# Chapter 10 Magnets and Earth's Magnetism¶

## Example 10.1 Page no 558¶

In [11]:
#Given
F=0.8*10**-3*9.8                     #N
d=0.1                                #m
u=10**-7

#Calculation
import math
m=math.sqrt(F*d**2/(u*5))
m1=5*m

#Result
print"Strength of pole M1 is", round(m,2),"Am"
print"Strength of pole M2 is",round(m1,1),"Am"

Strength of pole M1 is 12.52 Am
Strength of pole M2 is 62.6 Am


## Example 10.2 Page no 559¶

In [19]:
#Given
F=14.4*10**-4                       #N
d=0.05                              #m
F1=1.6*10**-4

#Calculation
import math
u=4*math.pi*10**-7
m=math.sqrt((F*4*math.pi*d**2)/u)
d1=1/(math.sqrt((F1*4*math.pi)/(u*m**2)))

#Result
print "Distance is",d1,"m"

Distance is 0.15 m


## Example 10.5 Page no 560¶

In [27]:
#given
M=8
d=0.2

#Calculation
B=u*2*M/(4*math.pi*d**3)
Beqa=B/2.0

#Result
print"(i) Magnetic induction at axial point", B*10**4,"*10**-4 T"
print"(ii) Magnetic induction at equatorial point is",Beqa*10**4,"*10**-4 T"

(i) Magnetic induction at axial point 2.0 *10**-4 T
(ii) Magnetic induction at equatorial point is 1.0 *10**-4 T


## Example 10.6 Page no 560¶

In [33]:
#Given
d=6.4*10**6                     #m
B=0.4*10**-4                   #T

#Calculation
import math
M=(B*4*math.pi*d**3)/u

#Result
print"Earth's dipole moment is", round(M*10**-23,2)*10**23,"Am**2"

Earth's dipole moment is 1.05e+23 Am**2


## Example 10.7 Page no 560¶

In [39]:
#Given
M=0.40
d=0.5

#Calculation
Beqa=u*M/(4*math.pi*d**3)
Baxial=2*Beqa

#Result
print"Magnitude of axial field is", Baxial,"T"
print"Magnitude of equatorial field is",Beqa,"T"

Magnitude of axial field is 6.4e-07 T
Magnitude of equatorial field is 3.2e-07 T


## Example 10.8 Page no 560¶

In [46]:
#Given
e=1.6*10**-19
f=6.8*10**15
n=1
r=0.53*10**-10

#Calculation
import math
I=e*f
M=n*I*math.pi*r**2

#Result
print"Equivalent magnetic moment is", round(M*10**24,1)*10**-24,"Am**2"

Equivalent magnetic moment is 9.6e-24 Am**2


## Example 10.9 Page no 561¶

In [58]:
#Given
n=50
r=0.2                            #m
I=12                             #A

#Calculation
B=(u*n*I)/(2.0*r)
M=n*I*math.pi*r**2

#Result
print"(i) Magnetic field at the centre of the coil is", round(B*10**3,3),"*10**-3 T"
print"(ii) Magnetic moment is",round(M,1),"Am**2"

(i) Magnetic field at the centre of the coil is 1.885 *10**-3 T
(ii) Magnetic moment is 75.4 Am**2


## Example 10.10 Page no 561¶

In [62]:
#Given
A=7.5*10**-4                                #m**2
I=12                                          #A

#Calculation
M=A*I

#Result
print"Magnitude of the magnetic moment is", M*10**3,"*10**-3  Am**2"

Magnitude of the magnetic moment is 9.0 *10**-3  Am**2


## Example 10.11 Page no 561¶

In [70]:
#Given
n=100
I=0.1                       #A
r=0.05
B=1.5                        #T

#Calculation
import math
M=n*I*math.pi*r**2
W=2*M*B

#Result
print"Magnitude of the coil is", round(M,4),"Am**2"
print"Workdone is",round(W,4),"J"

Magnitude of the coil is 0.0785 Am**2
Workdone is 0.2356 J


## Example 10.12 Page no 561¶

In [81]:
#Given
n=10
I=3
A=7.85*10**-3
B=10**-2                         #T

#Calculation
import math
M=n*I*A
U1=-M*B*math.cos(0)
Uf=-M*B*math.cos(90)
w=-U1
t=M*B*math.sin(90*3.14/180.0)

#Result
print"Work done is", round(t*10**3,1),"*10**-3 Nm"

Work done is 2.4 *10**-3 Nm


## Example 10.13 Page no 562¶

In [86]:
#Given
M=4.8*10**-2                            #J/T
a=30                                    #degree
B=3*10**-2                              #t

#Calculation
import math
t=M*B*math.sin(a*3.14/180.0)

#Result
print"Torque acting on the needle is", round(t*10**4,1),"*10**-4 Nm"

Torque acting on the needle is 7.2 *10**-4 Nm


## Example 10.14 Page no 562¶

In [97]:
#Given
B=0.2                   #T
a=30                        #degree
t=0.06                         #Nm

#Calculation
import math
M=t/(B*math.sin(a*3.14/180.0))
U=M*B*math.cos(1*3.14/180.0)

#Result
print"(i) Magnetic moment of the magnet is", round(M,1),"Am**2"
print"(ii) Orientation of the magnet is", round(U,0)

(i) Magnetic moment of the magnet is 0.6 Am**2
(ii) Orientation of the magnet is 0.0


## Example 10.15 Page no 562¶

In [108]:
#given
a=30                              #degree
B=800*10**-4                      #T
t=0.016                           #Nm
A=2*10**-4                        #m**2
n=1000                            #turns

#Calculation
M=t/(B*math.sin(a*3.14/180.0))
W=2*M*B
I=M/(n*A)

#Result
print"(a) Magnetic moment of the magnet is", round(M,2),"Am**2"
print"(b) Work done is", round(W,3),"J"
print"(c) Current flowing through the solenoid is", round(I,0),"A"

(a) Magnetic moment of the magnet is 0.4 Am**2
(b) Work done is 0.064 J
(c) Current flowing through the solenoid is 2.0 A


## Example 10.16 Page no 563¶

In [113]:
#Given
t=6.70
n=10.0
I=7.5*10**-6                      #Kgm**2
M=6.7*10**-2                              #Am**2

#Calculation
T=t/n
B=(4*math.pi**2*I)/(M*T**2)

#Result
print"Magnitude of the magnetic field is", round(B,2),"T"

Magnitude of the magnetic field is 0.01 T


## Example 10.18 Page no 569¶

In [126]:
#Given
t=1.2*10**-3                      #nm
M=60
H=40*10**-6

#Calculation
import math
A=t/(M*H)
a=math.asin(A)*180/3.14

#Result
print"Angle of the declination is", round(a,0),"degree"

Angle of the declination is 30.0 degree


## Example 10.19 Page no 569¶

In [131]:
#Given
V=math.sqrt(3)

#calculation
import math
a=math.atan(V)*180/3.14

#Result
print"Angle of dip is", round(a,0),"Degree"

Angle of dip is 60.0 Degree


## Example 10.20 Page no 569¶

In [140]:
#Given
H=0.28                        #G
V=0.40                        #G

#Calculation
import math
A=V/H
a=math.atan(A)*180/3.14
R=math.sqrt(H**2+V**2)

#Result
print"(i) Angle of dip is", round(a,0),"Degree"
print"(ii) Earth's total magnetic field is", round(R,2),"G"

(i) Angle of dip is 55.0 Degree
(ii) Earth's total magnetic field is 0.49 G


## Example 10.22 Page no 570¶

In [145]:
#Given
H=0.40
a=18                  #degree

#Calculation
import math
R=H/(math.cos(a*3.14/180.0))

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

Magnitude of earth's magnetic field is 0.42 G


## Example 10.24 Page no 571¶

In [152]:
#Given
a=45                               #Degree
b=60                               #Degree

#Calculation
import math
A=math.tan(a*3.14/180.0)/(math.cos(b*3.14/180.0))
a=math.atan(A)*180/3.14

#Result
print"Apparant dip is", round(a,1),"Degree"

Apparant dip is 63.4 Degree


## Example 10.25 Page no 574¶

In [155]:
#Given
M=1.6                         #Am**2
d=0.20                           #m
u=10**-7                            #N/A**2

#Calculation
H=u*2*M/(d**3)

#Result
print"Horizontal component of the earth's magnetic field is", H,"T"

Horizontal component of the earth's magnetic field is 4e-05 T


## Example 10.26 Page no 574¶

In [162]:
#Given
l=0.05                          #m
d=0.12                          #m
H=0.34*10**-4                          #T

#Calculation
import math
u=4*math.pi*10**-7
M=(4*math.pi*H*(d**2+l**2)**1.5)/u

#Result
print"Magnetic moment of the magnet is", round(M,3),"J/T"

Magnetic moment of the magnet is 0.747 J/T


## Example 10.27 Page no 577¶

In [172]:
#Given
r=7*10**-2                       #m
H=2*10**-5                      #T
n=50

#calculation
import math
l=(2*r*H*math.tan(45*180/3.14))/u*n

#Result
print"Value of current is", round(l*10**-3,3),"A"

Value of current is 0.043 A


## Example 10.28 Page no 577¶

In [178]:
#Given
K=0.095                           #A
n=50
r=10*10**-2                        #m

#Calculation
H=K*u*n/(2.0*r)

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

Horizontal component of earth's magnetic field is 0.298 *10**-4 T


## Example 10.30 Page no 577¶

In [188]:
#Given
a=30                            #degree
b=45                             #degree

#Calculation
import math
m=(2*math.tan(a*3.14/180.0))/(math.tan(b*3.14/180.0))

#Result
print"Ratio of number of turns of the tangent galvanometers", round(m,3)

Ratio of number of turns of the tangent galvanometers 1.155