Magnetic constant of vacuum, linking current to magnetic field.Vacuum permeability, denoted μ₀, is a fundamental physical constant that quantifies how much magnetic field is generated per unit of electric current in a vacuum. It appears in Ampère's law and the Biot–Savart law, linking electric currents to the magnetic fields they produce. Its value is exactly 4π × 10⁻⁷ H/m (henries per meter) in the SI system, a definition that was chosen to make the ampere consistent with the meter, kilogram, and second.
The concept emerged from 19th-century work by Ampère and Maxwell, who introduced it as a proportionality constant. Its exact value was set by international agreement in 1948, and it remained a defined constant until the 2019 SI revision, after which it became a measured quantity with a tiny uncertainty.
In classical electromagnetism, μ₀ sets the strength of the magnetic interaction: a current I flowing through a long straight wire produces a magnetic field B = μ₀I/(2πr) at distance r. It also appears in the speed of light in vacuum, c = 1/√(ε₀μ₀), where ε₀ is vacuum permittivity. Because μ₀ is defined exactly, it fixes the ampere's definition in terms of force between parallel wires, though the 2019 SI redefinition tied the ampere to the elementary charge instead.
Vacuum permeability is essential for designing electromagnets, transformers, and inductors, and for calculating the impedance of transmission lines and antennas in telecommunications.
Because μ₀ is now measured rather than defined, its value has a small uncertainty, but it remains so close to 4π × 10⁻⁷ that the difference is negligible for almost all engineering purposes.
