CBSE Class 12 Physics: Electric Charges & Fields — Notes 2026

Electric Charge

• Properties: quantisation (q = ne), conservation, additivity
• Conductors and insulators; charging by conduction, induction and friction
• Coulomb's law: F = kq₁q₂/r²; k = 9×10⁹ N m² C⁻²; in medium: F' = F/εᵣ

Electric Field

• E = F/q₀; unit N/C = V/m; direction: force on positive test charge
• Electric field due to point charge: E = kq/r²
• Superposition principle: net field = vector sum of individual fields

Electric Field Lines

• Never cross; continuous curves from + to − charge; perpendicular to surface of conductor
• Density of lines ∝ field strength
• Field between two parallel plates (capacitor): uniform field E = σ/ε₀

Electric Dipole

• Pair of equal and opposite charges ±q separated by distance 2a
• Dipole moment p = q × 2a; direction from − to + charge; unit C·m
• Field on axial line: E = 2kp/r³; on equatorial: E = kp/r³

Continuous Charge Distributions

• Linear: λ = Q/L (C/m); surface: σ = Q/A (C/m²); volume: ρ = Q/V (C/m³)
• Field due to infinite line charge: E = λ/(2πε₀r) using Gauss's law
• Field due to infinite plane sheet: E = σ/(2ε₀)

Gauss's Law

• ∮E·dA = Q_enclosed/ε₀; total flux through closed surface equals enclosed charge divided by ε₀
• Application: derive E for sphere, cylinder, infinite sheet
• Gaussian surface choice: symmetrical surface where E is constant and parallel to dA

CBSE Exam Tips — Chapter 1

• Gauss's law derivations (sphere, cylinder, plane) are standard long-answer questions
• Torque on dipole in uniform field: τ = pE sin θ — derive and state position of stable/unstable equilibrium
• Numerical: find E at a point due to multiple charges using superposition