Coulomb's Torsion Balance
Charles-Augustin de Coulomb's 1785 apparatus for measuring the electrostatic force between charged bodies. A conductive sphere on a torsion fiber twists under the repulsion of a fixed charged sphere. The angular deflection reveals that force falls off with the square of the distance — the foundation of electrostatics.
About this lab
In 1785, Charles-Augustin de Coulomb published his landmark experiments using a torsion balance to measure the force between electrically charged bodies. The apparatus consisted of a lightweight horizontal arm suspended from a thin silver wire, with a small conductive sphere at one end and a counterweight at the other. A second charged sphere was brought near the first through an opening in the glass enclosure. The electrostatic repulsion between the two like-charged spheres caused the arm to rotate, twisting the fiber until the restoring torque of the wire balanced the electrostatic force.
By carefully measuring the angular deflection for various separations and charge magnitudes, Coulomb established that the electrostatic force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them: F = k·q₁·q₂/r². This inverse-square law parallels Newton's gravitational law and is the cornerstone of classical electrostatics. The proportionality constant k (Coulomb's constant) equals approximately 8.99 × 10⁹ N·m²/C² in SI units.
The torsion balance works because the restoring torque of a twisted fiber is proportional to the angle of twist (for small angles), following Hooke's law for torsion: τ = κ·θ, where κ is the torsional stiffness and θ is the angular displacement. At equilibrium, the electrostatic torque equals the restoring torque, allowing the force to be computed directly from the measured angle. This same principle was later used by Henry Cavendish to measure the gravitational constant, making the torsion balance one of the most important instruments in the history of physics.