NapkinCalc

Physics 3 — Electricity & Magnetism

Coulomb's law — the inverse square

ELI5: two charges push or pull with F = k·q₁q₂/r² — exactly the shape of gravity, but about 10³⁶ times stronger (which is why static cling beats the whole Earth's pull). "Inverse square" means double the distance, quarter the force.

ke=8988000000k_{e} = 8988000000 Coulomb constant (N·m²/C²)
q1=0.000002q_{1} = 0.000002 charge 1 (C) — a rubbed balloon's worth
q2=0.000003q_{2} = 0.000003 charge 2 (C)
rq=0.1r_{q} = 0.1 separation (m)
Fe=ke⋅q1⋅q2rq2F_{e} = \frac{k_{e} \cdot q_{1} \cdot q_{2}}{r_{q}^{2}} = 5.39285.3928 force (N) — about half a kilogram-force from microcoulombs!
✓ pass abs(ke⋅q1⋅q2(2⋅rq)2−Fe4)<10−9\mathrm{abs}\left(\frac{k_{e} \cdot q_{1} \cdot q_{2}}{\left(2 \cdot r_{q}\right)^{2}} - \frac{F_{e}}{4}\right) < 10^{-9} double the distance, quarter the force

Real-world hook: Coulomb's law is static cling, the spark off a doorknob, how a photocopier makes toner stick, and the force holding every atom together.

Try it yourself: two 1 µC (1e-6 C) charges sit 2 m apart. What force (N) do they feel? (F = k·q₁·q₂/r².)

forceyou=8988000000⋅0.000001⋅0.00000122force_{you} = \frac{8988000000 \cdot 0.000001 \cdot 0.000001}{2^{2}} = 0.00220.0022 ✏️ Your turn: plug q₁ = q₂ = 1e-6 C, r = 2 m into k·q₁·q₂/r² (k = 8.988e9).
✓ pass abs(forceyou−8988000000⋅0.000001⋅0.00000122)<0.000001\mathrm{abs}\left(force_{you} - \frac{8988000000 \cdot 0.000001 \cdot 0.000001}{2^{2}}\right) < 0.000001 green when your Coulomb force is correct