In [1]:

```
import math
#Given Data:
H=198 #Magnetizing Force in Ampere per meter
M=2300 #Magnetization in Ampere per meter
u0=4*math.pi*10**-7 #Permeability in vacuum
#Calculations:
#H=(B/u0)-M
B=u0*(H+M) #Flux Density
ur=B/(u0*H) #Relative Permeability
print"Corresponding Flux Density is =",B,"Wb/m^2"
print"Relative Permeability is =",ur
```

In [2]:

```
import math
#Given Data:
x=3.7*10**-3 #Susceptibility at T=300 K
T=300 #Temperature in kelvin
T1=250 #Temperature in kelvin
T2=600 #Temperature in kelvin
#Calculations:
C=x*T #Curie's law
ur1=C/T1 #Relative permeability at 250 K
ur2=C/T2 #Relative permeability at 600 K
print"Relative Permeability at 250 K is =",ur1
print"Relative Permeability at 600 K is =",ur2
```

In [3]:

```
import math
#Given Data:
u=0.8*10**-23 #Magnetic dipole moment of an atom in paramagnetic gas in J/T
B=0.8 #Magnetic field in tesla
K=1.38*10**-23 #Boltzmann constant
#To find Temperature at which Average thermal energy is equal to Magnetic energy
#i.e. uB=3KT/2
T=2*u*B/(3*K) #Required temperature
print"Required temperature is =",T,"Kelvin"
```

In [5]:

```
import math
#Given Data:
T=27+273 #Temperature in kelvin
B=0.5 #Magnetic field in tesla
C=2*10**-3 #Curie's Constant
u0=4*math.pi*10**-7 #Permeability in vacuum
# C=u0*M*T/B (Curie's law)
M=C*B/(u0*T) #Magnetization of material at 300 K
print"Magnetization of material at 300 K is =",M,"A/m"
```

In [7]:

```
import math
#Given Data:
B=10.9*10**-5 #Horizontal component of B in wb/m^2
u0=4*math.pi*10**-7 #Permeability in free space
H=B/u0 #Horizontal component of magnetic field
print"Horizontal component of magnetic field is =",H,"Ampere/meter"
print"(Print mistake in unit in book)"
```

In [8]:

```
import math
#Given Data:
u0=4*math.pi*10**-7 #Permeability in vacuum
ur=900 #Relative permeability of medium
l=2 #length in meter
A=60*10**-4 #Crosss sectional area of ring in m^2
phi=5.9*10**-3 #flux in weber
n=700 #Number of turns
#Calculations:
#We know, phi=B*A
B=phi/A #Flux density
#But, B=u*H
H=B/(u0*ur) #Magnetic field strength
I=H*l/n #Required current
print"Current required to produce given flux is =",I,"Ampere"
```

In [10]:

```
import math
#Given Data:
u0=4*math.pi*10**-7 #Permeability in vacuum
ur=900 #Relative permeability of medium
r=25*10**-2 #radius of ring
A=25*10**-4 #Crosss sectional area of ring in m^2
Ag=1*10**-3 #Air gap
phi=2.7*10**-3 #flux in weber
N=400 #Number of turns
#Calculations:
#We know, phi=B*A
B=phi/A #Flux density
#But, B=u*H
H=B/(u0*ur) #Magnetic field strength
L=H*2*math.pi*r+(B*Ag/u0) #Total amp turns required (iron+air)
I=L/N #Required current
print"Current required to produce given flux is =",I,"Ampere"
```

In [11]:

```
import math
#Given Data:
u0=4*math.pi*10**-7 #Permeability in vacuum
A=0.2*10**-4 #Crosss sectional area of iron bar in m^2
H=1600 #magnetising field in A/m
phi=2.4*10**-5 #Magnetic flux in weber
#Calculations:
#We know, phi=B*A
B=phi/A #Flux density
u=B/H #magnetic permeability
ur=u/u0 #relative permeability
xm=ur-1 #susceptibility of the iron bar
print"magnetic permeability of iron bar is =",u,"N/(A^2)"
print"susceptibility of the iron bar is =",xm
```

In [13]:

```
import math
#Given Data:
u0=4*math.pi*10**-7 #Permeability in vacuum
xm=948*10**-11 #susceptibility of the iron bar
#Calculations:
ur=1+xm #relative permeability
u=u0*ur #permeability of medium
print"Relative Permeability of medium is =",ur
print"Permeability of medium is =",u,"H/m"
```

In [14]:

```
import math
#Given Data:
B=2.5 #Magnetic field in tesla
u0=4*math.pi*10**-7 #Permeability in free space
i0=0.7 #current in the core
ri=11*10**-2 #inner radii of core
ro=12*10**-2 #outer radii of core
#Calculations:
r=(ri+ro)/2 #Average radii of core
n=3000/(2*math.pi*r) #Number of turns
#We know, B=u0*ur*n*i0 .Thus,
ur=B/(u0*n*i0)
print"Relative Permeability of medium is =",ur
```

In [15]:

```
import math
#Given Data:
B=1.0 #Flux density in tesla
u0=4*math.pi*10**-7 #Permeability in free space
i=2.0 #current in the core
n=10*100 #n=N/l i.e. turns per meter
#Calculations:
H=n*i #Magnetising force produced in wire
print"Magnetising force produced in wire is =",H,"Amp-turn/meter"
#We know that, B=u0(H+I).Thus,
I=B/u0-H #Magnetisation of material
print"Magnetisation of material is =",I,"Amp-turn/meter"
#u=B/H, i.e. ur*u0=B/H.
ur=B/(u0*H) #Relative permeability of core
print" Relative Permeability of core is =",ur
```

In [16]:

```
import math
#Given Data:
M=40 #Mass of an iron core
D=7.5*10**3 #Density of iron
f=100 #Frequency
A=3800*10**-1 #Loss due to Area of hysterisis loop in J/m^3
#Calculations:
V=M/D #Volume of iron core
L1=A*V #Loss of energy in core per cycle
print"Loss of energy in core per cycles is =",L1,"joules"
N=f*60 #Number of cycles per minute
L=L1*N #Loss of energy per minute
print"Loss of energy per minute is =",L,"joules"
```

In [17]:

```
import math
#Given Data:
u0=4*math.pi*10**-7 #Permeability in vacuum
l=30*10**-2 #length in meter
A=1*10**-4 #Crosss sectional area of ring in m^2
phi=2*10**-6 #flux in weber
N=300 #Number of turns
I=0.032 #Current in winding
#Calculations:
#(i):
B=phi/A #Flux density
print"(i)Flux Density in the ring is =",B,"Wb/m^2"
#(ii):
H=N*I/l #Magnetic intensity
print"(ii)Magnetic intensity is =",H,"Amp-turn/meter"
#(iii):
u=B/H #Permeability of ring
print"(iii)Permeability of ring is =",u," Wb/A-m"
ur=u/u0 #Relative permeability of ring
print"Relative Permeability of ring is =",ur
#(iv):
xm=ur-1 #susceptibility of the ring
print"(iv)Magnetic susceptibility of the ring is =",xm
```

In [18]:

```
import math
#Given Dta:
M=12*10**3 #Mass of an iron core in grams
D=7.5 #Density of iron in gm/cc
f=50 #Frequency
A=3000 #loss due to Area of hysterisis loop in ergs/cm^3
#Calculations:
V=M/D #Volume of iron core
L1=A*V #Loss of energy in core per cycle
L=L1*f*3600 #Loss of energy per hour
print"Loss of energy per hour is =",L,"Erg"
```

In [19]:

```
import math
#Given Data:
A=0.5*10**3 #Area of B-H loop in Joules per m^3
V=10**-3 #Volume of specimen in m^3
n=50 #Frequency of a.c.
#Calculations:
H=n*V*A #Hysteresis power loss
print"Hysteresis power loss is =",H,"Watt"
```

In [22]:

```
import math
#Given Data:
u0=4*math.pi*10**-7 #Permeability in vacuum
ur=1000 #Relative permeability of medium
V=10**-4 #Volume of iron rod in m^3
n=500 #Number of turns per meter
i=0.5 #Current in windings of solenoid in Amperes
#Calculations:
#We know I=(ur-1)H
#and H=ni , hence
I=(ur-1)*n*i #Intensity of magnetisation
M=I*V #Magnetic moment
print"Magnetic moment of the rod is =",M,"A-m^2"
```

In [23]:

```
import math
#Given Data:
u0=4*math.pi*10**-7 #Permeability in vacuum
ur=600 #Relative permeability of iron
d=12*10**-2 #mean diameter of ring in m
N=500 #Number of turns
i=0.3 #Current in windings of solenoid in Amperes
#Calculations:
r=d/2 #Radius of ring
B=u0*ur*N*i/(2*math.pi*r) #Flux densityin the core
print"Flux densityin the core is =",B,"Wb/m^2"
H=B/(u0*ur) #Magnetic intensity
print"Magnetic intensity is =",H,"Amp-turns/m"
#We know that, B=u0(H+I)
I1=(B-u0*H)/u0 #magnetisation
I2=u0*I1 #Electronic current loop
I=I2/B*100 #Percentage flux density due to electroniuc loop currents
print"Percentage flux density due to electroniuc loop currents is =",I,"percent"
```

In [24]:

```
import math
#Given Data:
u0=4*math.pi*10**-7 #Permeability in vacuum
ur=900 #Relative permeability of iron ring
d=40*10**-2 #diameter of ring
l=5*10**-3 #air gap in the ring
A=5.8*10**-4 #Crosss sectional area of ring in m^2
phi=1.5*10**-4 #flux in weber
N=600 #Number of turns
#Calculations:
r=d/2 #Radius of ring
#We know, phi=B*A
B=phi/A #Flux density
#But, B=u*H
H=B/(u0*ur) #Magnetic field strength
m1=H*ur*l #amp-turns in air gap
m2=H*2*math.pi*r #amp-turns by ring
m=m1+m2 #total mmf(amp-turns) required
I=m/N #Required current
print"Current required to produce given flux is =",I,"Amperes"
```

In [25]:

```
import math
#Given Data:
u0=4*math.pi*10**-7 #Permeability in vacuum
X=-0.5*10**-5 #Magnetic susceptibility of silicon
H=9.9*10**4 #Magnetic field intensity
#Calculations:
#As, X=I/H. thus,
I=X*H #intensity of magnetisation
print"Intensity of magnetisation is =",I
B=u0*(H+I) #Magnetic flux density
print"Magnetic flux density is =",B,"Wb/ m^2"
```

In [27]:

```
import math
#Given Data:
u0=4*math.pi*10**-7 #Permeability in vacuum
ur=380 #Relative permeability
d=20*10**-2 #diameter of solenoid in m
r=d/2 #radius of ring in m
A=5*10**-4 #Crosss sectional area of ring in m^2
phi=2*10**-3 #flux in weber
N=200 #Number of turns
#Calculations:
l=math.pi*d #air gap in the ring
S=(l/(u0*ur*A)) #Reluctance of iron ring
print"Reluctance of iron ring is =",S,"Amp-turn/ Wb "
#ohm's law for magnetic circuit is phi=N*I/S. thus,
I=S*phi/N #required current
print"Current required to obtain given magnetic flux is =",I,"Amperes"
```

In [28]:

```
import math
#Given Values:
u0=4*math.pi*10**-7 #Permeability in vacuum
ur=1 #Relative permeability of air
r=15*10**-2 #radius of ring in m
A=6*10**-4 #Crosss sectional area of ring in m^2
I=4 #Coil current in amp
N=500 #Number of turns
#Calculations:
m=N*I #MMF of coil
print"MMF of coil is =",m,"Ampere-turn"
l=2*math.pi*r #air gap
R=(l/(u0*ur*A)) #Reluctance of iron ring
print"Reluctance of iron ring is =",R,"Ampere-turn/Wb"
phi=m/R #Magnetic flux
print"Magnetic flux is =",phi,"Weber"
B=phi/A #Magnetic Flux density
print"Magnetic flux density is =",B,"Weber/m^2"
H=B/(u0*ur) #Magnetic field intensity
print"Magnetic field intensity is =",H,"Amperes/m"
```

In [29]:

```
import math
#Given Data:
u0=4*math.pi*10**-7 #Permeability in vacuum
ur=6*10**-3 #Relative permeability of iron
r=0.5 #radius of ring in m
l=1*10**-2 #air gap in the ring
A=5*10**-4 #Crosss sectional area of ring in m^2
i=5 #current in ampere
N=900 #Number of turns
#Calculations:
S=(l/(u0*A))+((2*math.pi*r-l)/ur*A) #Reluctance of iron
print"Reluctance of iron is =",S,"Ampere-turn/Wb"
m=N*i #mmf produced
print"mmf produced is =",m,"Ampere-turn"
```

In [30]:

```
import math
#Given Data:
H=5*10**3 #coercivity of bar magnet in amp/m
l=10*10**-2 #length of solenoid in m
N=50 #No of turns
#Calculations:
#We know that, H=NI/l ,hence
I=l*H/N #current through solenoid
print"Current through solenoid is =",I,"Amperes"
```

In [31]:

```
import math
#Given Data:
ur=1200 #Relative permeability of medium
V=10**-3 #volume of iron rod
N=5*10**2 #no of turns per m
i=0.5 #current through solenoid in amp
#Calculations:
x=ur-1 #susceptibility of the ring
H=N*i #Magnetisisng field
#We know, x=I/H
I=x*H #magnetisation
#Also, I=M/V , thus
M=I*V #magnetic moment
print"Magnetic moment is =",M,"Ampere-turn-m^2"
```

In [33]:

```
import math
#Given Dta:
ur=100 #Relative permeability of medium
l=0.2 #length of iron rod
d=10*10**-3 #diameter of solenoid in m
N=300 #no of turns per m
i=0.5 #current through solenoid in amp
r=d/2 #radius of solenoid
#Calculations:
x=ur-1 #susceptibility of the ring
H=N*i #Magnetisisng field
#We know, x=I/H
I=x*H #magnetisation
V=math.pi*(r**2)*l #volume of iron rod
#Also, I=M/V , thus
M=I*V #magnetic moment
print"Magnetic moment is =",M,"Ampere-turn-m^2"
```

In [34]:

```
import math
#Given Data:
l=1.2 #length of circuit in meter
u=7.3*10**-3 #permeability of silicon sheet
A=100 #cross sectional area in cm^2
N=150 #No of turns
B=0.3 #magmetic field in Wb/m^2
#Calculations:
#We know, B=u*H
H=B/u #Magnetic field strength
m=H*l #amp-turns in air gap
I1=m/N #Required current
print"Current required to obtain given magnetic field is =",I1,"Amperes"
I=I1/A #Required current per unit area
print"Current required per unit area to obtain given magnetic field is =",I,"Amperes"
```