Class 12 Physics – Chapter 1
Electric Charges and Fields - (Ref NCERT book)
1. Electrostatics
Definition: Electrostatics is the branch of physics that deals with the study of electric charges at rest and the forces, fields, and potentials arising from them.
Electrostatics forms the foundation of electricity. In this branch, we assume that charges are stationary. The concepts developed here help in understanding electric field, electric potential, capacitors, and many modern technologies.
In exam answers, always begin with a clear definition and then mention that electrostatics deals only with charges at rest, not moving charges.
2. Electric Charge
Definition: Electric charge is a fundamental property of matter due to which it experiences electrical force in the presence of other charges.
Electric charge is a scalar quantity. It is responsible for all electrical phenomena. Charges are carried by subatomic particles like electrons and protons.
SI Unit: Coulomb (C)
1 Coulomb: Charge transported by a current of 1 ampere in 1 second.
In numerical problems and theory answers, always mention the SI unit and nature (scalar) of electric charge.
3. Types of Electric Charges
There are
two types of electric charges:
- Positive charge (carried by protons)
- Negative charge (carried by electrons)
Like charges repel each other, while unlike charges attract each other. This basic rule must be clearly written in exam answers.
Common Mistake: Writing that positive charge moves in conductors. In reality, it is the electrons that move.
4. Properties of Electric Charge
- Additivity of charge: Total charge is the algebraic sum of individual charges.
- Conservation of charge: Charge can neither be created nor destroyed.
- Quantisation of charge: Charge exists in discrete packets.
5. Conservation of Electric Charge
Statement: The total electric charge of an isolated system remains constant.
During any physical process such as rubbing, charging by induction, or conduction, charge is only transferred from one body to another.
In board exams, always write the statement clearly and add one example, such as charging by friction.
6. Coulomb’s Law
Statement: The force of interaction between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Mathematical Form:
F = (1 / 4πϵ₀) × (|q₁q₂| / r²)
The force acts along the line joining the two charges. It is a central force and follows the inverse square law.
SI Unit of Force: Newton (N)
Value of 1 / 4πϵ₀: 9 × 10⁹ N m² C⁻²
Common Mistake: Forgetting to mention that Coulomb’s law is valid only for point charges at rest.
7. Force Between Multiple Charges – Superposition Principle
Statement: The net force on a charge due to multiple charges is the vector sum of forces exerted by individual charges.
Each force is calculated separately using Coulomb’s law, and then vector addition is applied. This principle is very important for numerical problems.
In exam answers, always use the words "vector sum" and "independent action of charges".
8. Continuous Charge Distribution
When charge is distributed continuously over a body, it is called continuous charge distribution.
- Linear charge density (λ): Charge per unit length (C/m)
- Surface charge density (σ): Charge per unit area (C/m²)
- Volume charge density (ρ): Charge per unit volume (C/m³)
These concepts are essential while calculating electric field due to extended bodies like rods, rings, and plates.
9. Important Conceptual Questions (Exam-Oriented)
Q1. Why Coulomb’s law is not applicable to moving charges?
Because Coulomb’s law is valid only for electrostatic conditions where charges are at rest.
Q2. Is charge a vector or scalar quantity?
Electric charge is a scalar quantity because it has magnitude but no direction.
Q3. Why quantisation of charge is not observed on a large scale?
Because the elementary charge is very small, and large charges involve a huge number of electrons.
Common Mistake: Saying that electric field lines are real. They are only a conceptual representation.
13. Electric Dipole
An electric dipole consists of two equal and opposite point charges separated by a small distance.
Dipole Moment:
p = q × 2a
Dipole moment is a vector quantity directed from negative charge to positive charge.
SI Unit: Coulomb–meter (C m)
14. Electric Field Due to an Electric Dipole
The electric field due to a dipole depends on the position of the point where the field is calculated.
(a) Axial Line:
E = (1 / 4πϵ₀) × (2p / r³)
(b) Equatorial Line:
E = (1 / 4πϵ₀) × (p / r³)
In exams, always specify whether the point lies on the axial or equatorial line.
15. Torque on an Electric Dipole in a Uniform Electric Field
When an electric dipole is placed in a uniform electric field, it experiences a torque but no net force.
τ = pE sinθ
The torque tends to align the dipole along the direction of the electric field. The torque is maximum when θ = 90° and zero when θ = 0° or 180°.
Common Mistake: Writing that a dipole accelerates linearly in a uniform electric field. Only rotation occurs.
Electric Flux
Definition: Electric flux through a surface is defined as the total number of electric field lines passing normally through that surface.
Mathematical Expression:
ΦE = E · A = EA cosθ
Here, θ is the angle between the electric field vector and the area vector. Electric flux is a scalar quantity.
SI Unit: N m² C⁻¹
Common Mistake: Students often write flux as a vector. Electric flux is always a scalar.
Gauss’s Theorem (Gauss’s Law)
Statement: The total electric flux through a closed surface is equal to 1/ϵ₀ times the total charge enclosed by the surface.
ΦE = ∮ E · dA = Qenclosed / ϵ₀
Gauss’s law is applicable for any closed surface and is especially useful for systems having high symmetry.
Common Mistake: Applying Gauss’s law to non-symmetric charge distributions without justification.
Application of Gauss’s Law
(a) Electric Field Due to an Infinitely Long Straight Charged Wire
Using a cylindrical Gaussian surface of radius r and length l:
E(2πrl) = λl / ϵ₀
E = λ / (2πϵ₀r)
The electric field varies inversely with distance from the wire and is directed radially outward for positive charge.
(b) Electric Field Due to a Uniformly Charged Infinite Plane Sheet
Using a pill-box Gaussian surface:
E(2A) = σA / ϵ₀
E = σ / (2ϵ₀)
The electric field is independent of distance from the plane sheet.
Common Mistake: Writing electric field depends on distance r, which is incorrect.
(c) Electric Field Due to a Uniformly Charged Thin Spherical Shell
(i) Outside the Shell (r > R):
E = (1 / 4πϵ₀) × (Q / r²)
The shell behaves as if the entire charge is concentrated at its centre.
(ii) Inside the Shell (r < R):
E = 0
Electric field inside a uniformly charged spherical shell is zero.
Common Mistake: Students assume non-zero field inside the shell.
10. Conclusion of the Chapter
This chapter introduces the basic concepts of electrostatics such as electric charge, its properties, Coulomb’s law, and the principle of superposition. A strong understanding of these topics is essential for mastering electric field and electric potential in later chapters.
For board exams, focus on clear definitions, correct formulas, and proper explanation of principles. Avoid common mistakes and always use scientific terminology.