Vacuum electric permittivity

Permittivity measures how much electric flux a vacuum "permits" for a given charge. It is the ε₀ in Gauss's law, the 1/(4πε₀) in Coulomb's law, and the ε₀A/d in the capacitance of parallel plates — one number that fixes the scale of all electrostatics. Its tiny size, 8.85 picofarads per metre, is why capacitors need large areas and thin gaps: a 1 m² plate pair separated by 1 mm of air comes to only 8.85 nF.

In 1856 Wilhelm Weber and Rudolf Kohlrausch measured the ratio of the electrostatic to the electromagnetic unit of charge and got a number close to 3.1×10⁸ m/s. Maxwell saw it, worked out that his electromagnetic waves must travel at 1/√(μ₀ε₀), and wrote in 1862 that the agreement with Fizeau's measured speed of light was too close to be coincidence: "we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena." Two bench measurements of charge and force had just identified light.