Electric Charge and Electric Field — Formula Sheet

Q = Ne

F = k × (q₁ × q₂) / r²

k = 1 / (4πε₀) = 9 × 10⁹ N m² C⁻²

F (vacuum) / F (medium) = ε / ε₀ = ε_r

F₁₂ = k × (q₁ q₂ / |r₁₂|²) × r̂₁₂

E = F / q₀

E = k × q / r² (or E = q / 4πε₀r²)

E = E₁ + E₂ + E₃ + ... (vector sum)

F = qE

p = q × 2l

E (end-on) = 2pr / [4πε₀(r² − l²)²] ≈ 2p / (4πε₀r³) for r >> l

E (broad-on) = p / (4πε₀r³) for r >> l

τ = pE sinθ → τ = p × E (vector form)

DIPOLE MOMENT (p) = q × 2l (product of charge magnitude and separation between charges).

Quantisation of Charge

Q = Ne, where N is an integer and e = 1.6 × 10⁻¹⁹ C.

Coulomb's Law

F = kq₁q₂/r², where k = 9 × 10⁹ N·m²/C².

ε₀ = 8.85 × 10⁻¹² C²·N⁻¹·m⁻² (permittivity of free space).