Experiment #76 · Scientific experiment

Coulomb's Torsion Balance

The inverse-square law of electrostatic force

Charles-Augustin de Coulomb · 1785 · Electromagnetism

First published: C. Coulomb, "Premier mémoire sur l'électricité et le magnétisme", *Mémoires de l'Académie Royale des Sciences* (1785): 569–577.

A delicate torsion balance reveals that electrostatic force follows the same inverse-square law as gravity.

Coulomb used a torsion balance — a horizontal rod suspended by a fine wire — with a charged pith ball at one end. Bringing another charged ball near caused the rod to twist; measuring the twist angle gave the force. He showed the force varied inversely as the square of the distance, and proportionally to the product of charges, establishing the law that bears his name: F = k·q₁q₂/r². The result was the empirical foundation of electrostatics, the basis for the unit of charge, and the crucial input Cavendish used to weigh the Earth using a similar apparatus for gravity a decade later.

Formulation

Torsion balance with charged sphere at one end; second charged sphere placed at variable distance r. Measure angular deflection ∝ torque ∝ force. Observed: F ∝ 1/r² and F ∝ q₁q₂. Conclusion: Coulomb's law, formally identical in form to Newtonian gravitation.

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Dimensions Engaged

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Matter

Establishes that charged matter exerts a quantitative force law on other charged matter — laying groundwork for the electromagnetic field concept.

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Space

The inverse-square dependence is geometric: force lines from a point source spread over a sphere of area 4πr².

Responses — How Schools Engage

Affirms / takes the bait 5

Naturalism

A canonical empirical law: precise quantitative measurement establishes the force's functional form. Electrostatics becomes a quantitative science.

Realism

The Coulomb force is a real interaction between charged bodies; the inverse-square dependence is a feature of the world, not a calculational artifact.

Structuralism

Coulomb's law is structural: it specifies a numerical relation between distance, charge, and force, with no commitment to *how* the force is mediated. The field concept fills in the structure later.

Pythagoreanism

Mathematical form (inverse square) governs physical interaction; the same form appears in gravity and electrostatics, signalling deep mathematical structure in nature.

Logical Positivism

Operationally exemplary: forces are reduced to measurable angles; the law is given empirical content directly.

Reframes the question 1

Relationalism

A direct action-at-a-distance reading is uncomfortable for relationalists; the inverse-square form invites a field-mediated interpretation (Faraday, Maxwell) that handles the metaphysics better.