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Coulomb's law is one line in your textbook: F = kq₁q₂/r². The experiment behind it was delicate enough that, for decades, others struggled to repeat it. This post covers who Coulomb was, how his torsion balance worked, his three readings from 1785 worked through, and what students can learn from his methods.
Who was Charles-Augustin de Coulomb?
The MacTutor biography records that he was born on 14 June 1736 in Angoulême and died on 23 August 1806 in Paris. He trained at the engineering school at Mézières, graduated in 1761 as a lieutenant in the Corps du Génie, and spent years building Fort Bourbon on Martinique. The illnesses he caught there affected his health for the rest of his life.
Back in France he wrote on applied mechanics. A 1773 memoir used the calculus of variations on problems of masonry and soil pressure. A prize memoir of 1781 on friction got him elected to the Académie des Sciences, and he moved to Paris. Between 1785 and 1791 he submitted seven memoirs on electricity and magnetism.
How does a torsion balance measure a tiny force?
Coulomb's 1777 prize memoir on magnetic compasses already contained his theory of twisting thin threads. MacTutor notes he was the first to show how a torsion suspension could measure extremely small forces.
The idea is simple. Hang a light horizontal arm from a fine wire. A force on the end of the arm twists the wire, and the wire twists back with a torque proportional to the angle of twist. In his 1785 memoir, Coulomb states that torsion forces are proportional to the angles of torsion, so measuring an angle measures a force.
In his apparatus a small pith ball on the arm sat next to a fixed ball. Both were charged with the same kind of electricity, so they pushed apart. A micrometer at the top of the wire let him twist it on purpose, forcing the balls closer, and read the twist in degrees.
What did Coulomb actually measure?
His first memoir is reprinted in the Société française de physique's collection of memoirs (volume 1, 1884, pages 111–112). He reports three trials:
With no twist at the top, the balls settled 36° apart. The wire was twisted by 36°.
He twisted the top by 126°. The balls came to 18° apart. Total twist: 126 + 18 = 144°.
He twisted the top by 567°. The balls came to 8.5° apart. Total twist: 567 + 8.5 = 575.5°.
He concluded that the repulsion between the two balls "suit la raison inverse du carré des distances": it follows the inverse square of the distances.
Worked example: does the data fit an inverse square law?
Treat the angle between the balls as the distance, which is fair for small angles, and the total twist as the force.
Trial 1 to trial 2: the distance halves, from 36° to 18°. An inverse square law predicts the force should multiply by 2² = 4. Prediction: 36 × 4 = 144°. Measured: 144°. A match.
Trial 2 to trial 3: if the distance halved again, to 9°, the force should be 144 × 4 = 576°. Coulomb measured 575.5° at 8.5°. He noted that the distance was only half a degree short of exactly half.
To check trial 3 strictly, scale by (18/8.5)² ≈ 4.48. Prediction: 144 × 4.48 ≈ 646°, against 575.5° measured, about 11% low. So the match at trial 3 is rough. Coulomb himself added remarks on the limits: even in calm air the rest position of the arm was uncertain by two or three degrees, the silver wire was so fine it broke at the slightest shock, and the charge on the balls slowly leaked away during a run. Real data rarely sits exactly on the line.
Now a modern exam version. Two point charges of 2 μC and 3 μC sit 0.3 m apart. With k = 9 × 10⁹ N m²/C²:
F = (9 × 10⁹ × 2 × 10⁻⁶ × 3 × 10⁻⁶) / (0.3)² = (5.4 × 10⁻²) / 0.09 = 0.6 N.
Halve the distance to 0.15 m and the force becomes 2.4 N, four times larger, exactly the pattern in trials 1 and 2.
Mistakes to avoid:
Forgetting to square the distance. Halving r multiplies F by four, not two.
Leaving μC unconverted. 1 μC is 10⁻⁶ C.
Dropping the direction. Coulomb's law gives a magnitude; decide attraction or repulsion from the signs.
Coulomb's law is listed in the electrostatics unit of the official JEE (Main) 2026 syllabus; check the syllabus for your own exam year. Our guide to common electrostatics mistakes covers the next steps. If the idea of a field around a charge feels abstract, the Fermi Concept Library has every concept in physics with its own lesson, so you can fill that one gap.
Why did others doubt him?
The result was not accepted at once. In a study that rebuilt the apparatus at the University of Oldenburg, Peter Heering (1992) notes that the inverse square law was strongly contested for about 40 years after 1785, especially in Germany, and investigated why none of Coulomb's contemporaries managed to reproduce his results. A torsion balance is easily upset by air currents and leaking charge, so the skill was as much in the handling as in the idea.
What can a student take from how he worked?
Turn a hard quantity into an easy one. He could not measure force directly, so he measured an angle.
Use ratios. Halving the distance and checking for a factor of four needs no absolute units.
Bring your other skills. His work on twisting threads and friction came from engineering problems.
Report the imperfect point. His third trial did not fit perfectly, and he said so.
The same twisting-wire method later let Henry Cavendish measure gravity between lead balls, as our post on Cavendish weighing the Earth explains.
Try it: if the balls in trial 1 had been 24° apart, what total twist would put them 12° apart?
