Chapter 13 Magnetic dipole

Example 13.1 Page no 415

In [4]:
#Given
F=14.4*10**-4                             #N
r=0.05                                    #m
u=10.0**-7
F1=1.6*10**-4                             #N

#Calculation
import math
m=math.sqrt(F*r**2/u)
r1=math.sqrt(u*6*6/F1)

#Result
print"Distance between the poles is", r1,"m"

Distance between the poles is 0.15 m

Example 13.2 Page no 415

In [11]:
#Given
F=0.8*10**-3
r=0.1                             #m
g=9.8
u=10.0**-7

#Calculation
import math
m=math.sqrt(F*g*r**2/(u*5.0))
a=5*m

#Result
print"Strength of each pole is", round(a,1),"A m"

Strength of each pole is 62.6 A m

Example 13.4 Page no 416

In [22]:
#Given
m=50                            #Am
r=0.2                           #m
l=0.05                          #M
M=5                             #Am**2
u=10**-7

#Calculation
Baxial=u*2*M*r/((r**2-l**2)**2)
Bequi=u*M/((r**2+l**2)**1.5)

#Result
print"(i) Magnetic field at a distance of 0.2 m from its centre on axial line is",round(Baxial*10**4,2),"*10**-4 T"
print"(ii) Magnetic field at a distance of 0.2 m from its centre on its equitorial line is",round(Bequi*10**5,3)*10**-5,"T"

(i) Magnetic field at a distance of 0.2 m from its centre on axial line is 1.42 *10**-4 T
(ii) Magnetic field at a distance of 0.2 m from its centre on its equitorial line is 5.707e-05 T

Example 13.5 Page no 416

In [34]:
#Given
M=12.5                              #Am**2
OP=0.05                              #m
u=10**-7

#Calculation
import math
b1=(u*2*M)/(OP**3)
b2=(u*M)/(OP**3)
B=math.sqrt(b1**2+b2**2)
a=b2/b1
a1=math.atan(a*180/3.14)

#Result
print"Magnetic field at a point midway between two magnets is",round(B*10**2,3),"10**-2 T"

Magnetic field at a point midway between two magnets is 2.236 10**-2 T

Example 13.6 Page no 416

In [38]:
#Given
B=0.3                #T
A=30                 #Degree
t=0.06               #Nn

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

#Result
print"Magnetic moment is",round(M,1),"Am**2"

Magnetic moment is 0.4 Am**2

Example 13.7 Page no 416

In [45]:
#Given
m=48                    #Am
l=0.25                  #m
a=30                   #degree
B=0.15

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

#Result 
print"(i) Magnetic moment is",M,"Am**2"
print"(ii) Torque is",round(T,1),"Mm"

(i) Magnetic moment is 12.0 Am**2
(ii) Torque is 0.9 Mm

Example 13.8 Page no 416

In [50]:
#Given
B=0.2                 #t
a=30
t=0.06

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

#Result
print"(a) Magnetic moment is",round(M,1),"An**2"
print"(b) When the magnet aligns itself parallel to the magnetic field"

(a) Magnetic moment is 0.6 An**2
(b) When the magnet aligns itself parallel to the magnetic field

Example 13.9 Page no 416

In [57]:
#Given
M=1.5                          #J/T
B=0.22                         #T
a=0
a1=90

#Calculation
import math
W=M*B*(math.cos(a*3.14/180.0)-math.cos(a1*3.14/180.0))
t=M*B*math.sin(a1*3.14/180.0)

#Result
print"Amount of work required is", round(W,2),"J"
print"Torque is",round(t,2),"Nm"

Amount of work required is 0.33 J
Torque is 0.33 Nm

Example 13.10 Page no 417

In [65]:
#Given
n=50
a=0.2 
I=12                          #A
u=10**-7

#Calculation
import math
B=u*2*math.pi*n*I/a
M=n*I*math.pi*a**2

#Result
print"(a) Magnetic moment at the centre is",round(B*10**3,3),"*10**-3 T"
print"(b) Magnetic moment associated is",round(M,1),"Am**2"

(a) Magnetic moment at the centre is 1.885 *10**-3 T
(b) Magnetic moment associated is 75.4 Am**2

Example 13.11 Page no 417

In [69]:
#Given
r=0.53*10**-10                      #m
v=6.8*10**15                         #Kz
e=1.6*10**-19                          #C

#Calculation
import math
M=math.pi*e*v*r**2

#Result
print"Magnetic moment is",round(M*10**24,1)*10**-24,"A m**2"

Magnetic moment is 9.6e-24 A m**2

Example 13.12 Page no 417

In [79]:
#Given
M=1.8*10**-23                         #Am**2
v=5*10**-6                            #m**3
a=7.8*10**3
N=6.02*10**26
A=56.0
B=1.5                              #T
a1=90                              #degree

#Calculation
import math
m=v*a
n=N*m/A
M1=M*n
t=M1*B*math.sin(a1*3.14/180.0)

#Result
print"(a) Magnetic moment is", round(M1,2),"A m**2"
print"(b) Torque required is",round(t,2),"N m"

(a) Magnetic moment is 7.55 A m**2
(b) Torque required is 11.32 N m

Example 13.13 Page no 417

In [83]:
#Given
B1=1.2*10**-2                          #T
a=15                                   #degree
a2=60

#Calculation
a3=a2-a
B2=B1*math.sin(a*3.14/180.0)/(math.sin(a3*3.14/180.0))

#Result
print round(B2*10**3,2),"*10**-3 T"

4.39 *10**-3 T

Example 13.14 Page no 417

In [92]:
#Given
n=1000
I=2               #A
A=2*10**-4             #m**@
a=30
B=0.16
a1=0                       #degree
a2=180 

#Calculation
import math
M=I*A*n
t=M*B*math.sin(a*3.14/180.0)
W=M*B*(math.cos(a1*3.14/180.0)-math.cos(a2*3.14/180.0))

#Result
print"(a) Torque required is", round(t,3),"Nm"
print"(b) Work needed is",round(W,3),"J"

(a) Torque required is 0.032 Nm
(b) Work needed is 0.128 J