Class 12 Physics Chapter 1 Electric Charges and Fields
Chapter 1: Electric Charges and Fields is a foundational chapter in MP Board Class 12 Physics, carrying significant weight (5–7 marks) in the annual board exam. This chapter introduces the concept of electric charge, Coulomb’s law, electric fields, electric flux, Gauss’s law and its applications. Questions range from 1-mark MCQs and VSA to 5-mark derivations and numerical problems. A strong grasp of vector mathematics and superposition principle is essential for mastering this chapter.
📑 Table of Contents
⚡ Electric Charge — Types & Properties
Electric charge is the fundamental property of matter responsible for all electromagnetic interactions. Charges are of two types: positive (proton-like, deficiency of electrons) and negative (electron-like, excess of electrons). Like charges repel, unlike charges attract.
🔑 Key Properties of Charge
🧪 Charging Methods
- Charging by Friction — Transfer of electrons between two objects rubbed together (glass rod + silk → glass positive, silk negative)
- Charging by Conduction — Direct contact transfers charge from charged to uncharged body (both acquire same sign charge)
- Charging by Induction — Redistribution of charge without direct contact; the uncharged body gets opposite sign charge
📘 Key Formula — Quantisation of Charge
q = ±ne where n = integer (1, 2, 3, …) and e = 1.602 × 10⁻¹⁹ C
SI unit of charge: Coulomb (C). 1 C = 6.25 × 10¹⁸ electrons
⚡ Coulomb’s Law — Force Between Charges
Coulomb’s law states that the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. The force acts along the line joining the two charges.
📐 Coulomb’s Law — Formula
F = k |q₁q₂| / r²
where k = 1/(4πε₀) = 9 × 10⁹ N·m²/C², ε₀ = 8.854 × 10⁻¹² C²/N·m²
Vector form: F₁₂ = k q₁q₂/r² · r̂₁₂ (force on q₁ due to q₂)
📐 Principle of Superposition
When multiple charges are present, the net force on any one charge is the vector sum of all forces exerted on it by all other individual charges. This principle is fundamental for solving numerical problems involving three or more charges.
⚡ Electric Field & Field Lines
The electric field at a point is defined as the force experienced by a unit positive test charge placed at that point. Electric field lines are imaginary lines that represent the direction of the electric field in space.
📐 Electric Field Formulas
📊 Properties of Electric Field Lines
- Field lines start from positive charges and end at negative charges
- Field lines never cross each other (unique field direction at every point)
- The tangent at any point gives the direction of electric field at that point
- Closer field lines indicate stronger electric field (density = field strength)
- Field lines are perpendicular to the surface of a conductor
- Inside a conductor in electrostatic equilibrium, electric field = 0
⚡ Electric Dipole
An electric dipole consists of two equal and opposite point charges (+q and -q) separated by a small distance 2a. The dipole moment p = q × 2a is a vector quantity directed from -q to +q. This is a highly exam-relevant topic with 3–5 mark questions.
📐 Dipole Key Formulas
Dipole moment: p = q × 2a (direction: -q → +q)
Field on axial line: E_axial = 2kp / r³ (for r >> a)
Field on equatorial line: E_eq = -kp / r³ (for r >> a)
Torque in uniform field: τ = p × E
Potential energy: U = -p·E = -pE cos θ
⚡ Gauss’s Law & Applications
Electric flux (Φ) through a surface is the dot product of electric field and area vector: Φ = ∮ E·dA. The SI unit of electric flux is N·m²/C. Gauss’s law states that the total electric flux through any closed surface is equal to the net charge enclosed divided by ε₀.
📐 Gauss’s Law — Formula
Φ = ∮ E·dA = q_enclosed / ε₀
This law is valid for any closed surface (Gaussian surface) enclosing any charge distribution.
📊 Applications of Gauss’s Law (High Exam Weightage)
📝 Frequently Asked Questions
Q1: State Coulomb’s law in vector form. (MP Board 2022, 3 marks)
Answer: F₁₂ = k q₁q₂/r² · r̂₁₂ where F₁₂ is the force on q₁ due to q₂, and r̂₁₂ is the unit vector from q₂ to q₁. The vector form specifies both magnitude and direction — repulsive for like charges (positive product) and attractive for unlike charges (negative product).
Q2: Define electric dipole moment. Derive expression for electric field on axial line. (MP Board 2023, 5 marks)
Answer: Electric dipole moment p = q × 2a, where 2a is separation between charges, directed from -q to +q. On the axial line, field due to +q and -q are in opposite directions. Using superposition: E = kq/(r-a)² – kq/(r+a)². For r >> a, E_axial = 2kp/r³.
Q3: State and explain Gauss’s theorem in electrostatics. (MP Board 2024, 3 marks)
Answer: Gauss’s theorem: The total electric flux through any closed surface is equal to 1/ε₀ times the net charge enclosed by the surface. Φ = ∮ E·dA = q/ε₀. It is applicable to any closed surface (Gaussian surface) and is particularly useful for calculating electric fields of symmetric charge distributions.
Q4: What is the electric field inside a charged conducting spherical shell? (MP Board 2023, 1 mark)
Answer: Inside a charged conducting spherical shell, the electric field is zero (E = 0). This is because all excess charge resides on the outer surface, and by Gauss’s law, flux through any Gaussian surface inside the shell is zero.
Q5: Derive the expression for torque on an electric dipole in a uniform electric field. (MP Board 2022, 3 marks)
Answer: Torque τ = force × perpendicular distance = qE × (2a sin θ) = (q × 2a) × E sin θ = pE sin θ. Hence τ = p × E. Direction is given by right-hand rule. Torque is maximum when θ = 90° (τ_max = pE) and zero when θ = 0° (stable equilibrium) or θ = 180° (unstable equilibrium).
— Best of luck for your MP Board 2027 exams! 📚 —