Electrostatics — Essential NEET Facts — Summary

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)