Electrostatics
Learn Electrostatics with notes, examples, and practice questions.
Chapter Overview
Like charges repel; unlike charges attract. Charge is quantised: q = ne.
Electrostatics studies charges at rest, the forces between them, and electric fields and potentials they create. Coulomb's law and Gauss's law are the pillars.
Fundamentals
Coulomb's law
F = k q₁q₂/r² ; k = 1/(4πε₀)
Electric field
E⃗ = F⃗/q ; E = kQ/r² (point charge)
Potential
V = kQ/r ; E = −dV/dr
Dipole field
On axis: E ∝ 1/r³
Gauss's Law
Gauss
∮ E⃗·dA⃗ = Q_enclosed/ε₀
Infinite wire
E = λ/(2πε₀r)
Infinite plane
E = σ/(2ε₀)
Capacitors
Parallel plate
C = ε₀A/d
Energy
U = ½CV² = ½Q²/C
Series
1/C_eq = 1/C₁ + 1/C₂
Parallel
C_eq = C₁ + C₂
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Coulomb force
Two 2μC charges 0.3 m apart in vacuum.
- 1F = k(2×10⁻⁶)²/(0.09)
- 2≈ 0.4 N
Answer
≈ 0.4 N (repulsive if same sign)
Capacitor
C=10μF, V=12V. Find Q and U.
- 1Q=CV=120μC
- 2U=½CV²=720μJ
Answer
Q=120μC, U=720μJ
Key Points to Remember
- ✓ Superposition for multiple charges
- ✓ Field lines: from + to −
- ✓ Dielectric increases capacitance
Exam Tips
- • Use SI units (C, m, F)
- • Draw field lines for symmetry problems
- • Gauss law needs high symmetry
Formula Cheat Sheet
Quick reference — NCERT board exam formulas
Coulomb & Electric Field
- Coulomb's law:F = k q₁q₂/r² ; k = 1/(4πε₀)
- Electric field:E⃗ = F⃗/q ; E = kQ/r² (point charge)
- Potential:V = kQ/r ; E = −dV/dr
- Dipole (on axis):E ∝ 1/r³
Gauss's Law & Capacitors
- Gauss:∮ E⃗·dA⃗ = Q_enclosed/ε₀
- Infinite wire:E = λ/(2πε₀r)
- Infinite plane:E = σ/(2ε₀)
- Parallel plate:C = ε₀A/d
- Energy:U = ½CV² = ½Q²/C
- Series:1/C_eq = 1/C₁ + 1/C₂
- Parallel:C_eq = C₁ + C₂
Practice MCQs — Electrostatics
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
SI unit of charge: