Electric constant

The electric constant (symbol: ε₀), also known as the vacuum permittivity or the permittivity of free space, is a physical constant that describes the force between two charged bodies in vacuum. The exact definition (and value) depends on the system of quantities used, but in the International System of Quantities (ISQ), it has a defined value of approximately 8.854 187 816 × 10⁻¹² F m⁻¹.

The electric constant is related to the magnetic constant μ₀ and the speed of light c₀ by the equation c20 = 1/ε₀μ₀. In SI units, the speed of light is exactly 299 792 458 m s⁻¹ (by the definition of the metre) and the magnetic constant is exactly 4π × 10⁻⁷ N A⁻¹ (by the definition of the ampere): hence, the electric constant is also fixed, and can be calculated to any desired precision (although the numerical value is a non-repeating decimal).

New SI

Under the proposals to redefine the ampere as a fixed number of elementary charges per second, the electric constant would no longer have an exact fixed value. Instead, it would be defined by the equation ε₀ = e²/2αhc₀, where e is the elementary charge, α is the fine structure constant and h is the Planck constant. The relative uncertainty in the value would be the same as that of the fine structure constant, 6.8 × 10⁻¹⁰ at present.