# Vacuum permeability

**magnetic constantpermeability of free spacepermeability of vacuumpermeabilitypermeability constantμ 0 magnetic permeabilityvacuum magnetic permeabilityμ'' 0 magnetic permeability of free space**

The physical constant μ 0, (pronounced "mu nought" or "mu zero"), commonly called the vacuum permeability, permeability of free space, permeability of vacuum, or magnetic constant, is the magnetic permeability in a classical vacuum.wikipedia

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### Ampère's force law

**Ampère's lawAmpere's force lawAmpere's law**

Ampère's force law states that the force per length L is given by

with μ 0 the magnetic constant, defined in SI units as

### Physical constant

**constantconstantsfundamental constants**

The physical constant μ 0, (pronounced "mu nought" or "mu zero"), commonly called the vacuum permeability, permeability of free space, permeability of vacuum, or magnetic constant, is the magnetic permeability in a classical vacuum.

### Centimetre–gram–second system of units

**CGScgs unitsCGS unit**

In the old "electromagnetic (emu)" system of equations defined in the late 19th century, k m was chosen to be a pure number, 2, distance was measured in centimetres, force was measured in the cgs unit dyne, and the currents defined by this equation were measured in the "electromagnetic unit (emu) of current" (also called the "abampere").

Furthermore, if we wish to describe the electric displacement field D and the magnetic field H in a medium other than vacuum, we need to also define the constants ε 0 and μ 0, which are the vacuum permittivity and permeability, respectively.

### Permeability (electromagnetism)

**permeabilitymagnetic permeabilityrelative permeability**

In particular, it appears in relationship to quantities such as permeability and magnetization density, such as the relationship that defines the magnetic H-field in terms of the magnetic B-field.

The permeability constant μ 0, also known as the magnetic constant or the permeability of free space, is a measure of the amount of resistance encountered when forming a magnetic field in a classical vacuum.

### Maxwell's equations

**Maxwell equationsMaxwell equationMaxwell’s equations**

The magnetic constant μ 0 appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation, and relate them to their sources.

*the permeability of free space,

### Speed of light

**clight speedspeed of light in vacuum**

In SI units, the speed of light in vacuum,

This subscripted notation, which is endorsed in official SI literature, has the same form as other related constants: namely, μ 0 for the vacuum permeability or magnetic constant, ε 0 for the vacuum permittivity or electric constant, and Z 0 for the impedance of free space.

### Magnetic field

**magnetic fieldsmagneticmagnetic flux density**

The magnetic constant μ 0 appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation, and relate them to their sources.

is a constant called the vacuum permeability, measuring 4 V·s/(A·m) and

### Fine-structure constant

**fine structure constant137coupling constant**

It is proportional to the dimensionless fine-structure constant with no other dependencies. Conversely, as the permittivity is related to the fine structure constant (\alpha), the permeability can be derived from the latter (using Planck's constant, h, and the electric charge on an electron, e):

is the magnetic constant or permeability of free space;

### Ampere

**AmAamp**

The ampere was that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 newton per meter of length.

### Vacuum

**free spaceevacuatedhigh vacuum**

The physical constant μ 0, (pronounced "mu nought" or "mu zero"), commonly called the vacuum permeability, permeability of free space, permeability of vacuum, or magnetic constant, is the magnetic permeability in a classical vacuum.

### Mathematical descriptions of the electromagnetic field

**Maxwell's equations in the potential formulationformulation of Maxwell's equationsgeometric algebra formulation of electromagnetism**

where ρ is the charge density, which can (and often does) depend on time and position, ε 0 is the electric constant, μ 0 is the magnetic constant, and J is the current per unit area, also a function of time and position.

### Impedance of free space

**Characteristic impedance of vacuumη 0 characteristic impedance of free space**

The impedance of free space (that is the wave impedance of a plane wave in free space) is equal to the product of the vacuum permeability

### Vacuum permittivity

**permittivity of free spaceelectric constantvacuum electric permittivity**

, is related to the magnetic constant and the electric constant (vacuum permittivity),

where c is the defined value for the speed of light in classical vacuum in SI units, and μ 0 is the parameter that international Standards Organizations call the "magnetic constant" (commonly called vacuum permeability).

### Magnetization

**magnetizedmagnetisationbound current**

In particular, it appears in relationship to quantities such as permeability and magnetization density, such as the relationship that defines the magnetic H-field in terms of the magnetic B-field.

The vacuum permeability μ 0 is, by definition, 4 V·s/(A·m).

### Electromagnetic radiation

**electromagnetic waveelectromagnetic waveselectromagnetic**

The magnetic constant μ 0 appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation, and relate them to their sources.

Thus Maxwell's equations connect the vacuum permittivity, the vacuum permeability \mu_0, and the speed of light, c 0, via the above equation.

### 2019 redefinition of the SI base units

**2019 redefinition of SI base unitsredefinitionredefinition of the SI base units**

In the new SI units, only the fine structure constant is an actual measured value in this formula.

Other consequences of the previous definition were that in SI the value of vacuum permeability (

### Committee on Data for Science and Technology

**CODATACODATA 2018CODATA 2014**

, the vacuum permeability μ 0 will no longer be a defined constant (per the former definition of the SI ampere), but rather will need to be determined experimentally; The 2018 CODATA value is given below.

### International Union of Pure and Applied Physics

**IUPAPC-13 CommitteeIUPAP red book**

In the 1987 IUPAP Red book, for example, this constant was still called permeability of vacuum.

### Dyne

**dyndyne-centimeters**

In the old "electromagnetic (emu)" system of equations defined in the late 19th century, k m was chosen to be a pure number, 2, distance was measured in centimetres, force was measured in the cgs unit dyne, and the currents defined by this equation were measured in the "electromagnetic unit (emu) of current" (also called the "abampere").

### Abampere

**Bibiot**

In the old "electromagnetic (emu)" system of equations defined in the late 19th century, k m was chosen to be a pure number, 2, distance was measured in centimetres, force was measured in the cgs unit dyne, and the currents defined by this equation were measured in the "electromagnetic unit (emu) of current" (also called the "abampere").

### International System of Units

**SISI unitsSI unit**

In 1948, international decisions were made by standards organizations to adopt the rmks system, and its related set of electrical quantities and units, as the single main international system for describing electromagnetic phenomena in the International System of Units.

### Electric field

**electricelectrostatic fieldelectrical field**

### Planck constant

**Planck's constantreduced Planck constantreduced Planck's constant**

Conversely, as the permittivity is related to the fine structure constant (\alpha), the permeability can be derived from the latter (using Planck's constant, h, and the electric charge on an electron, e):

### Electric charge

**chargeelectrical chargecharged**

Conversely, as the permittivity is related to the fine structure constant (\alpha), the permeability can be derived from the latter (using Planck's constant, h, and the electric charge on an electron, e):

### Electromagnetic wave equation

**electric fieldsequationsmultipole radiation fields**