Electric Charge And Its Properties | Class 12 Physics Electrostatics NCERT Based Notes

 

1. Introduction

Electricity is one of the most important forms of energy in nature. Almost every electrical and electronic device used in our daily life operates because of electric charge. From a small LED bulb to satellites and communication systems, the role of electric charge is fundamental.

The branch of Physics that deals with electric charges at rest is called Electrostatics.

The word Electrostatics is derived from two words:

Word	Meaning
Electro	Electricity
Statics	At rest

Hence, Electrostatics is the study of electric charges at rest and the forces acting between them.

This chapter forms the foundation of electricity and magnetism. It explains how electric charges interact, how electric fields are produced, and how these concepts are applied in science and technology.

Historical Background

The phenomenon of electricity was first observed over 2500 years ago. The ancient Greeks discovered that when a piece of amber was rubbed with wool or animal fur, it attracted light objects such as dry leaves, feathers and straw. The Greek word for amber is Elektron. The modern word Electricity is derived from this Greek word. At that time, people did not know the reason for this attraction. Today we know that rubbing transfers electrons from one body to another, producing electric charge.

Discovery of Positive and Negative Charges

Many scientists studied electricity, but Benjamin Franklin introduced the idea of positive and negative charges. He assumed that:

• A body having excess electric fluid is positively charged.
• A body having deficiency of electric fluid is negatively charged.

Although the modern electron theory is different, Franklin's naming convention is still used throughout Physics.

Electric Charge

Electric charge is one of the fundamental properties of matter. It is the property because of which bodies exert electrical forces on one another.

Definition

Electric charge is the physical property of matter due to which a body experiences an electric force when placed in the electric field of another charged body. In simple language, Electric charge is the property responsible for electrical attraction and repulsion. Electric charge is represented by Q or q. Generally,

Symbol	Meaning
Q	Large charge
q	Small charge

The SI unit of electric charge is Coulomb (C). One Coulomb is a comparatively large amount of charge.

Structure of an Atom

Every atom consists of three fundamental particles.

Particle	Symbol	Charge
Electron	e⁻	−1.602 × 10⁻¹⁹ C
Proton	p⁺	+1.602 × 10⁻¹⁹ C
Neutron	n	0

Important facts:

• Protons are present inside the nucleus.
• Neutrons are also present inside the nucleus.
• Electrons revolve around the nucleus in different energy levels.

Why Does a Body Become Charged?

Normally, Number of Protons = Number of Electrons, Therefore, Net Charge = Zero. Such a body is called an electrically neutral body. A body becomes charged only when the number of electrons changes.

Process	Result
Gain of electrons	Negative charge
Loss of electrons	Positive charge

Why Are Only Electrons Transferred?

During charging,

• Protons never move because they are tightly bound inside the nucleus.
• Neutrons also remain fixed inside the nucleus.
• Only electrons, which are loosely bound in the outermost shell, can move from one object to another.

Therefore,

Charging of a body always takes place due to the transfer of electrons only.

Elementary Charge

The smallest independent unit of electric charge is called the elementary charge. Its value is e = 1.602 × 10⁻¹⁹ C. This is the magnitude of the charge carried by:

Particle	Charge
One electron	−1.6 × 10⁻¹⁹ C
One proton	+1.6 × 10⁻¹⁹ C

The charges are equal in magnitude but opposite in sign.

Particle	Charge
Electron	−e
Proton	+e

Conductors and Insulators

Different materials behave differently when electric charge is given to them. On the basis of the movement of electric charges, materials are mainly classified into two categories:

1. Conductors & 2. Insulators

Conductors

A conductor is a material through which electric charges can move freely. Conductors contain a large number of free electrons. These electrons are loosely bound to the atoms and can move easily from one place to another when an electric field is applied. Because of the presence of free electrons, conductors allow the flow of electric charge.

Examples of Conductors

Copper, Aluminium, Silver, Gold, Iron, Graphite, Mercury, Human body (due to water and dissolved salts) In a conductor, the positive ions remain fixed, while only free electrons move. This movement of electrons is responsible for electrical conduction.

Insulators

An insulator is a material through which electric charges cannot move freely. In insulators, electrons are tightly bound to their atoms. Therefore, there are almost no free electrons available for conduction. As a result, electric charge remains localized at the place where it is produced. Examples of Insulators—Glass, Rubber, Plastic, Wood (dry), Mica, Porcelain, Dry air

Difference Between Conductors and Insulators

Conductors	Insulators
Charges move freely	Charges cannot move freely
Many free electrons	Almost no free electrons
Low electrical resistance	High electrical resistance
Allow electric current	Do not allow electric current
Example: Copper, Aluminium	Example: Rubber, Glass

Free Electrons

The electrons present in the outermost shell of atoms of conductors are weakly bound and can move freely throughout the material. These electrons are called free electrons. The movement of free electrons is responsible for the flow of electric current.

Earthing (Grounding)

Earthing is the process of connecting a conductor to the Earth through a conducting wire. The Earth is considered a huge reservoir of electric charge because it can accept or supply a large amount of charge without any noticeable change in its electric potential.

Importance of Earthing

• Protects people from electric shock.
• Prevents damage to electrical appliances.
• Removes excess charge from a conductor.
• Maintains safety in electrical installations.

Methods of Charging

1. Charging by Conduction (Charging by Contact)

Charging by conduction occurs when a charged conductor is brought into direct contact with an uncharged conductor.

Process

1. A charged conductor touches a neutral conductor.
2. Free electrons move from one conductor to the other.
3. After separation, both conductors become charged.

The charge acquired by the neutral conductor is of the same sign as the charged conductor.

Remember

• Direct contact is necessary.
• Electrons are transferred.
• Both bodies finally have the same type of charge.
• Total charge remains conserved.

Example

If a negatively charged metal sphere touches a neutral metal sphere:

• Electrons flow to the neutral sphere.
• Both spheres become negatively charged.

2. Charging by Induction

Charging by induction is the process of charging a conductor without direct contact. This is one of the most important concepts in electrostatics.

Principle

When a charged body is brought near an uncharged conductor, the free electrons inside the conductor rearrange themselves due to the electric force. No electrons are transferred between the charged body and the conductor unless the conductor is earthed.

Steps of Charging by Induction

Suppose a negatively charged rod is brought near a neutral metal sphere.

Step 1

The negative rod repels the free electrons of the sphere. Electrons move to the far end of the sphere.

Step 2

The end nearer to the rod becomes positively charged due to deficiency of electrons. The far end becomes negatively charged due to excess electrons. This process is called charge separation.

Step 3

Now connect the far end of the sphere to the Earth. The excess electrons flow into the Earth.

Step 4

Disconnect the Earth first.

Step 5

Finally remove the charged rod. The sphere is left with a net positive charge.

Characteristics of Charging by Induction

• No direct contact is required.
• Charge is produced due to redistribution of electrons.
• Earthing is generally required to obtain a permanent charge.
• The induced charge is opposite in sign to the inducing charge.

Comparison: Friction, Conduction and Induction

Method	Contact Required	Electron Transfer	Final Charge
Friction	Yes (Rubbing)	Yes	Opposite charges on both bodies
Conduction	Yes	Yes	Same sign as charging body
Induction	No	Redistribution first; with earthing, excess electrons flow	Opposite sign to inducing body

Basic Properties of Electric Charge

Electric charge possesses some fundamental properties which are valid in all situations. These properties help us understand the behaviour of charged bodies and form the basis of electrostatics.

The four fundamental properties of electric charge are:

1. Additivity of Charges
2. Conservation of Charge
3. Quantisation of Charge
4. Invariance of Charge

1. Additivity of Charges

The total charge on a system is the algebraic sum of all individual charges present in it. Since charge is a scalar quantity, charges are added algebraically and not vectorially.

If a system contains several charged particles, the total charge is:

Q = q₁ + q₂ + q₃ + … + qₙ

where:

• Q = Total charge of the system
• q₁, q₂, q₃, …, qₙ = Individual charges of the particles

Example 1

A body has three charges:

+5 C, −2 C and +3 C

Then,

Q = (+5) + (−2) + (+3) = +6 C

Hence, the net charge on the body is +6 C.

Example 2

If a system contains:

+4 μC, −7 μC and +1 μC

then,

Q = 4 − 7 + 1 = −2 μC

The system is negatively charged.

Important Points

• Charge is a scalar quantity.
• Only algebraic addition is used.
• Positive and negative signs must be considered while adding charges.

2. Conservation of Charge

The law of conservation of charge states:

The total electric charge of an isolated system always remains constant. Electric charge can neither be created nor destroyed; it can only be transferred from one body to another. This is one of the most fundamental laws of Physics.

Explanation

Suppose two neutral bodies are rubbed together:

• One body loses electrons.
• The other body gains the same number of electrons.

Therefore:

• One becomes positively charged.
• The other becomes negatively charged.

Although charges appear on both bodies, the total charge of the system remains unchanged.

Example

Initially:

Total charge = 0

After rubbing:

Glass rod = +Q
Silk cloth = −Q

Total charge:

= (+Q) + (−Q)
= 0

Hence, total charge remains conserved.

Everyday Example

When a plastic comb is rubbed with dry hair:

• The comb gains electrons and becomes negatively charged.
• The hair loses electrons and becomes positively charged.

No new charge is produced. Only electrons are transferred.

Importance of Conservation of Charge

• It is valid in all electrical phenomena.
• It is true for microscopic as well as macroscopic systems.
• It is one of the fundamental conservation laws of nature.

Quantization of Charge (Quantisation of Electric Charge)

Quantization of charge means that the electric charge on any isolated body always exists in discrete units. In other words, the total charge on a body is always an integral (whole number) multiple of the elementary charge. A body cannot possess a fractional amount of electric charge under ordinary conditions. Mathematically

Q = ± ne

Where

• Q = Total charge on the body (Coulomb)
• n = Number of electrons transferred (0, 1, 2, 3, …)
• e = Elementary charge = 1.6 × 10⁻¹⁹ C

Here, the value of n must always be a whole number (integer). Therefore, the possible values of charge are:

± e, ± 2e, ± 3e, ± 4e, …

while charges such as:

2.5e, 3.2e, 7.75e

are not possible, because they are not integral multiples of the elementary charge.

Why is Charge Quantized?

Electric charge is carried by electrons and protons. During charging, only electrons are transferred from one body to another. Since electrons cannot be transferred in fractions under ordinary conditions, a body can gain or lose only a whole number of electrons.

As each electron carries a fixed charge of 1.6 × 10⁻¹⁹ C, the total charge on a body must always be an integral multiple of this value.

Example

Suppose a body loses 5 electrons:

Q = +5e
= +5 × 1.6 × 10⁻¹⁹
= +8.0 × 10⁻¹⁹ C

Similarly, if a body gains 8 electrons:

Q = -8e
= -8 × 1.6 × 10⁻¹⁹
= -1.28 × 10⁻¹⁸ C

Key Points

• Electric charge is always quantized.
• Elementary charge is 1.6 × 10⁻¹⁹ C.
• The value of n is always an integer.
• Fractional values of charge are not possible.
• Loss of electrons gives a positive charge, while gain of electrons gives a negative charge.

Limitations

For ordinary objects, the value of n is extremely large. Therefore, charge appears to be continuous on macroscopic bodies even though it is actually quantised.

4. Invariance of Charge

Invariance of charge means that the value of electric charge remains unchanged under all conditions. It does not depend on the state of motion of the charged body or the frame of reference of the observer.

Whether a charged body is at rest or in motion, its electric charge always remains the same.

Key Points

• The value of electric charge remains constant.
• It is independent of the state of motion of the charged body.
• It is independent of the frame of reference.
• Electric charge is an invariant physical quantity.

Summary of Basic Properties

Property	Description
Additivity	Total charge is the algebraic sum of individual charges.
Conservation	Charge can neither be created nor destroyed; it is only transferred.
Quantisation	Charge always exists as an integral multiple of e.
Invariance	The value of electric charge remains the same in all frames of reference, whether the charged body is at rest or in motion.

Numerical Problems

Use: e = 1.6 × 10^-19 C, Q = n × e

1. A body has charge 3.2 × 10^-19 C. Find number of electrons (n).
2. A body has charge 9.6 × 10^-19 C. Find value of n.
3. A body has charge -4.8 × 10^-19 C. Find number of electrons (n).
4. A body has charge 1.6 × 10^-18 C. Find n.
5. A body has charge -8.0 × 10^-19 C. Find number of electrons (n).
6. A body has charge 6.4 × 10^-19 C. Find n.
7. A body has charge -1.28 × 10^-18 C. Find value of n.
8. A body has charge 3.2 × 10^-18 C. Find n.
9. A body has charge -9.6 × 10^-19 C. Find number of electrons (n).
10. A body has charge 4.8 × 10^-18 C. Find n.

11. A body loses 5 electrons. Find its charge.
12. A body gains 8 electrons. Find its charge.
13. A body loses 12 electrons. Find its charge.
14. A body gains 20 electrons. Find its charge.
15. A body loses 3 electrons. Find its charge.
16. A body gains 15 electrons. Find its charge.
17. A body loses 10 electrons. Find its charge.
18. A body gains 25 electrons. Find its charge.
19. A body loses 7 electrons. Find its charge.
20. A body gains 18 electrons. Find its charge.

21. A body loses 16 electrons. Find total charge.
22. A body gains 12 electrons. Find charge.
23. A body has charge -3.2 × 10^-18 C. Find number of electrons.
24. A body has charge +2.4 × 10^-18 C. Find number of electrons.
25. A body loses 6 electrons. Find charge.
26. A body gains 9 electrons. Find charge.
27. A body has charge -7.2 × 10^-19 C. Find n.
28. A body has charge 1.12 × 10^-18 C. Find n.
29. A body loses 14 electrons. Find charge.
30. A body gains 30 electrons. Find charge.

31. A charge of 2.5 × 10^-19 C is given. Is it possible? Find n if possible.
32. A body has charge 5 × 10^-19 C. Find number of electrons.
33. A body loses 50 electrons. Find charge.
34. A body gains 50 electrons. Find charge.
35. A body has charge -1.6 × 10^-17 C. Find n.
36. A body has charge 3.2 × 10^-17 C. Find number of electrons.
37. A body loses 100 electrons. Find charge.
38. A body gains 75 electrons. Find charge.
39. A body has charge -9.6 × 10^-18 C. Find number of electrons.
40. A body gains 250 electrons. Find charge.

41. Two charges are +3e and -5e. Find net charge.
42. A body has 10 electrons and 15 protons. Find net charge.
43. A body gains 2.5 × 10¹⁰ electrons. Find charge.
44. A body loses 3.2 × 10¹² electrons. Find charge.
45. Charges +16e and -9e are combined. Find total charge.
46. Find value of 5e in coulomb.
47. Find value of 12e in coulomb.
48. Find value of 20e in coulomb.
49. A body loses 100 electrons. Find charge.
50. A body gains 250 electrons. Find charge.

Solutions

1. n = (3.2 × 10^-19) / (1.6 × 10^-19) = 2
2. n = 9.6 / 1.6 = 6
3. n = 4.8 / 1.6 = 3 (negative sign shows electrons)
4. n = 1.6 × 10^-18 / 1.6 × 10^-19 = 10
5. n = 8.0 / 1.6 = 5
6. n = 6.4 / 1.6 = 4
7. n = 1.28 × 10^-18 / 1.6 × 10^-19 = 8
8. n = 3.2 × 10^-18 / 1.6 × 10^-19 = 20
9. n = 9.6 / 1.6 = 6
10. n = 4.8 × 10^-18 / 1.6 × 10^-19 = 30
11. Q = -5e = -5 × 1.6 × 10^-19 = -8.0 × 10^-19 C
12. Q = +8e = 1.28 × 10^-18 C
13. Q = -12e = -1.92 × 10^-18 C
14. Q = +20e = 3.2 × 10^-18 C
15. Q = -3e = -4.8 × 10^-19 C
16. Q = +15e = 2.4 × 10^-18 C
17. Q = -10e = -1.6 × 10^-18 C
18. Q = +25e = 4.0 × 10^-18 C
19. Q = -7e = -1.12 × 10^-18 C
20. Q = +18e = 2.88 × 10^-18 C
21. Q = -16e = -2.56 × 10^-18 C
22. Q = +12e = 1.92 × 10^-18 C
23. n = 3.2 × 10^-18 / 1.6 × 10^-19 = 20 electrons
24. n = 2.4 × 10^-18 / 1.6 × 10^-19 = 15 electrons
25. Q = -6e = -9.6 × 10^-19 C
27. Q = +9e = 1.44 × 10^-18 C
28. n = 7.2 × 10^-19 / 1.6 × 10^-19 = 4.5 → NOT POSSIBLE (quantization violated)
29. n = 1.12 × 10^-18 / 1.6 × 10^-19 = 7
30. Q = -14e = -2.24 × 10^-18 C
31. Q = +30e = 4.8 × 10^-18 C
NOT POSSIBLE (2.5 × 10^-19 is not multiple of e)
32. n = 5 × 10^-19 / 1.6 × 10^-19 = 3.125 → NOT POSSIBLE
33. Q = -50e = -8.0 × 10^-18 C
34. Q = +50e = 8.0 × 10^-18 C
35. n = 1.6 × 10^-17 / 1.6 × 10^-19 = 100
36. n = 3.2 × 10^-17 / 1.6 × 10^-19 = 200
37. Q = -100e = -1.6 × 10^-17 C
38. Q = +75e = 1.2 × 10^-17 C
39. n = 9.6 × 10^-18 / 1.6 × 10^-19 = 60
40. Q = +250e = 4.0 × 10^-17 C
41. +3e + (-5e) = -2e = -3.2 × 10^-19 C
42. 10 electrons = -10e, 15 protons = +15e → net = +5e = 8.0 × 10^-19 C
43. Q = 2.5 × 10¹⁰ × 1.6 × 10^-19 = 4.0 × 10^-9 C
44. Q = 3.2 × 10¹² × 1.6 × 10^-19 = 5.12 × 10^-7 C 
45. +16e + (-9e) = +7e = 1.12 × 10^-18 C
46. 5e = 8.0 × 10^-19 C
47. 12e = 1.92 × 10^-18 C
48. 20e = 3.2 × 10^-18 C
49. 100 electrons = -1.6 × 10^-17 C
45. 250 electrons = -4.0 × 10^-17 C