English
Coulomb's law mirrors gravitation with charge in place of mass — but with two signs:
$$F = \frac{kq_1q_2}{r^2}, \qquad k = \frac{1}{4\pi\varepsilon_0} \approx 9.0\times10^9\ \mathrm{N\,m^2/C^2}$$
Like charges repel, unlike attract. Charge is conserved — it moves, never appears or vanishes — and quantized: Millikan's oil-drop experiment (weight balanced by an electric force, $qE = mg$) found every drop's charge a whole-number multiple of $e = 1.6\times10^{-19}\ \mathrm{C}$, the electron charge.
Charge moves between bodies by friction (rubbing transfers electrons), by contact (shared on touching), and by induction — a charged body brought near a conductor separates its charges, and grounding (earthing) lets one sign drain away so the conductor is left with the opposite sign, without the charged body ever touching it.
The electric field strength is force per unit positive test charge, $E = F/q$, with field lines running from positive to negative, never crossing, denser where the field is stronger: radial around a point charge and outside a sphere, straight and equally spaced between opposite parallel plates where
$$E = \frac{V}{d}$$
Magnetic field lines close on themselves (no monopoles): a bar magnet runs N-out S-in; a straight wire carries concentric circles whose direction follows the right-hand grip rule (thumb along the current); a circular coil loops through its centre; a solenoid's interior is near-uniform, its outside like a bar magnet's.
Worked check (Coulomb). Two $+1.0\ \mu\mathrm{C}$ charges $0.050\ \mathrm{m}$ apart: $F = (9.0\times10^9 \times 1.0\times10^{-12})/(0.050)^2 = 3.6\ \mathrm{N}$ — repulsion, falling to one quarter in magnitude per doubling of separation.
Worked check (parallel plates). $12\ \mathrm{V}$ across $4.0\ \mathrm{mm}$: $E = V/d = 3000\ \mathrm{V/m}$, and the force on an electron between them is $F = eE = 4.8\times10^{-16}\ \mathrm{N}$.
Worked check (Millikan). A drop of mass $3.2\times10^{-15}\ \mathrm{kg}$ carrying three excess electrons floats when $qE = mg$: $E = mg/q = (3.2\times10^{-15} \times 9.8)/(4.8\times10^{-19}) = 6.5\times10^4\ \mathrm{V/m}$ — the whole-number charge pattern across many drops is the quantization evidence.
Key:
Electric and magnetic fields: Coulomb's $F = kq_1q_2/r^2$ with conserved, quantized charge (Millikan); $E = F/q$ read from field-line density, uniform $E = V/d$ between plates; charge moves by friction, contact or induction with grounding; magnetic field lines close on themselves — wire circles by the right-hand rule, solenoid like a bar magnet.
