Electrostatics (Chapters 1 and 2 of Class 12 Physics) carries about 8 marks in CBSE boards and 2–3 questions in JEE and NEET. Keep this formula sheet on your wall and revise it every week.
Charge and Coulomb’s law
- Charge is quantised: q = ±ne, e = 1.6 × 10⁻¹⁹ C
- Coulomb’s law: F = kq₁q₂/r², k = 1/4πε₀ = 9 × 10⁹ N m²/C²
- In a medium: F = F₀/K (K = dielectric constant)
Electric field
- E = F/q₀; point charge: E = kq/r²
- Dipole moment p = q × 2a (from −q to +q)
- Axial line: E = 2kp/r³; equatorial line: E = kp/r³ (for r ≫ a)
- Torque on dipole: τ = pE sin θ; potential energy U = −pE cos θ
Gauss’s law
Flux φ = ∮E·dA = qenclosed/ε₀. Results to memorise:
| Charge distribution | Field |
|---|---|
| Infinite line, λ per metre | E = λ/2πε₀r |
| Infinite plane sheet, σ per m² | E = σ/2ε₀ |
| Charged conducting sphere (outside) | E = kq/r²; inside E = 0 |
| Between two oppositely charged plates | E = σ/ε₀ |
Potential
- Point charge: V = kq/r; dipole on axis: V = kp/r²; on equatorial line V = 0
- E = −dV/dr; work W = q(VB − VA)
- Potential energy of two charges: U = kq₁q₂/r
- Equipotential surfaces are perpendicular to E; no work along them.
Capacitors
- C = Q/V; parallel plate: C = ε₀A/d; with dielectric: C = Kε₀A/d
- Series: 1/C = 1/C₁ + 1/C₂; Parallel: C = C₁ + C₂
- Energy: U = ½CV² = ½QV = Q²/2C; energy density = ½ε₀E²
- Dielectric inserted with battery disconnected: Q same, V and E drop by K, C rises by K.
Quick numerical
Two charges of 2 μC and −2 μC are 2 mm apart. Find p and the field on the axis at 10 cm. p = 2 × 10⁻⁶ × 2 × 10⁻³ = 4 × 10⁻⁹ C m. E = 2kp/r³ = 2 × 9 × 10⁹ × 4 × 10⁻⁹ / (0.1)³ = 72/10⁻³ = 7.2 × 10⁴ N/C.
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Common mistakes
- Using kq/r for field or kq/r² for potential.
- Forgetting that inside a conductor E = 0 but V is constant, not zero.
- Mixing series/parallel rules of capacitors with resistors (they are opposite).
Pair this with our Class 12 integration formulas sheet for the maths side.
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Frequently asked questions
What is the value of ε₀?
8.85 × 10⁻¹² C²/N m². The combination 1/4πε₀ equals 9 × 10⁹ N m²/C².
Why is the field inside a conductor zero?
Free charges move until the internal field cancels; all excess charge sits on the surface.
Which electrostatics topics are most asked in boards?
Gauss's law derivations, dipole field, capacitor combinations and energy stored.
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