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Electric Charges and Fields

NCERT Class 12 Physics Chapter 1

Electric Charges and Fields for Class 12 Physics, JEE and NEET: Coulomb’s law, electric field, field lines, dipoles, flux and Gauss’s law.

13 topics Updated 8 Nov 2026

For: Class 12, JEE and NEET

In the syllabus: JEE Class 12 syllabus, NEET Class 12 syllabus

With your textbook

NCERT Physics Part I (Class 12), Chapter 1 “Electric Charges and Fields”, reprint 2026-27.

Open the official NCERT chapter (PDF, 4.0 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Electric charge: positive, negative and charging

    Positive and negative charge, charging by rubbing as electron transfer, and how a gold-leaf electroscope works.

    NCERT Sections 1.1–1.2 10 min read 4 solved examples 8 practice questions

  2. Conductors and insulators

    How they differ, free electrons, where charge goes on each, the metal spoon and semiconductors.

    NCERT Section 1.3 6 min read 3 solved examples 6 practice questions

  3. Basic properties of electric charge

    Additivity, conservation and quantisation (q = ne), the value of e, and NCERT Examples 1.1, 1.2.

    NCERT Section 1.4 10 min read 4 solved examples 7 practice questions

  4. Coulomb’s law

    Statement and formula F = k|qq|/r, ε and k, the vector form, the force in a medium, and solved numericals.

    NCERT Section 1.5 14 min read 4 solved examples 10 practice questions

  5. Forces between multiple charges

    Forces between multiple charges as vector sums of Coulomb forces, and NCERT Examples 1.5 and 1.6.

    NCERT Section 1.6 12 min read 4 solved examples 7 practice questions

  6. Electric field

    E = F/q and the test charge, the field of a point charge and of many charges, the SI unit, and solved examples.

    NCERT Section 1.7 13 min read 4 solved examples 8 practice questions

  7. Electric field lines

    What they show, density and strength, diagrams of simple charges, and why they never cross or form loops.

    NCERT Section 1.8 11 min read 4 solved examples 6 practice questions

  8. Electric flux

    Definition, formula Δϕ = EΔS cos θ, the area vector, SI unit N C m, and NCERT Exercises 1.14 and 1.15 solved.

    NCERT Section 1.9 11 min read 4 solved examples 8 practice questions

  9. Electric dipole

    Dipole moment p = q × 2a, its electric field on the axis and equator with derivation, and the 1/r fall-off.

    NCERT Section 1.10 13 min read 4 solved examples 6 practice questions

  10. Dipole in a uniform external field

    τ = p × E = pE sin θ with derivation, zero net force, and non-uniform fields.

    NCERT Section 1.11 10 min read 4 solved examples 7 practice questions

  11. Continuous charge distribution

    Linear, surface and volume charge density with SI units, and the field of a charged ring.

    NCERT Section 1.12 9 min read 4 solved examples 6 practice questions

  12. Gauss’s law

    The statement ϕ = q/ε, the Gaussian surface, flux through a cube, and how it differs from Coulomb’s law.

    NCERT Section 1.13 12 min read 4 solved examples 8 practice questions

  13. Applications of Gauss’s law

    Derivations of the field of a long charged wire, an infinite plane sheet and a thin charged shell.

    NCERT Section 1.14 13 min read 4 solved examples 8 practice questions

Key formulas in this chapter

Electric charge

  • like charges repel; unlike charges attract
  • glass rubbed with silk: glass +, silk −
  • plastic rubbed with fur: plastic −, fur +
  • rubbing transfers electrons; total charge unchanged
  • charge on n electrons: q = −ne

Conductors and insulators

  • conductor: mobile charge carriers; excess charge redistributes on the surface
  • insulator: very few mobile carriers; deposited charge stays local
  • conductors: metals, human and animal bodies, earth
  • insulators: glass, porcelain, plastic, nylon, dry wood
  • semiconductor: resistance between the two

Basic properties of electric charge

  • Q = q + q + … + q (with signs)
  • q = ne, n an integer
  • e = 1.6 × 10 C
  • 1 C ≈ 6.25 × 10 e
  • 1 µC = 10 C; 1 mC = 10 C

Coulomb’s law

  • F = (1/4πε) |qq|/r
  • 1/4πε ≈ 9 × 10 N m C
  • ε = 8.854 × 10 C N m
  • F = (1/4πε)(qq/r) r̂, r = r − r
  • F = −F

Forces between multiple charges

  • F = F + F + … + F
  • F = (q/4πε) Σ (q/r) r̂, i = 2 to n
  • F = (1/4πε)(qq/r) r̂
  • two equal forces F at angle θ: 2F cos(θ/2)
  • three charges: F + F + F = 0

Electric field

  • E = F/q (q → 0)
  • E = (1/4πε) Q/r, along r̂
  • F = qE
  • E = E + E + … + E
  • unit: N C = V m

Electric field lines

  • ΔΩ = ΔS/r
  • lines per unit area ∝ E
  • point charge: lines per unit area ∝ 1/r
  • start on +q, end on −q (or at infinity)
  • never cross; no closed loops

Electric flux

  • Δϕ = E · ΔS = E ΔS cos θ
  • ΔS = ΔS n̂ (outward normal on a closed surface)
  • ϕ ≈ Σ E · ΔS
  • θ = 0: Δϕ = E ΔS; θ = 90°: Δϕ = 0
  • unit: N C m

Electric dipole

  • p = q × 2a, from −q to q
  • axis, r ≫ a: E = 2p/(4πεr), along p
  • equator, r ≫ a: E = p/(4πεr), opposite to p
  • Eaxis: Eequator = 2: 1 at the same r in the far field
  • far field E ∝ 1/r

Dipole in a uniform field

  • τ = p × E
  • τ = pE sin θ
  • uniform field: net force = 0
  • U = −pE cos θ (U = 0 at θ = 90°)
  • external work θ → θ: pE(cos θ − cos θ)

Continuous charge distribution

  • λ = ΔQ/Δl (C/m)
  • σ = ΔQ/ΔS (C/m)
  • ρ = ΔQ/ΔV (C/m)
  • ΔE = k ρΔV/r′, along r̂′
  • E ≈ Σ k ρΔV/r′ r̂′

Gauss’s law

  • ϕ = q/ε (closed surface, q enclosed)
  • point charge at sphere centre: Δϕ = qΔS/(4πεr)
  • no charge inside: ϕ = 0
  • charge at a cube’s centre: each face q/(6ε)
  • q = εϕ

Applications of Gauss’s law

  • wire: E = λ/(2πεr)
  • sheet: E = σ/(2ε)
  • shell, r > R: E = q/(4πεr)
  • shell, r < R: E = 0
  • atom model, 0 < r < R: E = (Ze/4πε)(1/r − r/R)

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