How does the force between two charges change with distance?

It follows an inverse-square law: F = k·q₁q₂/r², so the force falls with the square of the separation. Double the distance and the force drops to a quarter; triple it and it drops to a ninth. Our numbers show it exactly — for a +5 µC and −4 µC pair the attraction is 4.50 N at 0.2 m, 1.12 N at 0.4 m, 0.28 N at 0.8 m and 0.07 N at 1.6 m, each step a clean factor of four. It is the same 1/r² shape as gravity, which is why both reach so far yet weaken so fast.

Why does salt dissolve in water but not in oil or air?

Because water is an exceptional electrical screen. Coulomb’s law carries the medium’s relative permittivity εr in the denominator, F = k·q₁q₂/(εr·r²), and water’s εr is about 80 — so the attraction between two charges in water is 1/80 of its value in vacuum or air. In table salt the Na⁺ and Cl⁻ ions are locked together by that attraction; immerse the crystal in water and the pull drops 80-fold, weak enough for ordinary thermal motion to shake the ions loose. Oil (εr ≈ 2.2) barely screens at all, which is why ionic solids stay put in it.

Is Coulomb attraction the same as gravity?

They share the inverse-square form — both go as 1/r² — but Coulomb’s law is vastly stronger and comes in two signs. Like charges repel and opposite charges attract, whereas gravity only ever attracts. Between two protons the electrostatic repulsion outweighs their gravitational attraction by about 10³⁶, which is why chemistry and matter are held together by electric forces and gravity only takes over at planetary scales where charges cancel out.

Electricity

Coulomb’s Law, Measured

By Lucian — builder & engineer, LK Forge

The force between two charges has a famous shape — it falls with the square of the distance, the same law as gravity — and a quieter partner that almost nobody notices until it explains something everyday. Both live in one equation, and the second one is the reason salt vanishes into a glass of water. We took the numbers from the Coulomb’s-law lab.

September 10, 2026 · 5 min read · exact from F = k·q₁q₂/(εᵣ·r²)

1 / r²

double the distance, quarter the force

4.5 → 0.07 N

the pull from 0.2 m out to 1.6 m apart

÷ 80

water screens the force to 1.25% of vacuum

salt dissolves

that 80× screening is what frees Na⁺ and Cl⁻

The inverse-square falloff

The r² in the denominator is the whole character of the force. Pull the charges twice as far apart and the force does not halve — it quarters. The table is exact: each doubling of r divides the force by precisely four, the signature of a 1/r² law. Up close the force is enormous; a little distance tames it fast.

Force vs separation for the +5 / −4 µC pair in vacuum. Each dot is a doubling of distance: 4.50 → 1.12 → 0.28 → 0.07 N, a clean ÷4 each time — the fingerprint of 1/r².

The medium that dissolves salt

Keep the charges and the distance fixed and change only what surrounds them. Every medium carries a relative permittivity εᵣ that sits in the denominator, screening the force. Oil barely bothers (εᵣ ≈ 2.2, force down to 45%); glass more so; but water is the outlier at εᵣ ≈ 80, cutting the force to a hundred-and-a-quarter percent — 1.25% — of its vacuum strength. That is the single fact behind why water is the universal solvent for salts.

Same +5 / −4 µC charges at 0.8 m, force as a fraction of vacuum. Water screens it 80-fold to a sliver — the reason ionic crystals fall apart in it and not in oil.

Same shape as gravity — but a sign, and a lot more muscle

Coulomb’s 1/r² is the same falloff Newton found for gravity, which is why both forces reach across a room or a solar system. But two differences change everything. Charge comes in two signs, so the force can pull or push — our +5 / −4 µC pair attracts, with a bound-state potential energy of −0.22 J, while two like charges would repel and store positive energy. And it is overwhelmingly stronger: between two protons the electric repulsion beats their gravitational attraction by a factor of about 10³⁶. That is why matter is built and held by electric forces, and gravity only wins at planetary scale, where equal amounts of positive and negative charge have long since cancelled out.

Reproduce it yourself

One formula gives every number, including the ÷4-per-doubling and the ÷80 in water.

const k = 8.99e9;   // N·m²/C²
// charges in µC (×1e-6 C), r in m, eps_r = relative permittivity
const F = (q1, q2, r, eps = 1) => k * Math.abs(q1 * q2) * 1e-12 / (eps * r * r);

F(5, -4, 0.2);        // 4.495 N     F(5, -4, 0.4); // 1.124 N  (a quarter)
F(5, -4, 0.8);        // 0.281 N     F(5, -4, 1.6); // 0.070 N
F(5, -4, 0.8, 80);    // 0.0035 N — the same pair in water (eps_r = 80)

The force formula is lifted straight from the Coulomb’s-law solver; the distance and medium sweeps are the small script behind this post.

Push some charges around

Open the lab, drag the charges apart to watch the force curve collapse, flip a sign to switch attraction for repulsion, then drop them in water and see it nearly vanish.

Open the Coulomb’s-law lab →

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