Vacuum magnetic permeability

For 71 years μ₀ was exactly 4π×10⁻⁷ N/A², not because anyone measured it but because the ampere was defined to make it so: from 1948 the ampere was the current which, in two infinitely long parallel wires one metre apart in vacuum, produced a force of exactly 2×10⁻⁷ newtons per metre. Fix that force and you fix μ₀. The catch was that nobody could realise such a definition to better than a few parts in 10⁷: the current balances were beautiful and hopeless.

The 2019 SI redefinition fixed the elementary charge instead, and μ₀ became an experimental quantity for the first time since 1948. It is now tied to the fine-structure constant by μ₀ = 2αh/(ce²), so it inherits α's uncertainty: about 1.6 parts in 10¹⁰, a shift far too small to disturb any coil you will ever wind, but the reason this entry carries an uncertainty and the old textbook 4π×10⁻⁷ does not. Together with ε₀ it sets the speed of light: c = 1/√(μ₀ε₀).