⚡ ELECTROSTATICS · Charge, Field & Potential
Coulomb's law • Electric field • Gauss law • Electric potential • Capacitance • Dielectrics • NEET problems
🔋 COULOMB'S LAW
Force between two point charges: F = k q₁q₂ / r², where k = 1/(4πε₀) = 9×10⁹ Nm²/C²
ε₀ = permittivity of free space = 8.85×10⁻¹² C²/Nm²
In medium: F = q₁q₂/(4πε r²) = F₀/εr (εr = relative permittivity)
✏️ Force between two charges
🌀 ELECTRIC FIELD (E)
Force per unit charge: E = F/q (N/C). For point charge: E = kq/r² (radially outward for +q).
Electric field lines: Start at +ve, end at –ve; never cross; density ∝ field strength.
📈 Electric field lines of a dipole
📏 ELECTRIC POTENTIAL (V)
Work done per unit charge to bring a test charge from infinity: V = kq/r (for point charge).
Potential energy: U = qV = kq₁q₂/r
For system of charges: U = sum over all pairs.
Relation: E = –dV/dr (gradient). Equipotential surfaces are ⊥ to field lines.
🧲 GAUSS'S LAW
ΦE = ∮ E·dA = Qenc/ε₀
Applications
• Sphere (r>R): E = kQ/r²; inside (r
• Infinite sheet: E = σ/(2ε₀)
• Conducting sheet: E = σ/ε₀
Conductors
Inside conductor: E=0; all charge on surface; surface field = σ/ε₀.
🔌 CAPACITANCE (C)
C = Q/V. Parallel plate: C = ε₀A/d (air/vacuum). With dielectric: C = ε₀εrA/d = KC₀.
Energy stored: U = ½QV = ½CV² = ½Q²/C
Energy density: u = ½ε₀E²
Parallel: Ceq = C₁ + C₂ + ...
🔧 Parallel plate capacitor
🔮 DIELECTRICS
When dielectric inserted, capacitance increases by factor κ (dielectric constant).
Electric field inside dielectric: E = E₀/κ. Polarization P = ε₀χE, where χ = κ–1.
💡 NEET TIPS & SHORTCUTS
- For a point charge, E ∝ 1/r², V ∝ 1/r.
- Electric field inside a conductor is zero (electrostatic equilibrium).
- Potential inside a conductor is constant (equipotential).
- For spherical shell, potential inside is constant = kQ/R.
⚠️ COMMON MISTAKES
- Using Coulomb's law without considering the medium.
- Confusing potential energy with potential (U = qV).
- Applying Gauss law incorrectly – only for symmetric charge distributions.
- Forgetting that capacitance depends only on geometry and dielectric, not on Q or V.
📌 QUICK REVISION CARD
Coulomb's law: F = k q₁q₂/r²
Electric field (point charge): E = kq/r²
Potential (point charge): V = kq/r
Parallel plate C: C = ε₀A/d
Energy in capacitor: U = ½CV²
Gauss law: ∮E·dA = Qenc/ε₀
Electric field of sheet: E = σ/(2ε₀)
Dielectric insertion: C' = κC
🔋 CAPACITORS · Energy Storage & Circuits
Capacitance • Parallel plate • Dielectrics • Series/Parallel • Energy • RC circuits • NEET problems
🔌 CAPACITANCE (C)
Capacitance = charge per unit potential difference: C = Q/V (Farads, F).
Parallel plate capacitor (air): C₀ = ε₀A/d
With dielectric: C = κC₀ = ε₀εrA/d
εr = dielectric constant (κ).
📐 Parallel plate capacitor
🔗 SERIES & PARALLEL COMBINATIONS
Series: 1/Ceq = 1/C₁ + 1/C₂ + ...
Same charge on each, voltage divides.
Parallel: Ceq = C₁ + C₂ + ...
Same voltage, charge distributes.
🔌 Series & parallel capacitors
💾 ENERGY STORED IN CAPACITOR
U = ½QV = ½CV² = ½Q²/C
Energy density: u = ½ε₀E² (in vacuum) or ½ε₀εrE² (in dielectric).
🔮 DIELECTRICS IN CAPACITORS
Dielectric constant κ = C/C₀
When dielectric inserted:
• Battery connected: V constant, Q increases, C increases, E unchanged (E = V/d).
• Isolated capacitor: Q constant, V decreases, C increases, E decreases (E = E₀/κ).
⏱️ RC CIRCUITS (Charging & Discharging)
Charging: q(t) = CV(1 – e–t/RC), i(t) = (V/R)e–t/RC
Discharging: q(t) = Q₀e–t/RC, i(t) = –(Q₀/RC)e–t/RC
Time constant τ = RC (time to charge to 63% or discharge to 37%).
📈 Charging/discharging curves
💡 NEET TIPS & SHORTCUTS
- For parallel plate capacitor, C ∝ A/d ∝ κ.
- When dielectric is inserted in an isolated capacitor, energy decreases; with battery, energy increases.
- In series combination, the smallest capacitor gets the largest voltage.
- Time constant τ determines how fast capacitor charges/discharges.
⚠️ COMMON MISTAKES
- Using C = Q/V without considering that V is potential difference, not EMF.
- Applying series formula for parallel combination and vice versa.
- Forgetting that dielectric constant changes capacitance but not charge if isolated.
- Confusing charging and discharging equations.
📌 QUICK REVISION CARD
C = Q/V
Parallel plate (air): C = ε₀A/d
With dielectric: C = κε₀A/d
Energy: U = ½CV² = ½Q²/C
Series: 1/Ceq = Σ(1/C)
Parallel: Ceq = ΣC
RC time constant: τ = RC