Coulomb constant

Charles-Augustin de Coulomb hung a charged pith ball on a silk torsion fibre in 1785 and measured the twist as he brought a second charge near, establishing the inverse-square law that carries his name. (Henry Cavendish had found it a decade earlier with a more elegant shell experiment, and told nobody; the notes surfaced a century later.) The constant that scales the law, kₑ = 1/(4πε₀), is close to 9×10⁹ in SI units and is the reason electric forces dwarf gravity: two protons repel about 10³⁶ times harder than they attract.

Its value is not independent — kₑ = μ₀c²/4π, so it is a restatement of the vacuum constants. Before 2019, with μ₀ exactly 4π×10⁻⁷, kₑ was exactly c²×10⁻⁷ = 8.987551787×10⁹. Fixing the elementary charge instead moved a hair of uncertainty into it, hence the ±1.4 here on a number near nine billion.