Electric Charges and Fields Class 12 Notes (2026-27) — CBSE
Class 12 Physics Chapter 1 revision notes: Coulomb's law, electric field and field lines, dipoles, Gauss's law with all three applications, formulas and derivations.
Electric Charges and Fields — Class 12 Physics Notes
Chapter Snapshot
This chapter builds electrostatics from the ground up: what electric charge is, the force law between charges (Coulomb's law), the field picture that replaces action-at-a-distance, the electric dipole, and finally Gauss's law — the tool that makes hard field calculations easy when symmetry helps. It feeds directly into Chapter 2 (Potential and Capacitance) and is high-yield for JEE Main and NEET as well.
Board relevance: the 5-mark derivation almost always comes from here or Chapter 2 — dipole fields and the three Gauss's-law applications are the usual suspects. Numericals on Coulomb's law and flux are 2–3 markers.
Key Concepts & Definitions
Electric charge — the intrinsic property of matter responsible for electric forces. Two kinds: positive (glass rod rubbed with silk) and negative (plastic rod rubbed with fur). Like charges repel, unlike attract. SI unit: coulomb (C).
Three fundamental properties of charge:
1. Quantisation: q = ne, where n ∈ ℤ and e = 1.6 × 10⁻¹⁹ C. Charge comes in packets; you cannot have a free charge of 0.5e.
2. Conservation: the total charge of an isolated system never changes. Charge is neither created nor destroyed, only transferred.
3. Additivity: total charge = algebraic sum q₁ + q₂ + … (charges add like scalars, with sign).
Conductors vs insulators: conductors (metals) have free electrons that move readily; insulators (glass, plastic) do not. Charging methods: friction, conduction (contact), and induction (charging without contact — the induced charge is opposite in sign to the inducing charge).
Electric field — the region around a charge where another charge experiences a force. Defined as the force per unit positive test charge:
E = F / q₀ (unit: N/C or V/m; direction = direction of force on a positive charge)
Electric field lines — imaginary curves whose tangent at any point gives the field direction. Properties (a favourite 2-marker):
- Start on positive charges, end on negative charges (or at infinity); never form closed loops in electrostatics.
- Never intersect — the field can't have two directions at one point.
- Density of lines ∝ field strength (crowded = strong field).
- Always perpendicular to a conductor's surface; no lines inside a conductor.
Electric dipole — two equal and opposite charges (+q, −q) separated by distance 2a. Dipole moment p = q × 2a, direction from −q to +q. Unit: C·m.
Electric flux (φ) — the "number of field lines" through a surface: φ = E · A = EA cos θ, where θ is the angle between E and the area vector (normal to the surface). Unit: N·m²/C. Flux is a scalar.
Formulas
Coulomb's law and field
Quantity Formula Notes
Coulomb force F = kq₁q₂ / r² k = 1/4πε₀ = 9 × 10⁹ N·m²/C²
Permittivity of free space ε₀ = 8.854 × 10⁻¹² C²/N·m² In a medium: ε = ε₀εᵣ, force decreases by factor εᵣ
Field of a point charge E = kq / r² Radially outward for +q, inward for −q
Superposition F₁ = F₁₂ + F₁₃ + … (vector sum) Pairwise forces are unaffected by other charges
Charge quantisation q = ne e = 1.6 × 10⁻¹⁹ C
Dipole (for r ≫ a)
Position Field Direction
Axial point E = 2kp / r³ Parallel to p
Equatorial point E = kp / r³ Antiparallel to p
Torque in uniform field τ = pE sin θ, i.e. τ = p × E Zero at θ = 0° (stable equilibrium) and θ = 180° (unstable)
Note: dipole field falls off as 1/r³ (faster than a point charge's 1/r²), and a dipole in a uniform field feels zero net force but a torque.
Continuous charge distributions
- Linear density λ = q/L (C/m) · Surface density σ = q/A (C/m²) · Volume density ρ = q/V (C/m³)
Gauss's law and applications
Gauss's law: the total electric flux through any closed surface equals 1/ε₀ times the net charge enclosed:
φ = ∮ E · dA = qenclosed / ε₀
Charge configuration Field Key points
Infinite straight wire (λ) E = λ / 2πε₀r Cylindrical Gaussian surface; E ∝ 1/r
Infinite plane sheet (σ) E = σ / 2ε₀ Independent of distance; pillbox Gaussian surface
Spherical shell (Q), outside r R E = kQ / r² Shell behaves like a point charge at the centre
Spherical shell, on surface r = R E = kQ / R² = σ/ε₀ Maximum value
Spherical shell, inside r < R E = 0 Enclosed charge is zero
Choosing a Gaussian surface: pick a surface where E is either constant-and-perpendicular or parallel to the surface — cylinder for a wire, pillbox for a sheet, concentric sphere for shells.
Important Question Patterns
1. 5-mark derivations: (a) field at an axial or equatorial point of a dipole; (b) field due to an infinite line charge / plane sheet / spherical shell using Gauss's law; (c) torque on a dipole in a uniform field. Practise writing these with a labelled diagram — the diagram carries marks.
2. Coulomb-law numericals (2–3 marks): force between charges; effect of placing a dielectric between them; comparing electric and gravitational force between electron and proton (~10³⁹ ratio).
3. Flux questions (2 marks): flux through a cube face when a charge sits at the centre (q/6ε₀), at a corner (q/24ε₀); flux is independent of the surface's shape or size.
4. Conceptual 1–2 markers: why field lines never cross; why charge is quantised but we ignore it for macroscopic charges; force on a charge inside a shell (zero); what happens to a dipole in a non-uniform field (net force + torque).
5. Assertion–reason / MCQ: dipole field direction at axial vs equatorial points; sign conventions for flux; behaviour of E vs r graphs for a shell (zero → peak at surface → 1/r² fall).
⚡ Quick Revision
- Charge: q = ne (e = 1.6 × 10⁻¹⁹ C); conserved; additive like scalars. Like repel, unlike attract.
- Coulomb: F = kq₁q₂/r², k = 9 × 10⁹ N·m²/C²; in a medium force drops by εᵣ. Vector sum for many charges.
- Field: E = F/q₀; point charge E = kq/r². Field lines: +→−, never cross, never closed loops, density = strength.
- Dipole: p = q·2a (−q → +q). Axial E = 2kp/r³, equatorial E = kp/r³ (half, opposite direction). τ = pE sin θ; uniform field → torque only, no net force.
- Flux: φ = EA cos θ (scalar). Gauss: φclosed = qenc/ε₀. Cube with central charge → q/6ε₀ per face.
- Gauss applications: wire E = λ/2πε₀r · sheet E = σ/2ε₀ (distance-independent) · shell: outside like point charge, inside zero.
- 1/r² → point charge & outside shell; 1/r³ → dipole; 1/r → line charge; constant → infinite sheet.
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