Coulomb's Law of Force

- - - also measure the separations between thhe charges, r₁ and r₂, we can relate the ratio of forces to the ratio of separations. We find experimentally that F₁/F₂ = r₂²/r₁². This result is consistent with statement 4 that

F ∝ 1/ r² 　　　　　　　　　　　　　　　　　　　　　　　　(1.2)

It is of interest to quote briefly from the original papers of Coulomb¹⁾ part of his description of his quantitative measurements of the law of forces between charged particles. Coulomb had determined the law of torsion of wires, after which he applied the torsion method to the investigation of electrostatic forces. His torsion balance was arranged so that the force between two charged bodies resulted in a twisting of a fine suspension wire. He compared the amount of twisting for various separations between the charged bodies, and from this was able to induce the inverse-square law:

In a memoir presented to the Academy in 1784, I determined by experiment the laws of force of torsion of a metallic wire.. .

I showed in the same memoir that by using this force of torsion it was possible to measure with precision very small forces, as for example, a ten thousandth of a grain*.. .

I submit today to the Academy an electric balance constructed on the same principle; it measures very exactly the state and the electric force of a body, however slightly it is charged. .

. . we go on to give the method which we have used to determine the fundamental law according to which electrified bodies repel each other.

In the third trial the suspension wire was twisted through 567 degrees and the two balls are separated by only 8 degrees and a half. The total torsion was consequently 576 degrees, four times that of the second trial, and the distance of the two balls in this third trial lacked only one-half degree of being reduced to half of that at which it stood in the second trial. It results then from these three trials that the repulsive action which the two balls exert on each other when they are. electrified similarly is in the inverse ratio of the square of the distances.

Statement 5, which says that the force between two charges is proportional to the product of the two charges involved, can be verified experimentally by inverse-square experiments. For example, the

1) Charles Augustin de Coulomb, Memoires sur lélectricité et le magnétisme, Mem.

Acad. Roy. Sci., pp. 569ff. (1788). The quotation is from the 1785 volume, published in 1788-there were delays in publishing in those days too!

* 1 grain = 0.0648 g.