The vacuum magnetic permeability (variously vacuum permeability, permeability of free space, permeability of vacuum), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, conventionally written as μ0 (pronounced "mu nought" or "mu zero"). Its purpose is to quantify the strength of the magnetic field emitted by an electric current. Expressed in terms of SI base units, it has the unit kg⋅m⋅s−2·A−2. It can be also expressed in terms of SI derived units, N·A−2.
Since the redefinition of SI units in 2019 (when the values of e and h were fixed as defined quantities), μ0 is an experimentally determined constant, its value being proportional to the dimensionless fine-structure constant, which is known to a relative uncertainty of about , with no other dependencies with experimental uncertainty. Its value in SI units as recommended by CODATA 2018 (published in May 2019) is:
From 1948 to 2019, μ0 had a defined value (per the former definition of the SI ampere), equal to:
The deviation of the recommended measured value from the former defined value is statistically significant, at about 3.6σ, listed as μ0/() − 1 = .
The terminology of permeability and susceptibility was introduced by William Thomson, 1st Baron Kelvin in 1872. The modern notation of permeability as μ and permittivity as ε has been in use since the 1950s.
The ampere-defined vacuum permeability
Two thin, straight, stationary, parallel wires, a distance r apart in free space, each carrying a current I, will exert a force on each other. Ampère's force law states that the magnetic force Fm per length L is given by
From 1948 until 2019 the ampere was defined as "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 newton per meter of length". This is equivalent to a definition of of exactly ., since
The current in this definition needed to be measured with a known weight and known separation of the wires, defined in terms of the international standards of mass, length and time in order to produce a standard for the ampere (and this is what the Kibble balance was designed for). In the 2019 redefinition of the SI base units, the ampere is defined exactly in terms of the elementary charge and the second, and the value of is determined experimentally; 4 × is a recently measured value in the new system (and the Kibble balance has become an instrument for measuring weight from a known current, rather than measuring current from a known weight).
Terminology
Standards organizations have recently moved to magnetic constant as the preferred name for μ0, although the older name continues to be listed as a synonym. Historically, the constant μ0 has had different names. In the 1987 IUPAP Red book, for example, this constant was still called permeability of vacuum. Another, now rather rare and obsolete, term is "magnetic permittivity of vacuum". See, for example, Servant et al. The term "vacuum permeability" (and variations thereof, such as "permeability of free space") remains very widespread.
The name "magnetic constant" was used by standards organizations in order to avoid use of the terms "permeability" and "vacuum", which have physical meanings. This change of preferred name had been made because μ0 was a defined value, and was not the result of experimental measurement (see below). In the new SI system, the permeability of vacuum no longer has a defined value, but is a measured quantity, with an uncertainty related to that of the (measured) dimensionless fine structure constant.
Systems of units and historical origin of value of μ0
In principle, there are several equation systems that could be used to set up a system of electrical quantities and units. Since the late 19th century, the fundamental definitions of current units have been related to the definitions of mass, length, and time units, using Ampère's force law. However, the precise way in which this has "officially" been done has changed many times, as measurement techniques and thinking on the topic developed. The overall history of the unit of electric current, and of the related question of how to define a set of equations for describing electromagnetic phenomena, is very complicated. Briefly, the basic reason why μ0 has the value it does is as follows.