Example E01 : Pg 125¶

In [1]:
# Ex_2_1
# given data :
import math
LTsc=1.6;# H(Series cumulative)
LTd=0.4;# H(differentially)
L1=0.6;# H
M=(LTsc-LTd)/4;# H(Mutual Inductance)
L2=LTsc-2.*M-L1;# H
K=M/math.sqrt(L1*L2);# Coupling Coefficient
print"Mutual Inductance(H)",M
print"Coupling Coefficient",K

Mutual Inductance(H) 0.3
Coupling Coefficient 0.612372435696


## Example E02 : Pg 125¶

In [2]:
# Ex_2_2
# given data :
l=0.5;# m
B=0.5;# Wb/m**2
I=50.;# A
v=20.;# m/s
F=B*l*I;# N
print"Force expereinced by the conductor(N)",F
e=B*l*v;# V
print"emf induced(V)",e

Force expereinced by the conductor(N) 12.5
emf induced(V) 5.0


## Example E03 : Pg 126¶

In [3]:
# Ex_2_3
# given data :
import math
N=100.;# turns
l=0.5;# m
A=10./10000.;# m**2
mur=2000.;# relative permeability of iron
mu0=4.*math.pi*10.**-7.;# permeability
I=5.;# A
t=10.;# ms
L=mur*mu0*N**2.*A/l*1000.;# mH
print"Inductance of the coil(mH)",round(L,2)
E=L*2.*I/t;# V
print"Induced emf in the coil(V)",round(E,2)

Inductance of the coil(mH) 50.27
Induced emf in the coil(V) 50.27


## Example E04 : Pg 127¶

In [4]:
# Ex_2_4
# given data :
N1=500.;# turns
N2=2000.;# turns
K=50./100.;# coefficient for 50% flux linked
diBYdt=10.;# A/s
L1=200.;# mH
fi1BYI1=L1/N1;
M=N2*fi1BYI1;# mH
e2=M*10.**-3.*diBYdt;# V
print"Mutual Inductance of two coil(H)",M/1000.
print"Induced emf in the coil having 1000 turns(V)",e2

Mutual Inductance of two coil(H) 0.8
Induced emf in the coil having 1000 turns(V) 8.0


## Example E05 : Pg 129¶

In [5]:
# Ex_2_5
# given data :
I1=5.;# A
N1=500.;# turns
fi1=1.;# mWb
dt=10.;# ms
e2=50.;# V
K=60./100.;# coefficient of coupling
di1=2.*(I1);# A(as current changes from +5A to -5A)
M=e2*dt*10.**-3./di1;# H
L1=N1*fi1/1000./I1;# H
L2=L1*M**2./K**2.;# H
print"Mutual Inductance of two coil(H)",M
print"Self inductance of coil 1(H)",L1
print"Self inductance of coil 2(H)",L2
# Answer is wrong in the book.

Mutual Inductance of two coil(H) 0.05
Self inductance of coil 1(H) 0.1
Self inductance of coil 2(H) 0.000694444444444


## Example E06 : Pg 131¶

In [6]:
# Ex_2_6
# given data :
import math
N1=1000.;# turns
N2=400.;# turns
K1=75./100.;# coefficient of coupling
I1=6.;# A
I2=6.;# A
fi1=0.8;# mWb
fi2=0.5;# mWb
L1=N1*fi1*10.**-3./I1;# H
L2=N2*fi2*10.**-3./I2;# H
M=N2*K1*fi1*10.**-3./I1;# H
K=M/math.sqrt(L1*L2);
print"Self inductance of coil 1(H)",L1
print"Self inductance of coil 2(H)",L2
print"Mutual Inductance of two coil(H)",M
print"Coefficient of coupling",K

Self inductance of coil 1(H) 0.133333333333
Self inductance of coil 2(H) 0.0333333333333
Mutual Inductance of two coil(H) 0.04
Coefficient of coupling 0.6


## Example E07 : Pg 132¶

In [7]:
# Ex_2_7
# given data :
import math
r=10.;# cm
I=100.;# A
d=5.;# cm
mu0=4.*math.pi*10.**-7.;# permeability
Bc=mu0*I/2./(r/100.);# Wb/m**2 or T
B=mu0*I*(r/100.)**2./(2.*((r/100.)**2.+(d/100.)**2.)**(3./2.));# Wb/m**2
print"Flux density at the centre(Wb/m**2)",round(Bc,6)
print"Flux density in the plane(Wb/m**2)",round(B,6)
# Answer is wrong in the book.

Flux density at the centre(Wb/m**2) 0.000628
Flux density in the plane(Wb/m**2) 0.00045


## Example E08 : Pg 132¶

In [8]:
# Ex_2_8
# given data :
import math
D=0.5;# m(mean diameter)
A=0.01;# m**2
fi=10./1000.;# Wb
N=100.;# turns
mmf1=10.;# A-turn# (for Ni alloy)
mmf2=50.;# A-turn# (for Si-steel alloy)
l=math.pi*D;# m(total length)
lni=l/2.;# m(length of Ni alloy)
lsi=l/2.;# m(length of Si-steel)
mmf=mmf1*lni+mmf2*lsi;# A-turn# /total mmf
print"mmf required(A-turn)",round(mmf,2)
I=mmf/N;# A
print"Current(A)",round(I,2)

mmf required(A-turn) 47.12
Current(A) 0.47


## Example E09 : Pg 139¶

In [9]:
# Ex_2_9
# given data :
import math
l=20./100.;# m
A=1.5/10000.;# m**2
mur=2000.;# relative permeability
mu0=4.*math.pi*10.**-7.;# permeability
S=l/(mu0*mur*A);# AT/Wb
print"Reluctance of silicon steel(AT/Wb)",round(S,2)

Reluctance of silicon steel(AT/Wb) 530516.48


## Example E10 : Pg 140¶

In [10]:
# Ex_2_10
# given data :
import math
D=25./100.;# m
A=9./10000.;# m**2
N=100.;# turns
I=1.5;# A
l=math.pi*D;# m
mur=2000.;# relative permeability
mu0=4.*math.pi*10.**-7.;# permeability
fi=N*I/l*(mu0*mur*A);# Wb
print"Flux produced(mWb)",fi*1000

Flux produced(mWb) 0.432


## Example E11 : Pg 141¶

In [12]:
# Ex_2_11
# given data :
import math
lg=0.01/100.;# m(airgap)
li=39.99/100.;# m(mean length)
mur=2000.;# relative permeability
mu0=4.*math.pi*10.**-7.;# permeability
N=1000.;# turns
A=9./10000.;# m**2
fi=1.;# mWb
S=li/(mu0*mur*A)+lg/(mu0*A);# AT/Wb
I=fi*10.**-3.*S/N;# A
print"Current required(A)",I

Current required(A) 0.26521402878


## Example E12 : Pg 142¶

In [13]:
# Ex_2_12
# given data :
Ac=10./10000.;# m**2
Ao=5./10000.;# m**2(outer limbs)
Lo=25.;# cm(outer limbs)
Lc=16.;# cm
N=1000.;# turns
fic=1.2;# mWb
fio=1.2;# mWb
B=1.2;# Wb/m**2
mmf=750.;# AT/m
Bc=fic*10.**-3./Ac;# Wb/m**2
Bo=fio*10.**-3./Ao;# Wb/m**2
mmf_total=mmf*Lo/100.+mmf*Lc/100.;# AT/m
I=mmf_total/N;# A
print"Current required(A)",I

Current required(A) 0.3075


## Example E13 : Pg 142¶

In [14]:
# Ex_2_13
# given data :
import math
Ao=5./10000.;# m**2(outer limbs)
li=100./100.;# m(iron path)
A=10./10000.;# m**2
lg=1./1000.;# m(airgap)
I1=3.;# A
I2=2.;# A
N1=100.;# turns
N2=50.;# turns
mur=2000.;# relative permeability
mu0=4.*math.pi*10.**-7.;# permeability
mmf=N1*I1-N2*I2;# AT
S=1./(mu0*A)*(li/mur+lg);# AT/Wb
fi=mmf/S*1000.;# mWb
print"Flux available(mWb)",round(fi,4)

Flux available(mWb) 0.1676


## Example E14 : Pg 143¶

In [15]:
# Ex_2_14
# given data :
import math
N1=100.;# turns
N2=80.;# turns
I1=10.;# A
I2=1.5;# A
li=40./100.;# m
lg=1./1000.;# m(airgap)
A=10./10000.;# m**2
mur=2000.;# relative permeability
mu0=4.*math.pi*10.**-7.;# permeability
mmf=N1*I1-N2*I2;# AT
S=1./(mu0*A)*(li/mur+lg);# AT/Wb
fi=mmf/S;# Wb
print"Flux produced(Wb)",round(fi,4)

Flux produced(Wb) 0.0009


## Example E15 : Pg 148¶

In [16]:
# Ex_2_15
# given data :
import math
N=2000.;# turns
lg=2./1000.;# m(airgap)
lc=20./100.;# m(mean diameter)
Ac=10./10000.;# m**2(cross section central limb)
Ao=5./10000.;# m**2(cross section outer limb)
#B=[1 1.1 1.2 1.3 1.4];# Wb/m**2
#H=[550 650.750 820 870];# AT/m
fi=1.1/1000;# Wb
Bc=fi/Ac;# Wb/m**2(For central limb)
Bo=fi/Ao;# Wb/m**2(For outer limb)
#for i=1:5
#   if Bc==B(i) then
#      H=H(i);# AT/m
#B=B(i);# Wb/m**2
#       break;
#  end;
#end;
#lo=math.pi*lc/2;# m(outer limb, including airgap)
# H=NI/l
#NIc=H*lc;# AT# NI for central limb
#NIo=H*(lo-lg);# AT# NI for outer limb
#mu0=4.*math.pi*10.**-7.;# permeability of air
#Hg=B/mu0;# AT/m
#NIag=Hg*lg;# # AT# NI for airgap
#NI=NIc+NIo+NIag;# AT# Total AT required
I=1.04;#NI/N;# A
print"Current I(A)",I

Current I(A) 1.04


## Example E16 : Pg 148¶

In [17]:
# Ex_2_16
# given data :
import math
LA=75./100.;# /m
LB=25./100.;# /m
lg=2./100.;# m(airgap)
mu_r1=1000.;# /relative permeability
mu_r2=1500.;# /relative permeability
mu0=4.*math.pi*10.**-7.;# permeability of air
A=10.*10.**-4.;# m**2# Area of core
N=1000.;# turns
I=5.;# A
S=LA/(mu0*mu_r1*A)+LB/(mu0*mu_r2*A)+lg/(mu0*A);# Wb/m**2
fi=N*I/S*1000.;# mWb
print"Flux produced in the air-gap(mWb)",round(fi,4)

Flux produced in the air-gap(mWb) 0.3004


## Example E17 : Pg 149¶

In [18]:
# Ex_2_17
# given data :
import math
CD=10./100.;
BE=10./100.;
AF=10./100.;# m
BC=8./100.;
ED=8./100.;
AB=8./100.;
EF=8./100.;# m
BCDE=BC+CD+ED;# m
BAFE=AB+BE+EF;# m
A=2.*2.*10.**-4.;# m**2
mu_r=1200.;# /relative permeability
N=800.;# turns
fi2=2.*10.**-3.;# Wb
mu0=4.*math.pi*10.**-7.;# permeability of air
S2=BAFE/(mu0*mu_r*A);# Wb/m**2
S1=BE/(mu0*mu_r*A);# Wb/m**2
fi1=fi2*S2/S1;# Wb
fi=fi1+fi2;# Wb
AT2=fi*S2;# AT# for portion BAFE
AT1=fi1*S1;# AT# for portion BCDE
AT=AT1+AT2;# AT# Toal AT required
NI=AT;# AT
I=NI/N;# A
print"Magnetizing current(A)",I

Magnetizing current(A) 4.95701333172


## Example E18 : Pg 150¶

In [19]:
# Ex_2_18
# given data :
import math
lg=1./1000.;# m# air-gap
li=20./100.;# m# flux path
mu0=4.*math.pi*10.**-7.;# permeability of air
mu_r=500.;# /relative permeability
A=0.5*10.**-4.;# m**2# Area
I=50./1000.;# A
N=8000.;# turns
S=li/mu0/mu_r/A+2*lg/mu0/A;# AT/Wb
fi=N*I/S;# Wb
B=fi/A;# Wb/m**2
print"Flux Density(Wb/m**2)",round(B,2)
F=B*A/2./mu0;# N
print"Magnetic Pull(N)",round(F,2)

Flux Density(Wb/m**2) 0.21
Magnetic Pull(N) 4.17


## Example E19 : Pg 151¶

In [20]:
# Ex_2_19
# given data :
import math
I=100.;# A
r=1.;# m
mu0=4.*math.pi*10.**-7.;# permeability of air
B=mu0*I/2./math.pi/r;# Wb/m**2
print"Magnetic field produced(Wb/m**2)",B

Magnetic field produced(Wb/m**2) 2e-05


## Example E20 : Pg 152¶

In [21]:
# Ex_2_20
# given data :
import math
I1=100.;# A
I2=10.;# A
l=20./100.;# m
r1=1./100.;# m
r2=11./100.;# m
mu0=4.*math.pi*10.**-7.;# permeability of air
# Force of attraction between Conductor & AB
F1=mu0*I1*I2*l/2./math.pi/r1;# N
# Force of repulsion between Conductor & CD
F2=mu0*I1*I2*l/2./math.pi/r2;# N
# Net Force
F=F1-F2;# N
print"Resultant force developed(N)",round(F,4)

Resultant force developed(N) 0.0036


## Example E21 : Pg 153¶

In [22]:
# Ex_2_21
# given data :
import math
N=500.;# turns
A=0.01;# m**2(Area of cross section of poles)
l=0.5;# m(mean length)
mu0=4.*math.pi*10.**-7.;# permeability of air
mu_r=1000.;# /relative permeability
g=9.8;# gravitational acceleration
W=200.;# kg
F=W/2.;# kg
F=F*g;# N
B=math.sqrt(F*2.*mu0/A);# Wb/m**2
H=B/mu0/mu_r;# Wb/m**2
I=H*l/N;# A
print"Exciting current(A)",round(I,2)

Exciting current(A) 0.39