Part of ES-01 — Electrostatics

Exam Cheat Sheet — Electrostatics Ultra-Condensed

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CHARGES: q = ne; e = 1.6×10191.6 \times 10^{-19} C; conservation + quantization + additive

COULOMB: F = kq_{1}q_{2}/r2r^{2}; k = 9×1099 \times 10^{9} N m2m^{2}/C2C^{2}; [F] = [MLT2LT^{-2}]

FIELD: E = kQ/r2r^{2}; [E] = [MLT^{-3}$$A^{-1}]; inside conductor E = 0; inside insulator E = kQr/R3R^{3}

DIPOLE: p = q·2l; E_axial = 2kp/r3r^{3}; E_eq = kp/r3r^{3}; V_eq = 0; τ = pE sinθ

GAUSS: Φ = q_enc/ε_{0}; Wire: λ/2πε_{0}r; Plane: σ/2ε_{0}; Sphere: kQ/r2r^{2} (outside)

POTENTIAL: V = kQ/r; E = −dV/dr; W_equipotential = 0

CAPACITOR: C = ε_{0}A/d; with dielectric: KC; Series: 1/C_eq = Σ1/Cᵢ; Parallel: C_eq = ΣCᵢ

ENERGY: U = ½CV2CV^{2} = Q2Q^{2}/2C = ½QV

DIELECTRIC RULE: Connected → V constant, C↑K, U↑K | Disconnected → Q constant, V↓K, U↓K

KEY RATIOS: E_axial : E_eq = 2:1 | Series smaller C → more energy | Parallel larger C → more energy

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