Vacuum permeability
Physical constant quantifying magnetic field strength induced by electric current in vacuum.
The vacuum magnetic permeability, also known as the permeability of free space or the magnetic constant, is a physical constant that quantifies the strength of the magnetic field induced by an electric current in a classical vacuum. Conventionally written as μ0, it was historically defined as exactly 4π × 10⁻⁷ H/m based on the former definition of the ampere, but after the 2019 revision of the SI it became an experimentally determined constant proportional to the fine-structure constant.
- symbol
- μ0
- value (2022 CODATA)
- 4π × 0.99999999987(16) × 10⁻⁷ H/m
- SI unit
- kg·m·s⁻²·A⁻² (or N·A⁻², H·m⁻¹, T·m·A⁻¹)
- relative uncertainty
- 1.6 × 10⁻¹⁰
- former defined value
- 4π × 10⁻⁷ H/m
- terminology introduced
- William Thomson, 1st Baron Kelvin in 1872
- modern notation (μ, ε)
- since the 1950s
Lore & Background
The terminology of permeability and susceptibility was introduced by William Thomson, 1st Baron Kelvin in 1872, while the modern notation of μ for permeability and ε for permittivity has been in use since the 1950s. From 1948 until 2019, the ampere was defined such that two parallel conductors 1 meter apart carrying 1 ampere would produce a force of 2 × 10⁻⁷ N/m, which fixed μ0 at exactly 4π × 10⁻⁷ N/A². This definition relied on measuring current using known mass, length, and time standards, a task for which the Kibble balance was designed.
Reader's Guide
The vacuum magnetic permeability is fundamental to electromagnetism, appearing in Ampère's force law and defining the relationship between electric current and magnetic force. Its historical defined value of 4π × 10⁻⁷ H/m was a consequence of the ampere's definition from 1948 to 2019. With the 2019 revision of the SI, the ampere was redefined in terms of the elementary charge and the second, making μ0 an experimentally measured quantity. The 2022 CODATA value shows a relative deviation of 1.3 × 10⁻¹⁰ from the former defined value, within its uncertainty of 1.6 × 10⁻¹⁰. This change transformed the Kibble balance from a device for measuring current from known weight to one for measuring weight from known current. The constant is now proportional to the dimensionless fine-structure constant, linking it to quantum electrodynamics.
Did You Know?
- μ0 was formerly defined as exactly 4π × 10⁻⁷ H/m based on the ampere's definition from 1948 to 2019.
- After the 2019 SI revision, μ0 became an experimentally determined constant proportional to the fine-structure constant.
- The 2022 CODATA value for μ0 is 4π × 0.99999999987(16) × 10⁻⁷ H/m.
- The terminology of permeability was introduced by William Thomson, 1st Baron Kelvin in 1872.
Frequently Asked Questions
Who is Vacuum permeability?
Vacuum permeability, written as μ0, is a fundamental constant of classical electromagnetism that tells you how strongly an electric current produces a magnetic field in empty space. The name was introduced by Lord Kelvin (William Thomson) in 1872.
What are Vacuum permeability's powers/role?
It sets the proportionality between a steady current and the magnetic field it generates in a classical vacuum, appearing directly in Ampère's law and the magnetic-force equations. It also links to the speed of light and vacuum permittivity through the identity c² = 1/(μ0·ε0).
How does Vacuum permeability's story end?
The 2019 SI redefinition of the ampere removed μ0's long-held exact value of 4π × 10⁻⁷ H/m, reclassifying it as a quantity that must now be determined experimentally. Its magnitude is now tied to the fine-structure constant, so it carries a small but nonzero measurement uncertainty.
Why is Vacuum permeability important?
You cannot calculate magnetic forces, inductance, or the characteristic impedance of free space without it, making μ0 indispensable in classical electrodynamics. Its post-2019 dependence on the fine-structure constant also connects it to quantum electrodynamics.
What are Vacuum permeability's stats?
The 2022 CODATA recommended value is roughly 4π × 0.99999999987 × 10⁻⁷ H/m with a relative uncertainty of about 1.6 × 10⁻¹⁰. Its SI unit is expressible as kg·m·s⁻²·A⁻², N·A⁻², or H·m⁻¹.
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