Charles-Augustin de Coulomb

A fibre converts a tiny force into an angle.

Coulomb suspended a horizontal needle from an extremely fine fibre made from materials such as silver, copper or silk. A small charged pith ball sat at one end of the needle and a counterweight balanced the other. Because the needle could rotate with very little friction, a weak electrical force could twist the suspension fibre through a measurable angle.

The torsion balance was calibrated: the amount of twist required to hold the needle at a chosen angle revealed the force acting on the charged ball. The instrument therefore translated an invisible interaction into a mechanical measurement.

Same-sign charges establish the inverse-square law.

Coulomb brought a second, similarly charged pith ball close to the ball on the suspended needle. The repulsion rotated the needle. He changed the separation between the centres of the two balls and measured the restoring twist at each distance.

The result was an inverse-square relationship: the force is proportional to the product of the charges and inversely proportional to the square of the distance. If the separation doubles, the force falls to one quarter; if it triples, the force falls to one ninth.

• Measure centre-to-centre distance, not the gap between surfaces.
• Keep the charges and apparatus geometry as stable as possible.
• Compare force ratios rather than relying on a single reading.

Opposite charges required a second method.

Oppositely charged pith balls tended to jump together and stick when they came too close, ending the measurement. Coulomb therefore used an independent arrangement: a small charged plate on the suspended needle and an opposite charge distributed on a large hollow conducting sphere.

The second method again supported an inverse-square dependence for attraction. Agreement between two different experimental approaches made the conclusion much stronger and launched the quantitative study of electrostatics.