# Chapter 12 Electromagnetic induction¶

## Example 12.1 Page no 665¶

In [6]:
#Given
a=20                   #mWb
a1=-20                  #mWb
t=2*10**-3              #s
N=100

#Calculation
a2=(a1-a)*10**-3
e=(-N*a2)/t

#Result
print"Average e.m.f induced in the coil is", e,"V"

Average e.m.f induced in the coil is 2000.0 V


## Example 12.2 Page no 665¶

In [12]:
#Given
r=5*10**-2                         #m
N=1
B=0.35
t=0.12                               #S

#Calculation
import math
A=math.pi*r**2
a1=B*A
a2=-B*a1
e=(N*a1)/t

#Result
print round(e,2),"V"

0.02 V


## Example 12.3 Page no 665¶

In [24]:
#Given
A=10**-2                           #m**2
a=45                               #degree
B1=0.1                             #T
R=0.5                              #ohm
t=0.7                              #S

#Calculation
import math
a1=B1*A*math.cos(a*3.14/180.0)
a2=0
a3=a1-a2
e=a3/t
I=e/R

#Result
print"Current during this time interval is", round(I*10**3,1),"*10**-3 A"
print"Magnitude of induced emf is",round(e*10**3,0),"*10**-3 V"

Current during this time interval is 2.0 *10**-3 A
Magnitude of induced emf is 1.0 *10**-3 V


## Example 12.4 Page no 666¶

In [28]:
#Given
I=1.2*10**-3                              #A
N=1.0
R=10                              #ohm

#Calculation
e=I*R
a=e/N

#Result
print"Necessary rate is", a*10**2,"*10**-2 Wb/second"

Necessary rate is 1.2 *10**-2 Wb/second


## Example 12.5 Page no 666¶

In [47]:
#Given
r=10**-1                   #m
B=3.0*10**-5                  #T
t=0.25                           #S
N=500
R=2                                #ohm

#Calculation
import math
a1=B*math.pi*r**2*math.cos(0*3.14/180.0)
a2=B*math.pi*r**2*math.cos(180*3.14/180.0)
a3=a1-a2
e=(N*a3)/t
I=e/R

#Result
print"Magnitude of the emf is", round(e*10**3,1),"*10**-3 V"
print"Current induced in the coil is",round(I*10**3,1),"*1)**-3 A"

Magnitude of the emf is 3.8 *10**-3 V
Current induced in the coil is 1.9 *1)**-3 A


## Example 12.6 Page no 666¶

In [53]:
#Given
e=10**-2                        #V
B=5*10**-5                      #T
r=0.5                          #m
N=1

#Calculation
import math
A=math.pi*r**2
n=(e*N)/(math.pi*r**2*B)

#Result
print"Rate of rotation of the blade is", round(n,1),"revolutions/second"

Rate of rotation of the blade is 254.6 revolutions/second


## Example 12.7 Page no 667¶

In [59]:
#Given
a=12
b=7
t=2

#Calculation
e=((a*t)+b)*10**-3

#Result
print"(i) Magnitude of induced emf is", e*10**3,"mV"
print"(ii) The current induced in the coil will be anticlockwise"

(i) Magnitude of induced emf is 31.0 mV
(ii) The current induced in the coil will be anticlockwise


## Example 12.8 Page no 673¶

In [63]:
#Given
B=1                          #T
l=0.5                        #m
v=40                         #m/s

#Calculation
import math
e=B*l*v*math.sin(60*3.14/180.0)

#Result
print"emf induced in the conductor is", round(e,2)

emf induced in the conductor is 17.32


## Example 12.9 Page no 673¶

In [68]:
#Given
g=9.8
h=10
B=1.7*10**-5
l=1               #m

#Calculation
import math
v=math.sqrt(2*g*h)
e=B*l*v

#Result
print"Potential difference between its end is", e*10**4,"*10**4 V"

Potential difference between its end is 2.38 *10**4 V


## Example 12.10 Page no 673¶

In [77]:
#Given
v=72 *(5/18.0)                         #Km/h
B=40*10**-6                    #T
A=40
l=2                           #m
t=1.0
N=1

#Calculation
A=l*v
a=B*A
e=N*a/t

#Result
print"e.m.f generated in the axle of the car", e*10**3,"mV"

e.m.f generated in the axle of the car 1.6 mV


## Example 12.11 Page no 673¶

In [84]:
#Given
w=1000/60.0
r=0.3
B=0.5                      #T

#Calculation
v=w*r
vav=v/2.0
e=B*r*vav

#Result
print"e.m.f induced is",e,"V"

e.m.f induced is 0.375 V


## Example 12.12 Page no¶

In [91]:
#Given
r=0.5                             #m
n=2                                 #r.p.s
B=0.4*10**-4                        #T

#Calculation
import math
w=2*math.pi*n
e=0.5*B*r**2*w

#Result
print"Magnitude of induced e.m.f between the axle and rim is", round(e*10**5,2)*10**-5,"V"

Magnitude of induced e.m.f between the axle and rim is 6.28e-05 V


## Example 12.13 Page no 674¶

In [96]:
#Given
R=1                    #m
B=1
f=50

#Calculation
import math
e=math.pi*R**2*B*f

#Result
print"e.m.f between the centre and the matallic ring is", round(e,1),"V"

e.m.f between the centre and the matallic ring is 157.1 V


## Example 12.14 Page no 679¶

In [100]:
#Given
N=500
a=1.4*10**-4                   #Wb
l=2.5                         #A

#Calculation
L=(N*a)/l

#Result
print"Inductance of the coil is", L*10**3,"mH"

Inductance of the coil is 28.0 mH


## Example 12.15 Page no 679¶

In [106]:
#Given
L=130*10**-3                   #H
I1=20                           #mA
I2=28                           #mA
t=140.0*10**-3                    #S

#Calculation
l=I2-I1
e=(-L*l)/t

#Result
print"Magnitude of induced e.m.f is", round(e,2),"*10**-3 V"
print"Direction oppose the increase in current"

Magnitude of induced e.m.f is -7.43 *10**-3 V
Direction oppose the increase in current


## Example 12.16 Page no 679¶

In [115]:
#Given
N=4000
l=0.6                              #m
r=16*10**-4                        #m

#Calculation
u=4*math.pi*10**-7
L=(u*N**2*((math.pi*r)/4.0))/l
Liron=N*L

#Result
print"Inductance of the solenoid is", round(Liron,0),"H"

Inductance of the solenoid is 168.0 H


## Example 12.17 Page no 679¶

In [119]:
#Given
L=10.0                       #H
e=300                        #V
t=10**-2                       #S

#Calculation
dl=(e*t)/L
a=e*t

#Result
print"Charge in magnetic flux is", a,"Wb"

Charge in magnetic flux is 3.0 Wb


## Example 12.18 Page no 680¶

In [125]:
#Given
L=10*10**-3
I=4*10**-3
N=200.0

#Calculation
N1=L*I
a=N1/N

#Result
print"Total flux linked with the coil is", N1,"Wb"
print"Magnetic flux through the cross section of the coil is",a,"Wb"

Total flux linked with the coil is 4e-05 Wb
Magnetic flux through the cross section of the coil is 2e-07 Wb


## Example 12.19 Page no 680¶

In [134]:
#Given
L=500*10**-3
I1=20*10**-3                  #A
I2=10*10**-3                  #A

#Calculation
U1=0.5*L*I1**2
U2=0.5*L*I2**2

#Result
print "Magnetic energy stored in the coil is",U1*10**6,"*10**-4 J"
print"New value of energy is",U2,"J"

Magnetic energy stored in the coil is 100.0 *10**-4 J
New value of energy is 2.5e-05 J


## Example 12.20 Page no 680¶

In [144]:
#Given
E=12
R=30.0                    #ohm
L=0.22

#Calculation
I0=E/R
I=I0/2.0
P=E*I
dl=(E-(I*R))/L
du=L*I*dl

#Result
print"(i) Energy being delivered by the battery is", P,"W"
print"(ii) ENergy being stored in the magnetic field of inductor is",du,"W"

(i) Energy being delivered by the battery is 2.4 W
(ii) ENergy being stored in the magnetic field of inductor is 1.2 W


## Example 12.21 Page no 680¶

In [147]:
#Given
L=2.0                         #H
i=2                              #A

#Calculation
U=0.5*L*i**2

#Result
print"Amount of energy spent during the period is", U,"J"

Amount of energy spent during the period is 4.0 J


## Example 12.22 Page no 686¶

In [150]:
#Given
e=1500                         #V
dl=3                               #A
dt=0.001                             #s

#Calculation
M=(e*dt)/dl

#Result
print"Mumtual induction between the two coils is", M,"H"

Mumtual induction between the two coils is 0.5 H


## Example 12.23 Page no 686¶

In [155]:
#Given
N2=1000
I1=5.0                          #A
a2=0.4*10**-4                  #Wb
dl=-24                             #A
dt=0.02                              #S

#Calculation
M=(N2*a2)/I1
eb=(-M*dl)/dt

#Result
print"(i) Mutual induction between A and B is", M,"H"
print"(ii) e.m.f induced by the coil is", eb

(i) Mutual induction between A and B is 0.008 H
(ii) e.m.f induced by the coil is 9.6


## Example 12.24 Page no 687¶

In [168]:
#Given
N=1200
A=12*10**-4                         #m**2
r=0.15                                     #m
N2=300
a=0.05

#Calculation
import math
u=4*math.pi*10**-7
L=(u*N**2*A)/(2*math.pi*r)
M=(u*N*N2*A)/(2*math.pi*r)
dl=2/a
e=M*dl

#Result
print"(i) Self inductance of the toroid is", round(L*10**3,1),"*10**-3 H"
print"(ii) Induced e.m.f. in the second coil is",round(e,3),"V"

(i) Self inductance of the toroid is 2.3 *10**-3 H
(ii) Induced e.m.f. in the second coil is 0.023 V


## Example 12.25 Page no 688¶

In [181]:
#Given
I=2.0
a1=20*10**-2
x=0.15
A2=0.3*10**-2

#Calculation
import math
u=4*math.pi*10**-7
B1=(u*I*a1**2)/(2.0*(a1**2+x**2)**1.5)
a=B1*math.pi*A2**2
M=a/I

#Result
print"(i) Flux linking the bigger loop is", round(a*10**11,1)
print"(ii) Mutual induction between the two loops is",round(M*10**11,2),"!0**-11 H"

(i) Flux linking the bigger loop is 9.1
(ii) Mutual induction between the two loops is 4.55 !0**-11 H


## Example 12.26 Page no 688¶

In [188]:
#Given
l=0.5                        #m
n=20                         #turns
r=50                         #cm
A1=40*10**-4                  #m**2
n1=25
A2=25*10**-4                   #m**2

#Calculation
u=4*math.pi*10**-7
N=n*r
N2=n1*r
M=(u*N*N2*A2)/l

#Result
print"Mutual induction of the system is",round(M*10**3,2),"*10**-3 H"

Mutual induction of the system is 7.85 *10**-3 H