Chapter 14 Earths magnetism

Example 14.3 Page no 433

In [4]:
#Given
a=60                            #Degree
Bh=0.16                          #G

#Calculation
import math
B=Bh/cos(a*3.14/180.0)

#Result
print"Magnitude of earth's field is", round(B,2),"G"

Magnitude of earth's field is 0.32 G

Example 14.4 Page no 434

In [11]:
#Given
a=60
a2=45

#Calculation
import math
a1=math.tan(a2*3.14/180.0)/math.cos(a*3.14/180.0)
a3=math.atan(a1)*180/3.14

#Result
print"Apparent value of the dip is", round(a3,1),"degree"

Apparent value of the dip is 63.4 degree

Example 14.6 Page no 434

In [16]:
#Given
l=30                    #cm
l=0.15                  #m
r=0.30                   #m
Bh=0.34*10**-4            #T
u=10**-7

#Calculation
M=Bh*(r**2-l**2)**2/(2*u*r)
m=M/(2*l)

#Result
print"Pole strength of the magnet is",m,"Am"

Pole strength of the magnet is 8.60625 Am

Example 14.7 Page no 434

In [22]:
#Given
M=0.4                       #Am**2
r=0.1                       #m
l=0.05                         #m
u=10**-7

#Calculation
Bh=u*M/((r**2+l**2)**1.5)

#Result
print"Horizontal component of earth's magnetic field is", round(Bh*10**4,3)*10**-4,"T"

Horizontal component of earth's magnetic field is 2.86e-05 T

Example 14.8 Page no 435

In [28]:
#Given
B=0.33
a=0
u=10**-7
I=2.5                             #A

#Calculation
import math
Bh=B/math.cos(a*3.14/180.0)
a=u*2*I/(Bh*10**-4)

#Result
print"Neutral point is", round(a*10**2,1),"cm"

Neutral point is 1.5 cm

Example 14.9 Page no 435

In [32]:
#Given
Bh=0.32                     #G
B=0.48            

#Calculation
import math
a=B/Bh
a1=math.atan(a)*180/3.14

#Result
print"New stable equilibrium is", round(a1,1),"degree"

New stable equilibrium is 56.3 degree

Example 14.10 Page no 435

In [36]:
#Given
n=22
a=0.1                            #m
Bh=0.3*10**-4                         #T
u=10**-7

#Calculation
import math
K=2*a*Bh/(n*4*math.pi*u)

#Result
print"Reduction factor is", round(K,3),"A"

Reduction factor is 0.217 A

Example 14.11 Page no 435

In [51]:
#Given
n=40
a=0.12
I=0.15
a1=45                            #degree
u=10**-7

#Calculation
import math
Bh=(n*u*4*math.pi*I)/(2.0*a*math.tan(a1*3.14/180.0))

#Result
print"Strength of horizontal component is", round(Bh*10**4,3),"*10**-4 T"

Strength of horizontal component is 0.314 *10**-4 T

Example 14.12 Page no 435

In [5]:
#Given
a1=30
a2=45                             #degree

#Calculation
import math
n=2*math.tan(a1*3.14/180.0)/(math.tan(a2*3.14/180.0))

#Result
print"Ratio of number of turns is", round(n,3)

Ratio of number of turns is 1.155

Example 14.13 Page no 436

In [10]:
#Given
n=16
a=0.1                        #m
i=0.75                        #A
Bh=5*10**-2                  #T
v=2                           #/s

#Calculation
import math
M=n*i*math.pi*a**2
I=M*Bh/(4*math.pi**2*v**2)

#Result
print"Moment of inertia is",round(I*10**4,3),"*10**-4 Kg m**2"

Moment of inertia is 1.194 *10**-4 Kg m**2

Example 14.14 Page no 436

In [11]:
#Given
T1=2.5
T2=4.5
M2=1.5

#Calculation
M=T2**2/(M2*T1**2)

#Result
print"Ratio of magnetic moment is",M

Ratio of magnetic moment is 2.16

Example 14.15 Page no 436

In [15]:
#Given
T1=3.0
T2=4.0

#Calculation
M=(T2**2+T1**2)/(T2**2-T1**2)

#Result
print"Ratio of magnetic moments is",round(M,2)

Ratio of magnetic moments is 3.57

Example 14.16 Page no 436

In [39]:
#Given
a1=35                          #Degree
B=0.39
I=1                              #A
a=4.0*10**-2
u=10**-7

#Calculation
import math
Bh=B*math.cos(a1*3.14/180.0)
Bv=B*math.sin(a1*3.14/180.0)
B1=(u*2*I*4/a)*10**4
Rh=Bh-B1
R=math.sqrt(Rh**2+Bv**2)
Rh1=Bh+B1
R3=math.sqrt(Rh1**2+Bv**2)

#Result
print"Resultant magnetic field is", round(R3,3),"G"

Resultant magnetic field is 0.566 G

Example 14.17 Page no 436

In [51]:
#Given
M=5.25*10**-2                          #J/T
Bh=0.42*10**-4                         #T
u=10**-7

#Calculation
r=(u*M/Bh)**0.333
r1=(u*2*M/Bh)**0.333

#Result
print"(a) Distance from the centre of the magnet on its normal bisector is", round(r*10**2,1),"cm"
print"(b) Distance from the centre of the magnet on its axis is",round(r1*10**2,1),"cm"

(a) Distance from the centre of the magnet on its normal bisector is 5.0 cm
(b) Distance from the centre of the magnet on its axis is 6.3 cm

Example 14.18 Page no 437

In [60]:
#Given
I=0.35                    #A
n=30
a=12.0*10**-2
u=10**-7

#Calculation
import math
Bh=u*2*math.pi*n*I*0.707/a

#Result
print"(a) Horizontal component of the earth's magnetic field is", round(Bh*10**4,2),"G"
print"(b) The needle will reverse its original direction i.e.  it will point east to west."

(a) Horizontal component of the earth's magnetic field is 0.39 G
(b) The needle will reverse its original direction i.e.  it will point east to west.

Example 14.19 Page no 437

In [66]:
#given
t1=9                      #S
t2=4.5
Bh=0.34*10**-4                #T
u=10**-7
r=0.1                           #m

#Calculation
Baxial=Bh*((t1**2/t2**2)-1)
M2=Baxial*r**2/(2*u)

#Result
print"Magnetic moment is", M2*10**-1,"A m**2"

Magnetic moment is 0.51 A m**2