Electrostatics

Concept overview

Electrostatics deals with charges at rest. Coulomb's law gives the force between two point charges: F = kq₁q₂/r², with k = 9 × 10⁹ N·m²/C². The electric field E is force per unit test charge; near a point charge Q, E = kQ/r². Field lines diverge from positive charges and converge on negative ones.

Gauss's law is the workhorse for symmetric geometries: ∮E·dA = q_enc/ε₀. Choose a Gaussian surface matching the symmetry — sphere for a point charge, cylinder for a line charge, pillbox for a sheet — and evaluate the flux. This bypasses hard integrals for symmetric distributions.

Electric potential V is potential energy per unit charge: V = kQ/r for a point charge. The relation E = −dV/dr connects the two. For symmetric distributions, computing V first (a scalar integral) is often easier than computing E (a vector integral) and then differentiating.

Capacitors store energy in the electric field: C = Q/V. For a parallel-plate capacitor, C = ε₀A/d, increasing to Kε₀A/d when filled with a dielectric of dielectric constant K. Energy stored is U = ½CV² = Q²/(2C). Series and parallel combinations follow familiar rules — capacitors add in parallel, reciprocals add in series.

Key formulas & concepts

• Coulomb's law: F = k q₁q₂ / r², k = 9 × 10⁹
• Electric field (point charge): E = kQ/r²
• Gauss's law: ∮ E · dA = q_enc / ε₀
• Potential (point charge): V = kQ/r
• Field-potential relation: E = −dV/dr
• Parallel-plate capacitor: C = ε₀A/d (vacuum); Kε₀A/d (dielectric)
• Capacitor energy: U = ½CV² = Q²/(2C)
• Series vs parallel: 1/C_s = Σ 1/Cᵢ; C_p = Σ Cᵢ

Common mistakes to avoid

• Applying Gauss's law where symmetry doesn't allow evaluating the flux — you need spherical, cylindrical or planar symmetry.
• Forgetting that potential is a scalar — you can add potentials from multiple sources directly, without worrying about direction.
• Confusing dielectric constant K with permittivity ε = Kε₀ — formulas often use one or the other.
• Using capacitor formulas for series-parallel mixtures without simplifying step by step.

JEE Main relevance

JEE Main asks 2 electrostatics questions every paper — usually one Coulomb's-law or field/potential calculation and one capacitor numerical (energy, dielectric, combinations).

JEE Advanced relevance

Advanced problems apply Gauss's law to non-standard geometries (spherical shell with a cavity, non-uniform charge distribution) and combine capacitor energy with work done during dielectric insertion. Force between two half-charged spheres is another standard Advanced pattern.

Previous-year questions (PYQ)

Filter the PYQ bank by 'Electrostatics' — capacitor combination problems are the most repeated single archetype.