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