# 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