NCERT Textbook: Electric Charges & Fields | Physics Class 12 - NEET PDF Download

 Page 1


Chapter One
ELECTRIC CHARGES
AND FIELDS
1.1  INTRODUCTION
All of us have the experience of seeing a spark or hearing a crackle when
we take off our synthetic clothes or sweater, particularly in dry weather.
Have you ever tried to find any explanation for this phenomenon? Another
common example of electric discharge is the lightning that we see in the
sky during thunderstorms. We also experience a sensation of an electric
shock either while opening the door of a car or holding the iron bar of a
bus after sliding from our seat. The reason for these experiences is
discharge of electric charges through our body, which were accumulated
due to rubbing of insulating surfaces. You might have also heard that
this is due to generation of static electricity. This is precisely the topic we
are going to discuss in this and the next chapter. Static means anything
that does not move or change with time. Electrostatics deals with
the study of forces, fields and potentials arising from
static charges.
1.2  ELECTRIC CHARGE
Historically the credit of discovery of the fact that amber rubbed with
wool or silk cloth attracts light objects goes to Thales of Miletus, Greece,
around 600 BC. The name electricity is coined from the Greek word
2024-25 2024-25
Page 2


Chapter One
ELECTRIC CHARGES
AND FIELDS
1.1  INTRODUCTION
All of us have the experience of seeing a spark or hearing a crackle when
we take off our synthetic clothes or sweater, particularly in dry weather.
Have you ever tried to find any explanation for this phenomenon? Another
common example of electric discharge is the lightning that we see in the
sky during thunderstorms. We also experience a sensation of an electric
shock either while opening the door of a car or holding the iron bar of a
bus after sliding from our seat. The reason for these experiences is
discharge of electric charges through our body, which were accumulated
due to rubbing of insulating surfaces. You might have also heard that
this is due to generation of static electricity. This is precisely the topic we
are going to discuss in this and the next chapter. Static means anything
that does not move or change with time. Electrostatics deals with
the study of forces, fields and potentials arising from
static charges.
1.2  ELECTRIC CHARGE
Historically the credit of discovery of the fact that amber rubbed with
wool or silk cloth attracts light objects goes to Thales of Miletus, Greece,
around 600 BC. The name electricity is coined from the Greek word
2024-25 2024-25
2
Physics
elektron meaning amber. Many such pairs of materials were known which
on rubbing could attract light objects like straw, pith balls and bits of
papers.
It was observed that if two glass rods rubbed with wool or silk cloth
are brought close to each other, they repel each other [Fig. 1.1(a)]. The
two strands of wool or two pieces of silk cloth, with which the rods were
rubbed, also repel each other. However, the glass rod and wool attracted
each other. Similarly, two plastic rods rubbed with cat’s fur repelled each
other [Fig. 1.1(b)] but attracted the fur. On the other hand, the plastic
rod attracts the glass rod [Fig. 1.1(c)] and repel the silk or wool with
which the glass rod is rubbed. The glass rod repels the fur.
These seemingly simple facts  were established from years of efforts
and careful experiments and their analyses. It was concluded, after many
careful studies by different scientists, that there were only two kinds of
an entry which is called the electric charge. We say that the bodies like
glass or plastic rods, silk, fur and pith balls are electrified. They acquire
an electric charge on rubbing. There are two kinds of electrification and
we find  that (i) like charges repel and (ii) unlike charges attract each
other. The property which differentiates the two kinds of charges is called
the polarity of charge.
When a glass rod is rubbed with silk, the rod acquires one kind of
charge and the silk acquires the second kind of charge. This is true for
any pair of objects that are rubbed to be electrified. Now if the electrified
glass rod is brought in contact with silk, with which it was rubbed, they
no longer attract each other. They also do not attract or repel other light
objects as they did on being electrified.
Thus, the charges acquired after rubbing are lost when the charged
bodies are brought in contact. What can you conclude from these
observations? It just tells us that unlike charges acquired by the objects
neutralise or nullify each other’s effect. Therefore, the charges were named
as positive and negative by the American scientist Benjamin Franklin.
By convention, the charge on glass rod or cat’s fur is called positive and
that on plastic rod or silk is termed negative. If an object possesses an
electric charge, it is said to be electrified or charged. When it has no charge
it is said to be electrically neutral.
FIGURE 1.1 Rods: like charges repel and unlike charges attract each other.
2024-25 2024-25
Page 3


Chapter One
ELECTRIC CHARGES
AND FIELDS
1.1  INTRODUCTION
All of us have the experience of seeing a spark or hearing a crackle when
we take off our synthetic clothes or sweater, particularly in dry weather.
Have you ever tried to find any explanation for this phenomenon? Another
common example of electric discharge is the lightning that we see in the
sky during thunderstorms. We also experience a sensation of an electric
shock either while opening the door of a car or holding the iron bar of a
bus after sliding from our seat. The reason for these experiences is
discharge of electric charges through our body, which were accumulated
due to rubbing of insulating surfaces. You might have also heard that
this is due to generation of static electricity. This is precisely the topic we
are going to discuss in this and the next chapter. Static means anything
that does not move or change with time. Electrostatics deals with
the study of forces, fields and potentials arising from
static charges.
1.2  ELECTRIC CHARGE
Historically the credit of discovery of the fact that amber rubbed with
wool or silk cloth attracts light objects goes to Thales of Miletus, Greece,
around 600 BC. The name electricity is coined from the Greek word
2024-25 2024-25
2
Physics
elektron meaning amber. Many such pairs of materials were known which
on rubbing could attract light objects like straw, pith balls and bits of
papers.
It was observed that if two glass rods rubbed with wool or silk cloth
are brought close to each other, they repel each other [Fig. 1.1(a)]. The
two strands of wool or two pieces of silk cloth, with which the rods were
rubbed, also repel each other. However, the glass rod and wool attracted
each other. Similarly, two plastic rods rubbed with cat’s fur repelled each
other [Fig. 1.1(b)] but attracted the fur. On the other hand, the plastic
rod attracts the glass rod [Fig. 1.1(c)] and repel the silk or wool with
which the glass rod is rubbed. The glass rod repels the fur.
These seemingly simple facts  were established from years of efforts
and careful experiments and their analyses. It was concluded, after many
careful studies by different scientists, that there were only two kinds of
an entry which is called the electric charge. We say that the bodies like
glass or plastic rods, silk, fur and pith balls are electrified. They acquire
an electric charge on rubbing. There are two kinds of electrification and
we find  that (i) like charges repel and (ii) unlike charges attract each
other. The property which differentiates the two kinds of charges is called
the polarity of charge.
When a glass rod is rubbed with silk, the rod acquires one kind of
charge and the silk acquires the second kind of charge. This is true for
any pair of objects that are rubbed to be electrified. Now if the electrified
glass rod is brought in contact with silk, with which it was rubbed, they
no longer attract each other. They also do not attract or repel other light
objects as they did on being electrified.
Thus, the charges acquired after rubbing are lost when the charged
bodies are brought in contact. What can you conclude from these
observations? It just tells us that unlike charges acquired by the objects
neutralise or nullify each other’s effect. Therefore, the charges were named
as positive and negative by the American scientist Benjamin Franklin.
By convention, the charge on glass rod or cat’s fur is called positive and
that on plastic rod or silk is termed negative. If an object possesses an
electric charge, it is said to be electrified or charged. When it has no charge
it is said to be electrically neutral.
FIGURE 1.1 Rods: like charges repel and unlike charges attract each other.
2024-25 2024-25
Electric Charges
and Fields
3
A simple apparatus to detect charge on a body is the gold-leaf
electroscope [Fig. 1.2(a)]. It consists of a vertical metal rod housed in a
box, with two thin gold leaves attached to its bottom end. When a charged
object touches the metal knob at the top of the rod, charge flows on to
the leaves and they diverge. The degree of divergance is an indicator of
the amount of charge.
Try to understand why material bodies acquire charge. You know that
all matter is made up of atoms and/or molecules. Although normally the
materials are electrically neutral,  they do contain charges; but their charges
are exactly balanced. Forces that hold the molecules together, forces that
hold atoms together in a solid, the adhesive force of glue, forces associated
with surface tension, all are basically electrical in nature, arising from the
forces between charged particles. Thus the electric force is all pervasive and
it encompasses almost each and every field associated with our life. It is
therefore essential that we learn more about such a force.
To electrify a neutral body, we need to add or remove one kind of
charge. When we say that a body is charged, we always refer to this
excess charge or deficit of charge. In solids,  some of the electrons, being
less tightly bound in the atom, are the charges which are transferred
from one body to the other.  A body can thus be charged positively by
losing some of its electrons. Similarly, a body can be charged negatively
by gaining electrons. When we rub a glass rod with silk, some of the
electrons from the rod are transferred to the silk cloth. Thus the rod gets
positively charged and the silk gets negatively charged. No new charge is
created in the process of rubbing. Also the number of electrons, that are
transferred, is a very small fraction of the total number of electrons in the
material body.
1.3  CONDUCTORS AND INSULATORS
Some substances readily allow passage of electricity through them, others
do not.  Those which allow electricity to pass through them easily are
called conductors. They have electric charges (electrons) that are
comparatively free to move inside the material. Metals, human and animal
bodies and earth are conductors. Most of the non-metals like glass,
porcelain, plastic, nylon, wood offer high resistance to the passage of
electricity through them. They are called insulators. Most  substances
fall into one of the two classes stated above*.
When some charge is transferred to a conductor, it readily gets
distributed over the entire surface of the conductor. In contrast, if some
charge is put on an insulator, it stays at the same place. You will learn
why this happens in the next chapter.
This property of the materials tells you why a nylon or plastic comb
gets electrified on combing dry hair or on rubbing, but a metal article
* There is a third category called semiconductors, which offer resistance to the
movement of charges which is intermediate between the conductors and
insulators.
2024-25 2024-25
Page 4


Chapter One
ELECTRIC CHARGES
AND FIELDS
1.1  INTRODUCTION
All of us have the experience of seeing a spark or hearing a crackle when
we take off our synthetic clothes or sweater, particularly in dry weather.
Have you ever tried to find any explanation for this phenomenon? Another
common example of electric discharge is the lightning that we see in the
sky during thunderstorms. We also experience a sensation of an electric
shock either while opening the door of a car or holding the iron bar of a
bus after sliding from our seat. The reason for these experiences is
discharge of electric charges through our body, which were accumulated
due to rubbing of insulating surfaces. You might have also heard that
this is due to generation of static electricity. This is precisely the topic we
are going to discuss in this and the next chapter. Static means anything
that does not move or change with time. Electrostatics deals with
the study of forces, fields and potentials arising from
static charges.
1.2  ELECTRIC CHARGE
Historically the credit of discovery of the fact that amber rubbed with
wool or silk cloth attracts light objects goes to Thales of Miletus, Greece,
around 600 BC. The name electricity is coined from the Greek word
2024-25 2024-25
2
Physics
elektron meaning amber. Many such pairs of materials were known which
on rubbing could attract light objects like straw, pith balls and bits of
papers.
It was observed that if two glass rods rubbed with wool or silk cloth
are brought close to each other, they repel each other [Fig. 1.1(a)]. The
two strands of wool or two pieces of silk cloth, with which the rods were
rubbed, also repel each other. However, the glass rod and wool attracted
each other. Similarly, two plastic rods rubbed with cat’s fur repelled each
other [Fig. 1.1(b)] but attracted the fur. On the other hand, the plastic
rod attracts the glass rod [Fig. 1.1(c)] and repel the silk or wool with
which the glass rod is rubbed. The glass rod repels the fur.
These seemingly simple facts  were established from years of efforts
and careful experiments and their analyses. It was concluded, after many
careful studies by different scientists, that there were only two kinds of
an entry which is called the electric charge. We say that the bodies like
glass or plastic rods, silk, fur and pith balls are electrified. They acquire
an electric charge on rubbing. There are two kinds of electrification and
we find  that (i) like charges repel and (ii) unlike charges attract each
other. The property which differentiates the two kinds of charges is called
the polarity of charge.
When a glass rod is rubbed with silk, the rod acquires one kind of
charge and the silk acquires the second kind of charge. This is true for
any pair of objects that are rubbed to be electrified. Now if the electrified
glass rod is brought in contact with silk, with which it was rubbed, they
no longer attract each other. They also do not attract or repel other light
objects as they did on being electrified.
Thus, the charges acquired after rubbing are lost when the charged
bodies are brought in contact. What can you conclude from these
observations? It just tells us that unlike charges acquired by the objects
neutralise or nullify each other’s effect. Therefore, the charges were named
as positive and negative by the American scientist Benjamin Franklin.
By convention, the charge on glass rod or cat’s fur is called positive and
that on plastic rod or silk is termed negative. If an object possesses an
electric charge, it is said to be electrified or charged. When it has no charge
it is said to be electrically neutral.
FIGURE 1.1 Rods: like charges repel and unlike charges attract each other.
2024-25 2024-25
Electric Charges
and Fields
3
A simple apparatus to detect charge on a body is the gold-leaf
electroscope [Fig. 1.2(a)]. It consists of a vertical metal rod housed in a
box, with two thin gold leaves attached to its bottom end. When a charged
object touches the metal knob at the top of the rod, charge flows on to
the leaves and they diverge. The degree of divergance is an indicator of
the amount of charge.
Try to understand why material bodies acquire charge. You know that
all matter is made up of atoms and/or molecules. Although normally the
materials are electrically neutral,  they do contain charges; but their charges
are exactly balanced. Forces that hold the molecules together, forces that
hold atoms together in a solid, the adhesive force of glue, forces associated
with surface tension, all are basically electrical in nature, arising from the
forces between charged particles. Thus the electric force is all pervasive and
it encompasses almost each and every field associated with our life. It is
therefore essential that we learn more about such a force.
To electrify a neutral body, we need to add or remove one kind of
charge. When we say that a body is charged, we always refer to this
excess charge or deficit of charge. In solids,  some of the electrons, being
less tightly bound in the atom, are the charges which are transferred
from one body to the other.  A body can thus be charged positively by
losing some of its electrons. Similarly, a body can be charged negatively
by gaining electrons. When we rub a glass rod with silk, some of the
electrons from the rod are transferred to the silk cloth. Thus the rod gets
positively charged and the silk gets negatively charged. No new charge is
created in the process of rubbing. Also the number of electrons, that are
transferred, is a very small fraction of the total number of electrons in the
material body.
1.3  CONDUCTORS AND INSULATORS
Some substances readily allow passage of electricity through them, others
do not.  Those which allow electricity to pass through them easily are
called conductors. They have electric charges (electrons) that are
comparatively free to move inside the material. Metals, human and animal
bodies and earth are conductors. Most of the non-metals like glass,
porcelain, plastic, nylon, wood offer high resistance to the passage of
electricity through them. They are called insulators. Most  substances
fall into one of the two classes stated above*.
When some charge is transferred to a conductor, it readily gets
distributed over the entire surface of the conductor. In contrast, if some
charge is put on an insulator, it stays at the same place. You will learn
why this happens in the next chapter.
This property of the materials tells you why a nylon or plastic comb
gets electrified on combing dry hair or on rubbing, but a metal article
* There is a third category called semiconductors, which offer resistance to the
movement of charges which is intermediate between the conductors and
insulators.
2024-25 2024-25
4
Physics
like spoon does not. The charges on metal leak through
our body to the ground as both are conductors of
electricity. However, if a metal rod with a wooden or plastic
handle is rubbed without touching its metal part, it shows
signs of charging.
1.4  BASIC PROPERTIES OF ELECTRIC
CHARGE
We have seen that there are two types of charges, namely
positive and negative and their effects tend to cancel each
other. Here,  we shall now describe some other properties
of the electric charge.
If the sizes of charged bodies are very small as
compared to the distances between them, we treat them
as point charges. All the charge content of the body is
assumed to be concentrated at one point in space.
1.4.1  Additivity of charges
We have not as yet given a quantitative definition of a
charge; we shall follow it up in the next section. We shall
tentatively assume that this can be done and proceed. If
a system contains two point charges q
1
 and q
2
, the total
charge of the system is obtained simply by adding
algebraically q
1
 and q
2 
,
 
i.e., charges add up like real numbers or they
are scalars like the mass of a body. If a system contains n charges q
1
,
q
2
, q
3
, …, q
n
, then the total charge of the system is q
1
 + q
2
 + q
3
 + … + q
n
.  Charge has  magnitude but no direction, similar to mass. However,
there is one difference between mass and charge. Mass of a body is
always positive whereas a charge can be either positive or negative.
Proper signs have to be used while adding the charges in a system. For
example, the total charge of a system containing five charges +1, +2, –3,
+4 and –5, in some arbitrary unit, is (+1) + (+2) + (–3) + (+4) + (–5) = –1 in
the same unit.
1.4.2  Charge is conserved
We have already  hinted to the fact that when bodies are charged by
rubbing, there is transfer of electrons from one body to the other; no new
charges are either created or destroyed. A picture of particles of electric
charge enables us to understand the idea of conservation of charge. When
we rub two bodies, what one body gains in charge the other body loses.
Within an isolated system consisting of many charged bodies, due to
interactions among the bodies, charges may get redistributed but it is
found that the total charge of the isolated system is always conserved.
Conservation of charge has been established experimentally.
It is not possible to create or destroy net charge carried by any isolated
system although the charge carrying particles may be created or destroyed
FIGURE 1.2 Electroscopes: (a)
The gold leaf electroscope, (b)
Schematics of a simple
electroscope.
2024-25 2024-25
Page 5


Chapter One
ELECTRIC CHARGES
AND FIELDS
1.1  INTRODUCTION
All of us have the experience of seeing a spark or hearing a crackle when
we take off our synthetic clothes or sweater, particularly in dry weather.
Have you ever tried to find any explanation for this phenomenon? Another
common example of electric discharge is the lightning that we see in the
sky during thunderstorms. We also experience a sensation of an electric
shock either while opening the door of a car or holding the iron bar of a
bus after sliding from our seat. The reason for these experiences is
discharge of electric charges through our body, which were accumulated
due to rubbing of insulating surfaces. You might have also heard that
this is due to generation of static electricity. This is precisely the topic we
are going to discuss in this and the next chapter. Static means anything
that does not move or change with time. Electrostatics deals with
the study of forces, fields and potentials arising from
static charges.
1.2  ELECTRIC CHARGE
Historically the credit of discovery of the fact that amber rubbed with
wool or silk cloth attracts light objects goes to Thales of Miletus, Greece,
around 600 BC. The name electricity is coined from the Greek word
2024-25 2024-25
2
Physics
elektron meaning amber. Many such pairs of materials were known which
on rubbing could attract light objects like straw, pith balls and bits of
papers.
It was observed that if two glass rods rubbed with wool or silk cloth
are brought close to each other, they repel each other [Fig. 1.1(a)]. The
two strands of wool or two pieces of silk cloth, with which the rods were
rubbed, also repel each other. However, the glass rod and wool attracted
each other. Similarly, two plastic rods rubbed with cat’s fur repelled each
other [Fig. 1.1(b)] but attracted the fur. On the other hand, the plastic
rod attracts the glass rod [Fig. 1.1(c)] and repel the silk or wool with
which the glass rod is rubbed. The glass rod repels the fur.
These seemingly simple facts  were established from years of efforts
and careful experiments and their analyses. It was concluded, after many
careful studies by different scientists, that there were only two kinds of
an entry which is called the electric charge. We say that the bodies like
glass or plastic rods, silk, fur and pith balls are electrified. They acquire
an electric charge on rubbing. There are two kinds of electrification and
we find  that (i) like charges repel and (ii) unlike charges attract each
other. The property which differentiates the two kinds of charges is called
the polarity of charge.
When a glass rod is rubbed with silk, the rod acquires one kind of
charge and the silk acquires the second kind of charge. This is true for
any pair of objects that are rubbed to be electrified. Now if the electrified
glass rod is brought in contact with silk, with which it was rubbed, they
no longer attract each other. They also do not attract or repel other light
objects as they did on being electrified.
Thus, the charges acquired after rubbing are lost when the charged
bodies are brought in contact. What can you conclude from these
observations? It just tells us that unlike charges acquired by the objects
neutralise or nullify each other’s effect. Therefore, the charges were named
as positive and negative by the American scientist Benjamin Franklin.
By convention, the charge on glass rod or cat’s fur is called positive and
that on plastic rod or silk is termed negative. If an object possesses an
electric charge, it is said to be electrified or charged. When it has no charge
it is said to be electrically neutral.
FIGURE 1.1 Rods: like charges repel and unlike charges attract each other.
2024-25 2024-25
Electric Charges
and Fields
3
A simple apparatus to detect charge on a body is the gold-leaf
electroscope [Fig. 1.2(a)]. It consists of a vertical metal rod housed in a
box, with two thin gold leaves attached to its bottom end. When a charged
object touches the metal knob at the top of the rod, charge flows on to
the leaves and they diverge. The degree of divergance is an indicator of
the amount of charge.
Try to understand why material bodies acquire charge. You know that
all matter is made up of atoms and/or molecules. Although normally the
materials are electrically neutral,  they do contain charges; but their charges
are exactly balanced. Forces that hold the molecules together, forces that
hold atoms together in a solid, the adhesive force of glue, forces associated
with surface tension, all are basically electrical in nature, arising from the
forces between charged particles. Thus the electric force is all pervasive and
it encompasses almost each and every field associated with our life. It is
therefore essential that we learn more about such a force.
To electrify a neutral body, we need to add or remove one kind of
charge. When we say that a body is charged, we always refer to this
excess charge or deficit of charge. In solids,  some of the electrons, being
less tightly bound in the atom, are the charges which are transferred
from one body to the other.  A body can thus be charged positively by
losing some of its electrons. Similarly, a body can be charged negatively
by gaining electrons. When we rub a glass rod with silk, some of the
electrons from the rod are transferred to the silk cloth. Thus the rod gets
positively charged and the silk gets negatively charged. No new charge is
created in the process of rubbing. Also the number of electrons, that are
transferred, is a very small fraction of the total number of electrons in the
material body.
1.3  CONDUCTORS AND INSULATORS
Some substances readily allow passage of electricity through them, others
do not.  Those which allow electricity to pass through them easily are
called conductors. They have electric charges (electrons) that are
comparatively free to move inside the material. Metals, human and animal
bodies and earth are conductors. Most of the non-metals like glass,
porcelain, plastic, nylon, wood offer high resistance to the passage of
electricity through them. They are called insulators. Most  substances
fall into one of the two classes stated above*.
When some charge is transferred to a conductor, it readily gets
distributed over the entire surface of the conductor. In contrast, if some
charge is put on an insulator, it stays at the same place. You will learn
why this happens in the next chapter.
This property of the materials tells you why a nylon or plastic comb
gets electrified on combing dry hair or on rubbing, but a metal article
* There is a third category called semiconductors, which offer resistance to the
movement of charges which is intermediate between the conductors and
insulators.
2024-25 2024-25
4
Physics
like spoon does not. The charges on metal leak through
our body to the ground as both are conductors of
electricity. However, if a metal rod with a wooden or plastic
handle is rubbed without touching its metal part, it shows
signs of charging.
1.4  BASIC PROPERTIES OF ELECTRIC
CHARGE
We have seen that there are two types of charges, namely
positive and negative and their effects tend to cancel each
other. Here,  we shall now describe some other properties
of the electric charge.
If the sizes of charged bodies are very small as
compared to the distances between them, we treat them
as point charges. All the charge content of the body is
assumed to be concentrated at one point in space.
1.4.1  Additivity of charges
We have not as yet given a quantitative definition of a
charge; we shall follow it up in the next section. We shall
tentatively assume that this can be done and proceed. If
a system contains two point charges q
1
 and q
2
, the total
charge of the system is obtained simply by adding
algebraically q
1
 and q
2 
,
 
i.e., charges add up like real numbers or they
are scalars like the mass of a body. If a system contains n charges q
1
,
q
2
, q
3
, …, q
n
, then the total charge of the system is q
1
 + q
2
 + q
3
 + … + q
n
.  Charge has  magnitude but no direction, similar to mass. However,
there is one difference between mass and charge. Mass of a body is
always positive whereas a charge can be either positive or negative.
Proper signs have to be used while adding the charges in a system. For
example, the total charge of a system containing five charges +1, +2, –3,
+4 and –5, in some arbitrary unit, is (+1) + (+2) + (–3) + (+4) + (–5) = –1 in
the same unit.
1.4.2  Charge is conserved
We have already  hinted to the fact that when bodies are charged by
rubbing, there is transfer of electrons from one body to the other; no new
charges are either created or destroyed. A picture of particles of electric
charge enables us to understand the idea of conservation of charge. When
we rub two bodies, what one body gains in charge the other body loses.
Within an isolated system consisting of many charged bodies, due to
interactions among the bodies, charges may get redistributed but it is
found that the total charge of the isolated system is always conserved.
Conservation of charge has been established experimentally.
It is not possible to create or destroy net charge carried by any isolated
system although the charge carrying particles may be created or destroyed
FIGURE 1.2 Electroscopes: (a)
The gold leaf electroscope, (b)
Schematics of a simple
electroscope.
2024-25 2024-25
Electric Charges
and Fields
5
in a process. Sometimes nature creates charged particles: a neutron turns
into a proton and an electron. The proton and electron thus created have
equal and opposite charges and the total charge is zero before and after
the creation.
1.4.3  Quantisation of charge
Experimentally it is established that all free charges are integral multiples
of a basic unit of charge denoted by e. Thus charge q on a body is always
given by
q = ne
where n is any integer, positive or negative. This basic unit of charge is
the charge that an electron or proton carries. By convention, the charge
on an electron is taken to be negative; therefore charge on an electron is
written as –e and that on a proton as +e.
The fact that electric charge is always an integral multiple of e is termed
as quantisation of charge. There are a large number of situations in physics
where certain physical quantities are quantised. The quantisation of charge
was first suggested by the experimental laws of electrolysis discovered by
English experimentalist Faraday. It was experimentally demonstrated by
Millikan in 1912.
In the International System (SI) of Units, a unit of charge is called a
coulomb and is denoted by the symbol C. A coulomb is defined in terms
the unit of the electric current which you are going to learn in a
subsequent chapter. In terms of this definition, one coulomb is the charge
flowing through a wire in 1 s if the current is 1 A (ampere), (see Chapter 1
of Class XI, Physics Textbook , Part I). In this system, the value of the
basic unit of charge is
e = 1.602192 × 10
–19 
C
Thus, there are about 6 × 10
18 
electrons in a charge of  –1C. In
electrostatics, charges of this large magnitude are seldom encountered
and hence we use smaller units 1 mC (micro coulomb) = 10
–6
 C or 1 mC
(milli coulomb) = 10
–3
 C.
If the protons and electrons are the only basic charges in the
universe, all the observable charges have to be integral multiples of e.
Thus, if a body contains n
1
 electrons and n
2
 protons, the total amount
of charge on the body is n
2
 × e + n
1
 × (–e) = (n
2
 – n
1
) e. Since n
1
 and n
2
are integers, their difference is also an integer. Thus the charge on any
body is always an integral multiple of e and can be increased or
decreased also in steps of e.
The step size e is, however, very small because at the macroscopic
level, we deal with charges of a few mC. At this scale the fact that charge of
a body can increase or decrease in units of e is not visible. In this respect,
the grainy nature of the charge is lost and it appears to be continuous.
This situation can be compared with the geometrical concepts of points
and lines. A dotted line viewed from a distance appears continuous to
us but is not continuous in reality. As many points very close to
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