NCERT Textbook: Electromagnetic Induction | Physics Class 12 - NEET PDF Download

 Page 1


Physics
154
6.1  INTRODUCTION
Electricity and magnetism were considered separate and unrelated
phenomena for a long time. In the early decades of the nineteenth century,
experiments on electric current by Oersted, Ampere and a few others
established the fact that electricity and magnetism are inter-related. They
found that moving electric charges produce magnetic fields. For example,
an electric current deflects a magnetic compass needle placed in its vicinity.
This naturally raises the questions like: Is the converse effect possible?
Can moving magnets produce electric currents? Does the nature permit
such a relation between electricity and magnetism? The answer is
resounding yes! The experiments of Michael Faraday in England and
Joseph Henry in USA, conducted around 1830, demonstrated
conclusively that electric currents were induced in closed coils when
subjected to changing magnetic fields. In this chapter, we will study the
phenomena associated with changing magnetic fields and understand
the underlying principles. The phenomenon in which electric current is
generated by varying magnetic fields is appropriately called
electromagnetic induction.
When Faraday first made public his discovery that relative motion
between a bar magnet and a wire loop produced a small current in the
latter, he was asked, “What is the use of it?” His reply was: “What is the
use of a new born baby?” The phenomenon of electromagnetic induction
Chapter Six
ELECTROMAGNETIC
INDUCTION
2024-25
Page 2


Physics
154
6.1  INTRODUCTION
Electricity and magnetism were considered separate and unrelated
phenomena for a long time. In the early decades of the nineteenth century,
experiments on electric current by Oersted, Ampere and a few others
established the fact that electricity and magnetism are inter-related. They
found that moving electric charges produce magnetic fields. For example,
an electric current deflects a magnetic compass needle placed in its vicinity.
This naturally raises the questions like: Is the converse effect possible?
Can moving magnets produce electric currents? Does the nature permit
such a relation between electricity and magnetism? The answer is
resounding yes! The experiments of Michael Faraday in England and
Joseph Henry in USA, conducted around 1830, demonstrated
conclusively that electric currents were induced in closed coils when
subjected to changing magnetic fields. In this chapter, we will study the
phenomena associated with changing magnetic fields and understand
the underlying principles. The phenomenon in which electric current is
generated by varying magnetic fields is appropriately called
electromagnetic induction.
When Faraday first made public his discovery that relative motion
between a bar magnet and a wire loop produced a small current in the
latter, he was asked, “What is the use of it?” His reply was: “What is the
use of a new born baby?” The phenomenon of electromagnetic induction
Chapter Six
ELECTROMAGNETIC
INDUCTION
2024-25
Electromagnetic
Induction
155
is not merely of theoretical or academic interest but also
of practical utility. Imagine a world where there is no
electricity – no electric lights, no trains, no telephones and
no personal computers. The pioneering experiments of
Faraday and Henry have led directly to the development
of modern day generators and transformers. Today’s
civilisation owes its progress to a great extent to the
discovery of electromagnetic induction.
6.2 THE EXPERIMENTS OF FARADAY AND
HENRY
The discovery and understanding of electromagnetic
induction are based on a long series of experiments carried
out by Faraday and Henry. We shall now describe some
of these experiments.
Experiment 6.1
Figure 6.1 shows a coil C
1
* connected to a galvanometer
G. When the North-pole of a bar magnet is pushed
towards the coil, the pointer in the galvanometer deflects,
indicating  the presence of electric  current in the coil. The
deflection lasts as long as the bar magnet is in motion.
The galvanometer does not show any deflection when the
magnet is held stationary. When the magnet is pulled
away from the coil, the galvanometer shows deflection in
the opposite direction, which indicates reversal of the
current’s direction. Moreover, when the South-pole of
the bar magnet is moved towards or away from the
coil, the deflections in the galvanometer are opposite
to that observed with the North-pole for similar
movements. Further, the deflection (and hence current)
is found to be larger when the magnet is pushed
towards or pulled away from the coil faster. Instead,
when the bar magnet is held fixed and the coil C
1
 is
moved towards or away from the magnet, the same
effects are observed. It shows that it is the relative
motion between the magnet and the coil that is
responsible for generation (induction) of electric
current in the coil.
Experiment 6.2
In Fig. 6.2 the bar magnet is replaced by a second coil
C
2
 connected to a battery. The steady current in the
coil C
2
 produces a steady magnetic field. As coil C
2
 is
* Wherever the term ‘coil’ or ‘loop’ is used, it is assumed that they are made up of
conducting material and are prepared using wires which are coated with insulating
material.
FIGURE 6.1 When the bar magnet is
pushed towards the coil, the pointer in
the galvanometer G deflects.
Josheph Henry [1797 –
1878] American experimental
physicist, professor at
Princeton University and first
director of the Smithsonian
Institution. He made important
improvements in electro-
magnets by winding coils of
insulated wire around iron
pole pieces and  invented an
electromagnetic motor and a
new, efficient telegraph. He
discoverd self-induction and
investigated how currents in
one circuit induce currents in
another.
JOSEPH HENRY (1797 – 1878)
2024-25
Page 3


Physics
154
6.1  INTRODUCTION
Electricity and magnetism were considered separate and unrelated
phenomena for a long time. In the early decades of the nineteenth century,
experiments on electric current by Oersted, Ampere and a few others
established the fact that electricity and magnetism are inter-related. They
found that moving electric charges produce magnetic fields. For example,
an electric current deflects a magnetic compass needle placed in its vicinity.
This naturally raises the questions like: Is the converse effect possible?
Can moving magnets produce electric currents? Does the nature permit
such a relation between electricity and magnetism? The answer is
resounding yes! The experiments of Michael Faraday in England and
Joseph Henry in USA, conducted around 1830, demonstrated
conclusively that electric currents were induced in closed coils when
subjected to changing magnetic fields. In this chapter, we will study the
phenomena associated with changing magnetic fields and understand
the underlying principles. The phenomenon in which electric current is
generated by varying magnetic fields is appropriately called
electromagnetic induction.
When Faraday first made public his discovery that relative motion
between a bar magnet and a wire loop produced a small current in the
latter, he was asked, “What is the use of it?” His reply was: “What is the
use of a new born baby?” The phenomenon of electromagnetic induction
Chapter Six
ELECTROMAGNETIC
INDUCTION
2024-25
Electromagnetic
Induction
155
is not merely of theoretical or academic interest but also
of practical utility. Imagine a world where there is no
electricity – no electric lights, no trains, no telephones and
no personal computers. The pioneering experiments of
Faraday and Henry have led directly to the development
of modern day generators and transformers. Today’s
civilisation owes its progress to a great extent to the
discovery of electromagnetic induction.
6.2 THE EXPERIMENTS OF FARADAY AND
HENRY
The discovery and understanding of electromagnetic
induction are based on a long series of experiments carried
out by Faraday and Henry. We shall now describe some
of these experiments.
Experiment 6.1
Figure 6.1 shows a coil C
1
* connected to a galvanometer
G. When the North-pole of a bar magnet is pushed
towards the coil, the pointer in the galvanometer deflects,
indicating  the presence of electric  current in the coil. The
deflection lasts as long as the bar magnet is in motion.
The galvanometer does not show any deflection when the
magnet is held stationary. When the magnet is pulled
away from the coil, the galvanometer shows deflection in
the opposite direction, which indicates reversal of the
current’s direction. Moreover, when the South-pole of
the bar magnet is moved towards or away from the
coil, the deflections in the galvanometer are opposite
to that observed with the North-pole for similar
movements. Further, the deflection (and hence current)
is found to be larger when the magnet is pushed
towards or pulled away from the coil faster. Instead,
when the bar magnet is held fixed and the coil C
1
 is
moved towards or away from the magnet, the same
effects are observed. It shows that it is the relative
motion between the magnet and the coil that is
responsible for generation (induction) of electric
current in the coil.
Experiment 6.2
In Fig. 6.2 the bar magnet is replaced by a second coil
C
2
 connected to a battery. The steady current in the
coil C
2
 produces a steady magnetic field. As coil C
2
 is
* Wherever the term ‘coil’ or ‘loop’ is used, it is assumed that they are made up of
conducting material and are prepared using wires which are coated with insulating
material.
FIGURE 6.1 When the bar magnet is
pushed towards the coil, the pointer in
the galvanometer G deflects.
Josheph Henry [1797 –
1878] American experimental
physicist, professor at
Princeton University and first
director of the Smithsonian
Institution. He made important
improvements in electro-
magnets by winding coils of
insulated wire around iron
pole pieces and  invented an
electromagnetic motor and a
new, efficient telegraph. He
discoverd self-induction and
investigated how currents in
one circuit induce currents in
another.
JOSEPH HENRY (1797 – 1878)
2024-25
Physics
156
moved towards the coil C
1
, the galvanometer shows a
deflection. This indicates that electric current is induced in
coil C
1
. When C
2
 is moved away, the galvanometer shows a
deflection again, but this time in the opposite direction. The
deflection lasts as long as coil C
2
 is in motion. When the coil
C
2 
is held fixed and C
1
 is moved, the same effects are observed.
Again, it is the relative motion between the coils that induces
the electric current.
Experiment 6.3
The above two experiments involved relative motion between
a magnet and a coil and between two coils, respectively.
Through another experiment, Faraday showed that this
relative motion is not an absolute requirement. Figure 6.3
shows two coils C
1
 and C
2
 held stationary. Coil C
1
 is connected
to galvanometer G while the second coil C
2
 is connected to a
battery through a tapping key K.
FIGURE 6.2  Current is
induced in coil C
1
 due to motion
of the current carrying coil C
2
.
FIGURE 6.3 Experimental set-up for Experiment 6.3.
It is observed that the galvanometer shows a momentary deflection
when the tapping key K is pressed. The pointer in the galvanometer returns
to zero immediately. If the key is held pressed continuously, there is no
deflection in the galvanometer. When the key is released, a momentory
deflection is observed again, but in the opposite direction. It is also observed
that the deflection increases dramatically when an iron rod is inserted
into the coils along their axis.
6.3  MAGNETIC FLUX
Faraday’s great insight lay in discovering a simple mathematical relation
to explain the series of experiments he carried out on electromagnetic
induction. However, before we state and appreciate his laws, we must get
familiar with the notion of magnetic flux, F 
B
. Magnetic flux is defined in
the same way as electric flux is defined in Chapter 1. Magnetic flux through
2024-25
Page 4


Physics
154
6.1  INTRODUCTION
Electricity and magnetism were considered separate and unrelated
phenomena for a long time. In the early decades of the nineteenth century,
experiments on electric current by Oersted, Ampere and a few others
established the fact that electricity and magnetism are inter-related. They
found that moving electric charges produce magnetic fields. For example,
an electric current deflects a magnetic compass needle placed in its vicinity.
This naturally raises the questions like: Is the converse effect possible?
Can moving magnets produce electric currents? Does the nature permit
such a relation between electricity and magnetism? The answer is
resounding yes! The experiments of Michael Faraday in England and
Joseph Henry in USA, conducted around 1830, demonstrated
conclusively that electric currents were induced in closed coils when
subjected to changing magnetic fields. In this chapter, we will study the
phenomena associated with changing magnetic fields and understand
the underlying principles. The phenomenon in which electric current is
generated by varying magnetic fields is appropriately called
electromagnetic induction.
When Faraday first made public his discovery that relative motion
between a bar magnet and a wire loop produced a small current in the
latter, he was asked, “What is the use of it?” His reply was: “What is the
use of a new born baby?” The phenomenon of electromagnetic induction
Chapter Six
ELECTROMAGNETIC
INDUCTION
2024-25
Electromagnetic
Induction
155
is not merely of theoretical or academic interest but also
of practical utility. Imagine a world where there is no
electricity – no electric lights, no trains, no telephones and
no personal computers. The pioneering experiments of
Faraday and Henry have led directly to the development
of modern day generators and transformers. Today’s
civilisation owes its progress to a great extent to the
discovery of electromagnetic induction.
6.2 THE EXPERIMENTS OF FARADAY AND
HENRY
The discovery and understanding of electromagnetic
induction are based on a long series of experiments carried
out by Faraday and Henry. We shall now describe some
of these experiments.
Experiment 6.1
Figure 6.1 shows a coil C
1
* connected to a galvanometer
G. When the North-pole of a bar magnet is pushed
towards the coil, the pointer in the galvanometer deflects,
indicating  the presence of electric  current in the coil. The
deflection lasts as long as the bar magnet is in motion.
The galvanometer does not show any deflection when the
magnet is held stationary. When the magnet is pulled
away from the coil, the galvanometer shows deflection in
the opposite direction, which indicates reversal of the
current’s direction. Moreover, when the South-pole of
the bar magnet is moved towards or away from the
coil, the deflections in the galvanometer are opposite
to that observed with the North-pole for similar
movements. Further, the deflection (and hence current)
is found to be larger when the magnet is pushed
towards or pulled away from the coil faster. Instead,
when the bar magnet is held fixed and the coil C
1
 is
moved towards or away from the magnet, the same
effects are observed. It shows that it is the relative
motion between the magnet and the coil that is
responsible for generation (induction) of electric
current in the coil.
Experiment 6.2
In Fig. 6.2 the bar magnet is replaced by a second coil
C
2
 connected to a battery. The steady current in the
coil C
2
 produces a steady magnetic field. As coil C
2
 is
* Wherever the term ‘coil’ or ‘loop’ is used, it is assumed that they are made up of
conducting material and are prepared using wires which are coated with insulating
material.
FIGURE 6.1 When the bar magnet is
pushed towards the coil, the pointer in
the galvanometer G deflects.
Josheph Henry [1797 –
1878] American experimental
physicist, professor at
Princeton University and first
director of the Smithsonian
Institution. He made important
improvements in electro-
magnets by winding coils of
insulated wire around iron
pole pieces and  invented an
electromagnetic motor and a
new, efficient telegraph. He
discoverd self-induction and
investigated how currents in
one circuit induce currents in
another.
JOSEPH HENRY (1797 – 1878)
2024-25
Physics
156
moved towards the coil C
1
, the galvanometer shows a
deflection. This indicates that electric current is induced in
coil C
1
. When C
2
 is moved away, the galvanometer shows a
deflection again, but this time in the opposite direction. The
deflection lasts as long as coil C
2
 is in motion. When the coil
C
2 
is held fixed and C
1
 is moved, the same effects are observed.
Again, it is the relative motion between the coils that induces
the electric current.
Experiment 6.3
The above two experiments involved relative motion between
a magnet and a coil and between two coils, respectively.
Through another experiment, Faraday showed that this
relative motion is not an absolute requirement. Figure 6.3
shows two coils C
1
 and C
2
 held stationary. Coil C
1
 is connected
to galvanometer G while the second coil C
2
 is connected to a
battery through a tapping key K.
FIGURE 6.2  Current is
induced in coil C
1
 due to motion
of the current carrying coil C
2
.
FIGURE 6.3 Experimental set-up for Experiment 6.3.
It is observed that the galvanometer shows a momentary deflection
when the tapping key K is pressed. The pointer in the galvanometer returns
to zero immediately. If the key is held pressed continuously, there is no
deflection in the galvanometer. When the key is released, a momentory
deflection is observed again, but in the opposite direction. It is also observed
that the deflection increases dramatically when an iron rod is inserted
into the coils along their axis.
6.3  MAGNETIC FLUX
Faraday’s great insight lay in discovering a simple mathematical relation
to explain the series of experiments he carried out on electromagnetic
induction. However, before we state and appreciate his laws, we must get
familiar with the notion of magnetic flux, F 
B
. Magnetic flux is defined in
the same way as electric flux is defined in Chapter 1. Magnetic flux through
2024-25
Electromagnetic
Induction
157
a plane of area A placed in a uniform magnetic field B (Fig. 6.4) can
be written as
F 
B
  = B 
.
 A = BA cos q (6.1)
where q   is angle between B and A. The notion of the area as a vector
has been discussed earlier in Chapter 1. Equation (6.1) can be
extended to curved surfaces and nonuniform fields.
If the magnetic field has different magnitudes and directions at
various parts of a surface as shown in Fig. 6.5, then the magnetic
flux through the surface is given by
1 1 2 2
d d F = + + B A B A . .
B
... =
B A .
i i
d
all
?
(6.2)
where ‘all’ stands for summation over all the area elements dA
i
comprising the surface and B
i
 is the magnetic field at the area element
dA
i
. The SI unit of magnetic flux is weber (Wb) or tesla meter
squared (T m
2
). Magnetic flux is a scalar quantity.
6.4  FARADAY’S LAW OF INDUCTION
From the experimental observations, Faraday arrived at a
conclusion that an emf is induced in a coil when magnetic flux
through the coil changes with time. Experimental observations
discussed in Section 6.2 can be explained using this concept.
The motion of a magnet towards or away from coil C
1
 in
Experiment 6.1 and moving a current-carrying coil C
2
 towards
or away from coil C
1
 in Experiment 6.2, change the magnetic
flux associated with coil C
1
.  The change in magnetic flux induces
emf in coil C
1
. It was this induced emf which caused electric
current to flow in coil C
1 
and through the galvanometer. A
plausible explanation for the observations of Experiment 6.3 is
as follows: When the tapping key K is pressed, the current in
coil C
2
 (and the resulting magnetic field) rises from zero to a
maximum value in a short time. Consequently, the magnetic
flux through the neighbouring coil C
1
 also increases. It is the change in
magnetic flux through coil C
1
 that produces an induced emf in coil C
1
.
When the key is held pressed, current in coil C
2
 is constant. Therefore,
there is no change in the magnetic flux through coil C
1
 and the current in
coil C
1
 drops to zero. When the key is released, the current in C
2
 and the
resulting magnetic field decreases from the maximum value to zero in a
short time. This results in a decrease in magnetic flux through coil C
1
and hence again induces an electric current in coil C
1
*. The common
point in all these observations is that the time rate of change of magnetic
flux through a circuit induces emf in it. Faraday stated experimental
observations in the form of a law called Faraday’s law of electromagnetic
induction. The law is stated below.
FIGURE 6.4 A plane of
surface area A placed in a
uniform magnetic field B.
FIGURE 6.5 Magnetic field B
i
at the i
th
 area element. dA
i
represents area vector of the
i
th
 area element.
* Note that sensitive electrical instruments in the vicinity of an electromagnet
can be damaged due to the induced emfs (and the resulting currents)  when the
electromagnet is turned on or off.
2024-25
Page 5


Physics
154
6.1  INTRODUCTION
Electricity and magnetism were considered separate and unrelated
phenomena for a long time. In the early decades of the nineteenth century,
experiments on electric current by Oersted, Ampere and a few others
established the fact that electricity and magnetism are inter-related. They
found that moving electric charges produce magnetic fields. For example,
an electric current deflects a magnetic compass needle placed in its vicinity.
This naturally raises the questions like: Is the converse effect possible?
Can moving magnets produce electric currents? Does the nature permit
such a relation between electricity and magnetism? The answer is
resounding yes! The experiments of Michael Faraday in England and
Joseph Henry in USA, conducted around 1830, demonstrated
conclusively that electric currents were induced in closed coils when
subjected to changing magnetic fields. In this chapter, we will study the
phenomena associated with changing magnetic fields and understand
the underlying principles. The phenomenon in which electric current is
generated by varying magnetic fields is appropriately called
electromagnetic induction.
When Faraday first made public his discovery that relative motion
between a bar magnet and a wire loop produced a small current in the
latter, he was asked, “What is the use of it?” His reply was: “What is the
use of a new born baby?” The phenomenon of electromagnetic induction
Chapter Six
ELECTROMAGNETIC
INDUCTION
2024-25
Electromagnetic
Induction
155
is not merely of theoretical or academic interest but also
of practical utility. Imagine a world where there is no
electricity – no electric lights, no trains, no telephones and
no personal computers. The pioneering experiments of
Faraday and Henry have led directly to the development
of modern day generators and transformers. Today’s
civilisation owes its progress to a great extent to the
discovery of electromagnetic induction.
6.2 THE EXPERIMENTS OF FARADAY AND
HENRY
The discovery and understanding of electromagnetic
induction are based on a long series of experiments carried
out by Faraday and Henry. We shall now describe some
of these experiments.
Experiment 6.1
Figure 6.1 shows a coil C
1
* connected to a galvanometer
G. When the North-pole of a bar magnet is pushed
towards the coil, the pointer in the galvanometer deflects,
indicating  the presence of electric  current in the coil. The
deflection lasts as long as the bar magnet is in motion.
The galvanometer does not show any deflection when the
magnet is held stationary. When the magnet is pulled
away from the coil, the galvanometer shows deflection in
the opposite direction, which indicates reversal of the
current’s direction. Moreover, when the South-pole of
the bar magnet is moved towards or away from the
coil, the deflections in the galvanometer are opposite
to that observed with the North-pole for similar
movements. Further, the deflection (and hence current)
is found to be larger when the magnet is pushed
towards or pulled away from the coil faster. Instead,
when the bar magnet is held fixed and the coil C
1
 is
moved towards or away from the magnet, the same
effects are observed. It shows that it is the relative
motion between the magnet and the coil that is
responsible for generation (induction) of electric
current in the coil.
Experiment 6.2
In Fig. 6.2 the bar magnet is replaced by a second coil
C
2
 connected to a battery. The steady current in the
coil C
2
 produces a steady magnetic field. As coil C
2
 is
* Wherever the term ‘coil’ or ‘loop’ is used, it is assumed that they are made up of
conducting material and are prepared using wires which are coated with insulating
material.
FIGURE 6.1 When the bar magnet is
pushed towards the coil, the pointer in
the galvanometer G deflects.
Josheph Henry [1797 –
1878] American experimental
physicist, professor at
Princeton University and first
director of the Smithsonian
Institution. He made important
improvements in electro-
magnets by winding coils of
insulated wire around iron
pole pieces and  invented an
electromagnetic motor and a
new, efficient telegraph. He
discoverd self-induction and
investigated how currents in
one circuit induce currents in
another.
JOSEPH HENRY (1797 – 1878)
2024-25
Physics
156
moved towards the coil C
1
, the galvanometer shows a
deflection. This indicates that electric current is induced in
coil C
1
. When C
2
 is moved away, the galvanometer shows a
deflection again, but this time in the opposite direction. The
deflection lasts as long as coil C
2
 is in motion. When the coil
C
2 
is held fixed and C
1
 is moved, the same effects are observed.
Again, it is the relative motion between the coils that induces
the electric current.
Experiment 6.3
The above two experiments involved relative motion between
a magnet and a coil and between two coils, respectively.
Through another experiment, Faraday showed that this
relative motion is not an absolute requirement. Figure 6.3
shows two coils C
1
 and C
2
 held stationary. Coil C
1
 is connected
to galvanometer G while the second coil C
2
 is connected to a
battery through a tapping key K.
FIGURE 6.2  Current is
induced in coil C
1
 due to motion
of the current carrying coil C
2
.
FIGURE 6.3 Experimental set-up for Experiment 6.3.
It is observed that the galvanometer shows a momentary deflection
when the tapping key K is pressed. The pointer in the galvanometer returns
to zero immediately. If the key is held pressed continuously, there is no
deflection in the galvanometer. When the key is released, a momentory
deflection is observed again, but in the opposite direction. It is also observed
that the deflection increases dramatically when an iron rod is inserted
into the coils along their axis.
6.3  MAGNETIC FLUX
Faraday’s great insight lay in discovering a simple mathematical relation
to explain the series of experiments he carried out on electromagnetic
induction. However, before we state and appreciate his laws, we must get
familiar with the notion of magnetic flux, F 
B
. Magnetic flux is defined in
the same way as electric flux is defined in Chapter 1. Magnetic flux through
2024-25
Electromagnetic
Induction
157
a plane of area A placed in a uniform magnetic field B (Fig. 6.4) can
be written as
F 
B
  = B 
.
 A = BA cos q (6.1)
where q   is angle between B and A. The notion of the area as a vector
has been discussed earlier in Chapter 1. Equation (6.1) can be
extended to curved surfaces and nonuniform fields.
If the magnetic field has different magnitudes and directions at
various parts of a surface as shown in Fig. 6.5, then the magnetic
flux through the surface is given by
1 1 2 2
d d F = + + B A B A . .
B
... =
B A .
i i
d
all
?
(6.2)
where ‘all’ stands for summation over all the area elements dA
i
comprising the surface and B
i
 is the magnetic field at the area element
dA
i
. The SI unit of magnetic flux is weber (Wb) or tesla meter
squared (T m
2
). Magnetic flux is a scalar quantity.
6.4  FARADAY’S LAW OF INDUCTION
From the experimental observations, Faraday arrived at a
conclusion that an emf is induced in a coil when magnetic flux
through the coil changes with time. Experimental observations
discussed in Section 6.2 can be explained using this concept.
The motion of a magnet towards or away from coil C
1
 in
Experiment 6.1 and moving a current-carrying coil C
2
 towards
or away from coil C
1
 in Experiment 6.2, change the magnetic
flux associated with coil C
1
.  The change in magnetic flux induces
emf in coil C
1
. It was this induced emf which caused electric
current to flow in coil C
1 
and through the galvanometer. A
plausible explanation for the observations of Experiment 6.3 is
as follows: When the tapping key K is pressed, the current in
coil C
2
 (and the resulting magnetic field) rises from zero to a
maximum value in a short time. Consequently, the magnetic
flux through the neighbouring coil C
1
 also increases. It is the change in
magnetic flux through coil C
1
 that produces an induced emf in coil C
1
.
When the key is held pressed, current in coil C
2
 is constant. Therefore,
there is no change in the magnetic flux through coil C
1
 and the current in
coil C
1
 drops to zero. When the key is released, the current in C
2
 and the
resulting magnetic field decreases from the maximum value to zero in a
short time. This results in a decrease in magnetic flux through coil C
1
and hence again induces an electric current in coil C
1
*. The common
point in all these observations is that the time rate of change of magnetic
flux through a circuit induces emf in it. Faraday stated experimental
observations in the form of a law called Faraday’s law of electromagnetic
induction. The law is stated below.
FIGURE 6.4 A plane of
surface area A placed in a
uniform magnetic field B.
FIGURE 6.5 Magnetic field B
i
at the i
th
 area element. dA
i
represents area vector of the
i
th
 area element.
* Note that sensitive electrical instruments in the vicinity of an electromagnet
can be damaged due to the induced emfs (and the resulting currents)  when the
electromagnet is turned on or off.
2024-25
Physics
158
 EXAMPLE 6.1
The magnitude of the induced emf in a circuit is equal
to the time rate of change of magnetic flux through the
circuit.
Mathematically, the induced emf is given by
d
–
d
B
t
F
e =
(6.3)
The negative sign indicates the direction of e  and hence
the direction of current in a closed loop. This will be
discussed in detail in the next section.
In the case of a closely wound coil of N turns, change
of flux associated with each turn, is the same. Therefore,
the expression for the total induced emf is given by
d
–
d
B
N
t
F
e =
(6.4)
The induced emf can be increased by increasing the
number of turns N of a closed coil.
From Eqs. (6.1) and (6.2), we see that the flux can be
varied by changing any one or more of the terms B, A and
q. In Experiments 6.1 and 6.2 in Section 6.2, the flux is
changed by varying B. The flux can also be altered by
changing the shape of a coil (that is, by shrinking it or
stretching it) in a magnetic field, or rotating a coil in a
magnetic field such that the angle q  between B and A
changes. In these cases too, an emf is induced in the
respective coils.
Example 6.1  Consider Experiment 6.2. (a) What would you do to obtain
a large deflection of the galvanometer? (b) How would you demonstrate
the presence of an induced current in the absence of a galvanometer?
Solution
(a) To obtain a large deflection, one or more of the following steps can
be taken:  (i) Use a rod made of soft iron inside the coil C
2
, (ii) Connect
the coil to a powerful battery, and (iii) Move the arrangement rapidly
towards the test coil C
1
.
(b) Replace the galvanometer by a small bulb, the kind one finds in a
small torch light. The relative motion between the two coils will cause
the bulb to glow and thus demonstrate the presence of an induced
current.
In experimental physics one must learn to innovate. Michael Faraday
who is ranked as one of the best experimentalists ever , was legendary
for his innovative skills.
Example 6.2 A square loop of side 10 cm and resistance 0.5 W is
placed vertically in the east-west  plane. A uniform magnetic field of
0.10 T is set up across the plane in the north-east direction. The
magnetic field is decreased to zero in 0.70 s at a steady rate. Determine
the magnitudes of induced emf and current during this time-interval.
Michael Faraday  [1791–
1867] Faraday made
numerous contributions to
science, viz., the discovery
of electromagnetic
induction, the laws of
electrolysis, benzene, and
the fact that the plane of
polarisation is rotated in an
electric field. He is also
credited with the invention
of the electric motor, the
electric generator and the
transformer. He is widely
regarded as the greatest
experimental scientist of
the nineteenth century.
MICHAEL FARADAY (1791–1867)
 EXAMPLE 6.2
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