# Chapter 16 Electromagnetic induction¶

## Example 16.1 Page no 508¶

In [6]:
#Given
R=5.0                            #ohm
t=2
a=15
b=8

#Calculation
e=-a*t**2-(b*t)-t
I=-e/R

#Result
print"Induced current is", I,"A"

Induced current is 15.6 A


## Example 16.2 Page no 508¶

In [9]:
#Given
S1=75*10**-4                               #m**2
B1=0.8                                       #wb/m**2
S2=100*10**-4
B2=1.4
t=0.05

#Calculation
a1=B1*S1
a2=B2*S2
a=a2-a1
e=-a/t

#Result
print"Induced e.m.f is", e,"Volt"

Induced e.m.f is -0.16 Volt


## Example 16.3 Page no 508¶

In [27]:
#Given
a1=5.5*10**-4                            #Wb
a2=0.5*10**-4
N=1000
t=0.1
R=10                                        #ohm

#Calculation
a=a2-a1
a11=N*a
e=-(a11/t)
I1=e/R
I2=I1*t

#Result
print" Induced e.m.f produced is",e,"V"
print" Charge flowing through the coil in 0.1 is",I2,"C"

 Induced e.m.f produced is 5.0 V
Charge flowing through the coil in 0.1 is 0.05 C


## Example 16.5 Page no 509¶

In [31]:
#Given
B=2.5*10**-3                   #Wb**-2
L=1                            #m
v=30                           #r.p.s

#Calculation
import math
e=-B*math.pi*L**2*v

#Result
print"The produced e.m.f. between its ends is",round(e,3),"V"

The produced e.m.f. between its ends is -0.236 V


## Example 16.6 Page no 509¶

In [37]:
#Given
L=1.2                              #m
e=10**-2                           #v
B=5*10**-5                         #tesla

#Calculation
import math
V=e/(B*math.pi*L**2)

#Result
print"The rate of rotation of the wheel is",round(V,1),"Rotation a**-1"

The rate of rotation of the wheel is 44.2 Rotation a**-1


## Example 16.7 Page no 509¶

In [45]:
#Given
D=10
L=0.50                         #m
B=0.40*10**-4                  #T
V=2                            #r.p.s.

#Calculation
import math
E=-B*math.pi*L**2*V

#Result
print"The induced e.m.f. between the axle and the rim of the wheel is",round(E*10**5,3),"10**-5","V"

The induced e.m.f. between the axle and the rim of the wheel is -6.283 10**-5 V


## Example 16.8 Page no 509¶

In [56]:
#Given
B=0.2                            #T
r=0.1                            #m
R=2                              #ohm

#Calculation
import math
V=D/(2*math.pi)
E=-B*math.pi*r**2*V
I=E/R

#Result
print"(i) The potential difference is",round(E,4),"V"
print"(ii) The induced current is",round(I,4),"A"

(i) The potential difference is -0.0628 V
(ii) The induced current is -0.0314 A


## Example 16.9 Page no 509¶

In [61]:
#Given
B=8.0*10**-5                                #Wb m**-2
L=2                                         #m
v=30                                        #m s**-1

#Calculation
e=B*L*v

#Result
print"The vertical component of earth's field is",e*10**3,"10**-3"

The vertical component of earth's field is 4.8 10**-3


## Example 16.10 Page no 509¶

In [64]:
#Givem
l=10                               #m
v=5                                 #m/s
Bh=0.30*10**-4                       #Wb/m**2

#Calculation
e=Bh*l*v

#Result
print "Instantaneous value of e.m.f. induced is",e*10**3,"*10**-3 V"

Instantaneous value of e.m.f. induced is 1.5 *10**-3 V


## Example 16.11 Page no 509¶

In [72]:
#Given
B=0.3                                   #T
v=10**-2                              #m/s
l=8*10**-2
L=1
v1=1.0
l2=2*10**-2
L1=8

#Calculation
e=B*l*v
l=L/v1
e1=B*l2*v
t1=L1/v1

#Result
print"(i) Voltage developed in the direction of motion normal to the longer side is", e*10**3,"mv"
print"(ii) Voltage developed in the direction of motion normal to the shorter side is",e1*10**3,"mV"

(i) Voltage developed in the direction of motion normal to the longer side is 0.24 mv
(ii) Voltage developed in the direction of motion normal to the shorter side is 0.06 mV


## Example 16.12 Page no 510¶

In [75]:
#Given
B=0.4                                   #T
v=5                                     #m/s
l=0.25                                 #m
e=0.5
R=5.0

#Calculation
e=B*l*v
I=e/R

#Result
print"New current is",I,"A"
print"Direction is from the end S to R"

New current is 0.1 A
Direction is from the end S to R


## Example 16.13 Page no 510¶

In [80]:
#Given
v=500                                  #m/s
B=5*10**-4                           #t
a=30                                     #degree
l=25                                    #m

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

#Result
print"Voltage difference is", round(e,3),"V"

Voltage difference is 3.124 V


## Example 16.14 Page no 510¶

In [85]:
#Given
L=10*10**-3                         #H
I=4*10**-3                           #A
N=200.0

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

#Result
print"Total magnetic flux is",a,"Weber"
print"Magnetic flux through the cross section is",A,"Weber"

Total magnetic flux is 4e-05 Weber
Magnetic flux through the cross section is 2e-07 Weber


## Example 16.15 Page no 510¶

In [89]:
#Given
L=10**-2                                    #H
I1=0
I2=1                                         #A
l=1
t=0.01

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

#Result
print"Self induced e.m.f is", e,"V"
print"The self-induced e.m.f. will act so as to oppose the growth of current."

Self induced e.m.f is -1.0 V
The self-induced e.m.f. will act so as to oppose the growth of current.


## Example 16.16 Page no 510¶

In [97]:
#Given
n=1500                         #turns/m
A=2*10**-4                        #m**2
l=20                                  #A/s

#Calculation
import math
e=-4*math.pi*n*A*l*10**-7

#Result
print"Induced e.m.f. is",round(e*10**6,2)*10**-6,"V"

Induced e.m.f. is -7.54e-06 V


## Example 16.17 Page no 511¶

In [101]:
#Given
e=50*10**-3                         #V
a=8
b=4
t=0.5

#Calculation
l=a-b
M=e*t/l

#Result
print"Mutual inductance is",M*10**3,"*10**-3 H"

Mutual inductance is 6.25 *10**-3 H


## Example 16.18 Page no 511¶

In [109]:
#Given
n1=5000                                #turns/m
A=4*10**-4                              #m**2
n2l=200
u=10**-7

#Calculation
import math
M=4*math.pi*u*n1*n2l*A

#Result
print"Mutual inductance is", round(M*10**4,3),"*10**-4 H"

Mutual inductance is 5.027 *10**-4 H


## Example 16.19 Page no 511¶

In [124]:
#Given
N=1200
A=12*10**-4
r=15*10**-2                            #m
u=10**-7
I=1.0
N2=300
I1=0
I2=2
t=0.05

#Calculation
import math
n=N/(2*math.pi*r)
B=4*math.pi*u*n
a=B*A*N
L=a/I
a1=B*A*N2
a11=a1*I1
a12=a1*I2
a13=a12-a11
e=-a13/t

#Result
print"(a) Self inductance is", L*10**3,"*10**-3 H"
print"(b) Induced e.m.f is", round(e,3),"V"

(a) Self inductance is 2.304 *10**-3 H
(b) Induced e.m.f is -0.023 V


## Example 16.20 Page no 511¶

In [130]:
#Given
A=25*10**-4
N=500
l=30.0*10**-2                 #m
I=2.5
u=10**-7
t=10.0**-3

#Calculation
import math
n=N/l
B=4*math.pi*u*n*I
a=B*A*N
a1=0-a
e=-a1/t

#Result
print"Average induced e.m.f. produced is",  round(e,3),"V"

Average induced e.m.f. produced is 6.545 V


## Example 16.21 Page no 511¶

In [136]:
#Given
N=25.0
A=2*10**-4                               #m**2
q=7.5*10**-3
R=0.50

#Calculation
B=R*q/(N*A)

#Result
print"Field strength of the magnet is" ,B,"T"

Field strength of the magnet is 0.75 T


## Example 16.22 Page no 512¶

In [156]:
#Given
B=0.50                      #T
l=15*10**-2                    #m
R=9.0*10**-3                     #ohm
v=12*10**-2                    #m/s

#Calculation
e=B*v*l
F=B*l*(e/R)
P=F*v
P1=e**2/R

#Result
print"(a) Induced e.m.f is", e*10**3,"*10**3 V"
print"The end P of the rod will become positive and the end Q will become negative"
print"(b) on closing the switch, electrons collects at the end Q. Therefore , excess charge is built up i.e it doesn't open when switch is open"
print"(c) The magnetic lorentz force on electron is cancelled due to the electric field set up across the two end"
print"(d) Retarding force is",F*10**2,"*10**-2 N"
print"(e) Power is",P*10**3,"*10*-3 W"
print"(f) Dissipated power is",P*10**3,"*10**-3 W"
print"(g) The motion of the rod does not cut field lines,hence no induced e.m.f. is produced"

(a) Induced e.m.f is 9.0 *10**3 V
The end P of the rod will become positive and the end Q will become negative
(b) on closing the switch, electrons collects at the end Q. Therefore , excess charge is built up i.e it doesn't open when switch is open
(c) The magnetic lorentz force on electron is cancelled due to the electric field set up across the two end
(d) Retarding force is 7.5 *10**-2 N
(e) Power is 9.0 *10*-3 W
(f) Dissipated power is 9.0 *10**-3 W
(g) The motion of the rod does not cut field lines,hence no induced e.m.f. is produced


## Example 16.23 Page no 512¶

In [168]:
#Given
a1=20*10**-2
a2=0.3*10**-2                       #m
x=15*10**-2
I=2.0                                    #A
u=10**-7

#Calculation
import math
B1=u*2*math.pi*I*a1**2/((a1**2+x**2)**1.5)
a=B1*math.pi*a2**2
M=a/I

#Result
print"(a) Flux is", round(B1*10**6,3)*10**-6 ,"T"
print"(b) Mutual inductance is",round(M*10**11,3)*10**-11,"H"

(a) Flux is 3.217e-06 T
(b) Mutual inductance is 4.548e-11 H


## Example 16.25 Page no 513¶

In [181]:
#Given
N1=1500
l1=80.0*10**-2
l2=4*10**-2
r2=2*10**-2
I=3.0                        #A

#Calculation
import math
A2=math.pi*r**2
n1=N1/l1
a=4*math.pi*10**-7*n1*I*4*math.pi*10**-4*100
M=a/I

#Result
print"Flux is",round( a*10**4,3),"*10**-4 Wb"
print"Mutual inductance is",round(M*10**4,2),"*10**-4 H"

Flux is 8.883 *10**-4 Wb
Mutual inductance is 2.96 *10**-4 H