NapkinCalc

Physics 3 — Electricity & Magnetism

Coulomb’s law — the inverse square

Charges push with F = k·q₁q₂/r² — same shape as gravity, but ~10³⁶ times stronger. The inverse square means doubling the distance quarters 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