First Memoir on Electricity and Magnetism
Two charges push or pull as the inverse square of their distance — electricity gets its first exact law.
How hard do two specks of static electricity push on each other — and how fast does that push fade as you pull them apart? In 1785 Coulomb built a balance delicate enough to weigh the answer.
The idea
Rub a balloon on your hair and it crackles; two charged objects plainly push or pull on each other. But by how much? Coulomb pinned it to a clean rule. The force depends on two things: how much charge each object carries, and how far apart they are. More charge means more force. And distance matters enormously — move the objects twice as far apart and the force doesn't just halve, it drops to a quarter; three times as far, to a ninth. That steep fade is called an inverse-square law.
It was the very same shape Newton had found for gravity a century earlier — and that was the thrilling part. The silent pull of gravity and the crackle of static electricity, two utterly different forces, turned out to obey mathematics of exactly the same form.
How he measured it
Forces between little charged balls are far too feeble for an ordinary scale, so Coulomb built one of the most sensitive instruments of his age: the torsion balance. He hung a light arm from a long, fine silver wire, with a small charged ball on the end. When he brought a second charged ball close, the first was pushed away and the wire twisted — and a stronger push twisted it more. By reading the twist, he could weigh a force thousands of times too small to feel. He set the balls at a certain distance, then half of it, then a quarter, and watched the force climb in the tell-tale 1, 4, 16 pattern of an inverse square.
Why it mattered
Before Coulomb, electricity was a parlour curiosity — sparks, shocks and crackles with no numbers attached. He turned it into a measured science with a law you could calculate. That law is the reason atoms hold together: electrons are bound to their nuclei by exactly this force, so it quietly underlies all of chemistry, and every battery, screen and circuit you own. And by echoing Newton's law of gravity so precisely, it whispered that the forces of nature might share one deep design.
A picture
Think of the light from a single candle spreading into the dark. Step twice as far away and the candle looks a quarter as bright; three times as far, a ninth. The same fixed amount of light is being smeared over a bigger and bigger sphere as it travels outward. Electric force thins out with distance in exactly the same way, and for a related reason — it reaches out from a charge into all the space around it. That shared inverse-square fingerprint quietly links electricity, gravity, sound and light.
Where it sits
Coulomb took the mathematical machinery Newton had built for gravity (see newton-1687) and showed it fit electricity too. His law became the bedrock on which the nineteenth century raised the rest: Faraday's lines of force (see faraday-1831), Ohm's law of the current (see ohm-1827), and at last Maxwell's union of electricity, magnetism and light (see maxwell-1865), where Coulomb's law reappears as the first of the four famous equations. The unit of electric charge is named the coulomb in his honour.
La force répulsive de deux petits globes électrisés de la même nature d'électricité est en raison inverse du carré de la distance du centre des deux globes.