1. Electric charge is quantized (q = ne), conserved in isolated systems, and additive, with the elementary unit e = \$1.6 \times 10^{-19}$ C.
2. Coulomb's law gives the force between two point charges as F = kq_{1}q_{2}/$r^{2}$ where k = \$9 \times 10^{9}$ N $m^{2}$ $C^{-2}$, and the net force on any charge is the vector sum of all such pairwise forces (superposition).
3. The electric field E = kQ/$r^{2}$ at a point gives the force per unit positive test charge; its dimensional formula is [M$LT^{-3}$$A^{-1}$] and it is zero everywhere inside a conductor.
4. Inside a uniformly charged insulating sphere at radius r < R, the electric field is E = kQr/$R^{3}$, which increases linearly from zero at the center to a maximum at the surface.
5. For an electric dipole, the axial field is E_axial = 2kp/$r^{3}$ and the equatorial field is E_eq = kp/$r^{3}$, giving a ratio of 2:1; the potential on the equatorial line is zero.
6. Gauss's law states Φ = q_enc/ε_{0} and gives E = λ/2πε_{0}r for an infinite wire, E = σ/2ε_{0} for an infinite plane, and E = kQ/$r^{2}$ (outside) or 0 (inside) for a conducting sphere.
7. Electric potential V = kQ/r is related to field by E = −dV/dr; equipotential surfaces are perpendicular to field lines and no work is done moving a charge along them.
8. Capacitance C = ε_{0}A/d increases by a factor K when a dielectric of constant K is inserted; energy stored is U = ½$CV^{2}$ = $Q^{2}$/2C = ½QV.
9. When a dielectric is inserted with the battery connected, V is constant and energy increases by K; when disconnected, Q is constant and energy decreases by K.
10. In series capacitor combinations, charge is the same on all and the smallest capacitor stores the most energy; in parallel combinations, voltage is the same and the largest capacitor stores the most energy.$
Part of ES-01 — Electrostatics
Electrostatics — 10 Core Sentences
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