- Electric charge is quantized: q = ne, e = \$1.6 \times 10^{-19}$ C; charge is conserved and additive
- Coulomb's law: F = kq_{1}q_{2}/$r^{2}$; k = \$9 \times 10^{9}$ N $m^{2}$ $C^{-2}$; ε_{0} = \$8.85 \times 10^{-12}$ $C^{2}$ $N^{-1}$ $m^{-2}$
- Electric field E = kQ/$r^{2}$; SI unit: N/C; [E] = [M$LT^{-3}$$A^{-1}$]; field lines never cross
- Inside a **conductor**: E = 0 everywhere, regardless of charge on it
- Inside a uniformly charged **insulator** at r < R: E = kQr/$R^{3}$ (increases linearly with r)
- Outside both conductor and insulator (r > R): E = kQ/$r^{2}$ (identical, like a point charge)
- Dipole moment p = q·2l; direction from −q to +q; [p] = [ATL]; unit: C·m
- E_axial = 2kp/$r^{3}$; E_equatorial = kp/$r^{3}$; ratio = **2:1** (most tested dipole fact)
- Potential on equatorial line of dipole = **0** (contributions from ±q cancel)
- Gauss's law: Φ = q_enc/ε_{0}; units of flux: V·m or N $m^{2}$ $C^{-1}$
- Infinite wire: E = λ/2πε_{0}r; infinite plane: E = σ/2ε_{0} (independent of distance)
- Electric potential V = kQ/r; E = −dV/dr; [V] = [$ML^{2}$$T^{-3}$$A^{-1}$]; unit: volt
- Work done moving charge along equipotential surface = 0 ($\Delta V$ = 0 → W = q$\Delta V$ = 0)
- Capacitance C = Q/V = ε_{0}A/d; [C] = [$M^{-1}$$L^{-2}$$T^{4}$$A^{2}$]; unit: farad (F)
- With dielectric K: C' = KC always; what changes depends on whether battery is connected
- Battery **connected** → V constant → Q' = KQ, U' = KU (energy increases)
- Battery **disconnected** → Q constant → V' = V/K, U' = U/K (energy decreases)
- Series: same Q on all capacitors; 1/C_eq = Σ1/Cᵢ; smaller C → more energy stored
- Parallel: same V across all capacitors; C_eq = ΣCᵢ; larger C → more energy stored
- Energy: U = ½$CV^{2}$ = $Q^{2}$/2C = ½QV; [U] = [$ML^{2}$$T^{-2}$]; unit: joule (J)$
Part of ES-01 — Electrostatics
Electrostatics — Essential NEET Facts
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