Electrostatics

Coulomb's law, electric field, capacitors.

Practice — 0 questions Ask AI

Coulomb's law

F = kq₁q₂/r²; superposition.

Electrostatics — Coulomb, field, potential, Gauss law

Notes

ELECTRIC CHARGE

Two types: positive, negative. Like repels, unlike attracts.
Quantized: q = ne (e = 1.6 × 10⁻¹⁹ C).
Conserved in isolated systems.
Additive (scalars).

COULOMB'S LAW

F = (1/4πε₀) · q₁q₂/r²

k = 1/(4πε₀) ≈ 9 × 10⁹ N·m²/C² (in vacuum).
In medium of permittivity ε: divide by εᵣ (dielectric constant).

ELECTRIC FIELD (E)

E = F/q₀ = (1/4πε₀)·Q/r² (point charge).

Vector field. Lines: from + to −, never cross.
Continuous charge distribution: dE = kdq/r².

Field of common charges:

Point charge: kQ/r².
Infinite line of charge: λ/(2πε₀r).
Infinite plane sheet: σ/(2ε₀).
Between parallel plates: σ/ε₀.
Dipole on axis (far): 2kp/r³; on equator: kp/r³.
Uniformly charged ring axis: kQx/(R²+x²)^(3/2).

ELECTRIC POTENTIAL (V)

V = work done per unit positive charge in bringing it from ∞ to that point.
V = (1/4πε₀)·Q/r (point charge).

Scalar — easier to handle.
E = −dV/dr (gradient).

Potential difference: V_A − V_B = W_AB/q.

ELECTRIC DIPOLE

Two equal and opposite charges separated by 2a.
Dipole moment: p = q · 2a, directed from −q to +q.
Torque in field: τ = p × E. (|τ| = pE sin θ.)
Potential energy: U = −p·E (= −pE cos θ).
Min U at θ = 0 (stable); max at θ = π (unstable).

GAUSS'S LAW

∮ E · dA = Q_enc / ε₀

Total electric flux through closed surface = (1/ε₀) × charge enclosed.

Applications (use symmetry):

Spherical shell: outside acts as point charge at center; inside E = 0.
Solid sphere of uniform charge: E_outside = kQ/r²; E_inside = kQr/R³.
Infinite line: E = λ/(2πε₀r).
Infinite plane sheet: E = σ/(2ε₀).
Spherical capacitor.

CONDUCTORS IN ELECTROSTATIC EQUILIBRIUM

E = 0 inside conductor.
Charge resides on surface.
E just outside ⊥ surface, magnitude σ/ε₀.
Potential constant inside and on surface.
Sharp points have higher charge density (corona discharge).

CAPACITORS

C = Q/V.

Parallel plate (vacuum): C = ε₀A/d.
With dielectric: C = εᵣ ε₀ A/d.
Series: 1/C = 1/C₁ + 1/C₂ + ...
Parallel: C = C₁ + C₂ + ...
Energy: U = ½CV² = ½QV = Q²/2C.

Dielectric: insulator that polarizes in field. Reduces E inside → increases C.

EXAM HOOKS:

E from a uniformly charged sphere outside acts as if all charge at center.
For a conductor, inside E = 0 (always).
Gauss law: use symmetry (spherical/cylindrical/planar).
Force on dipole in uniform field = 0; torque ≠ 0.
Equipotential surfaces perpendicular to E at every point.

Capacitors

Q=CV, parallel plate, dielectrics.