Vacuum permeability
Encyclopedia
The physical constant
μ0, commonly called the vacuum permeability, permeability of free space, or magnetic constant is an ideal, (baseline) physical constant, which is the value of magnetic permeability in a classical vacuum. Vacuum permeability is derived from production of a magnetic field by an electric current or by a moving electric charge and in all other formulas for magnetic-field production in a vacuum. In the reference medium of classical vacuum, µ0 has an exact defined value:
in the SI
system of units.
As a constant, it can also be defined as a fundamental invariant quantity, and is also one of three components that defines free space through Maxwell's equations
. In classical physics
, free space is a concept of electromagnetic theory, corresponding to a theoretically perfect vacuum
and sometimes referred to as the vacuum of free space, or as classical vacuum, and is appropriately viewed as a reference medium.
Adopted in 1948, the effect of this definition is to fix the magnetic constant (permeability of vacuum) at exactly . To further illustrate:
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 force per unit length is given by
The ampere is defined such that if the wires are 1 m apart and the current in each wire is 1 A, the force between the two wires is .
Hence the value of μ0 is defined to be exactly
The term "vacuum permeability" (and variations thereof, such as "permeability of free space") remains very widespread. However, 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.
The name "magnetic constant" is used by standards organizations in order to avoid use of the terms "permeability" and "vacuum", which have physical meanings. This change of preferred name has been made because μ0 is a defined value, and is not the result of experimental measurement (see below).
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.
Ampère's force law describes the experimentally-derived fact that, for two thin, straight, stationary, parallel wires, a distance r apart, in each of which a current I flows, the force per unit length, Fm, that one wire exerts upon the other in the vacuum of free space would be given by
Writing the constant of proportionality as km gives
The form of km needs to be chosen in order to set up a system of equations, and a value then needs to be allocated in order to define the unit of current.
In the old "electromagnetic (emu)" system of equations
defined in the late 1800s, km 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
"). A practical unit to be used by electricians and engineers, the ampere, was then defined as equal to one tenth of the electromagnetic unit of current.
In another system, the "rationalized-metre-kilogram-second (rmks) system" (or alternatively the "metre-kilogram-second-ampere (mksa) system"), km is written as μ0/2π, where μ0 is a measurement-system constant called the "magnetic constant".
The value of μ0 was chosen such that the rmks unit of current is equal in size to the ampere in the emu system: μ0 is defined to be 4π × 10−7 N A−2.
Historically, several different systems (including the two described above) were in use simultaneously. In particular, physicists and engineers used different systems, and physicists used three different systems for different parts of physics theory and a fourth different system (the engineers' system) for laboratory experiments. 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
.
Ampère's law as stated above describes a physical property of the world. However, the choices about the form of km and the value of μ0 are totally human decisions, taken by international bodies composed of representatives of the national standards organizations of all participating countries. The parameter μ0 is a measurement-system constant, not a physical constant that can be measured. It does not, in any meaningful sense, describe a physical property of the vacuum. This is why the relevant Standards Organizations prefer the name "magnetic constant", rather than any name that carries the hidden and misleading implication that μ0 describes some physical property of the vacuum.
, which describe the properties of electric
and magnetic
fields and electromagnetic radiation
, and relate them to their sources. 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. In real media, this relationship has the form:
where M is the magnetization density. In free space, M = 0.
Maxwell's laws show that speed of light
in a vacuum, c is related to the magnetic constant and the electric constant (vacuum permittivity), ε0, by the formula
Physical constant
A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.There are many physical constants in...
μ0, commonly called the vacuum permeability, permeability of free space, or magnetic constant is an ideal, (baseline) physical constant, which is the value of magnetic permeability in a classical vacuum. Vacuum permeability is derived from production of a magnetic field by an electric current or by a moving electric charge and in all other formulas for magnetic-field production in a vacuum. In the reference medium of classical vacuum, µ0 has an exact defined value:
-
- µ0 = VVoltThe volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...
·sSecondThe second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....
/(AAmpereThe ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...
·m) ≈ or N·AAmpereThe ampere , often shortened to amp, is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère , French mathematician and physicist, considered the father of electrodynamics...
−2 or TTesla (unit)The tesla is the SI derived unit of magnetic field B . One tesla is equal to one weber per square meter, and it was defined in 1960 in honour of the inventor, physicist, and electrical engineer Nikola Tesla...
·m/A or WbWeber (unit)In physics, the weber is the SI unit of magnetic flux. A flux density of one Wb/m2 is one tesla.The weber is named for the German physicist Wilhelm Eduard Weber .- Definition :...
/(A·m)
- µ0 = V
in the SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
system of units.
As a constant, it can also be defined as a fundamental invariant quantity, and is also one of three components that defines free space through Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
. In classical physics
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...
, free space is a concept of electromagnetic theory, corresponding to a theoretically perfect vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...
and sometimes referred to as the vacuum of free space, or as classical vacuum, and is appropriately viewed as a reference medium.
The ampere defines vacuum permeability
The ampere is 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.Adopted in 1948, the effect of this definition is to fix the magnetic constant (permeability of vacuum) at exactly . To further illustrate:
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
Ampère's force law
In magnetostatics, the force of attraction or repulsion between two current-carrying wires is often called Ampère's force law...
states that the force per unit length is given by
The ampere is defined such that if the wires are 1 m apart and the current in each wire is 1 A, the force between the two wires is .
Hence the value of μ0 is defined to be exactly
- μ0 = ≈ .
Terminology
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. However, 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.
The name "magnetic constant" is used by standards organizations in order to avoid use of the terms "permeability" and "vacuum", which have physical meanings. This change of preferred name has been made because μ0 is a defined value, and is not the result of experimental measurement (see below).
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
Ampère's force law
In magnetostatics, the force of attraction or repulsion between two current-carrying wires is often called 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.
Ampère's force law describes the experimentally-derived fact that, for two thin, straight, stationary, parallel wires, a distance r apart, in each of which a current I flows, the force per unit length, Fm, that one wire exerts upon the other in the vacuum of free space would be given by
Writing the constant of proportionality as km gives
The form of km needs to be chosen in order to set up a system of equations, and a value then needs to be allocated in order to define the unit of current.
In the old "electromagnetic (emu)" system of equations
Centimetre gram second system of units
The centimetre–gram–second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time...
defined in the late 1800s, km was chosen to be a pure number, 2, distance was measured in centimetres, force was measured in the cgs unit dyne
Dyne
In physics, the dyne is a unit of force specified in the centimetre-gram-second system of units, a predecessor of the modern SI. One dyne is equal to exactly 10 µN...
, and the currents defined by this equation were measured in the "electromagnetic unit (emu) of current" (also called the "abampere
Abampere
The abampere , also called the biot after Jean-Baptiste Biot, is the basic electromagnetic unit of electric current in the emu-cgs system of units . One abampere is equal to ten amperes in the SI system of units...
"). A practical unit to be used by electricians and engineers, the ampere, was then defined as equal to one tenth of the electromagnetic unit of current.
In another system, the "rationalized-metre-kilogram-second (rmks) system" (or alternatively the "metre-kilogram-second-ampere (mksa) system"), km is written as μ0/2π, where μ0 is a measurement-system constant called the "magnetic constant".
The value of μ0 was chosen such that the rmks unit of current is equal in size to the ampere in the emu system: μ0 is defined to be 4π × 10−7 N A−2.
Historically, several different systems (including the two described above) were in use simultaneously. In particular, physicists and engineers used different systems, and physicists used three different systems for different parts of physics theory and a fourth different system (the engineers' system) for laboratory experiments. 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
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...
.
Ampère's law as stated above describes a physical property of the world. However, the choices about the form of km and the value of μ0 are totally human decisions, taken by international bodies composed of representatives of the national standards organizations of all participating countries. The parameter μ0 is a measurement-system constant, not a physical constant that can be measured. It does not, in any meaningful sense, describe a physical property of the vacuum. This is why the relevant Standards Organizations prefer the name "magnetic constant", rather than any name that carries the hidden and misleading implication that μ0 describes some physical property of the vacuum.
Significance in electromagnetism
The magnetic constant μ0 appears in Maxwell's equationsMaxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
, which describe the properties of electric
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
and magnetic
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
fields and electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
, and relate them to their sources. In particular, it appears in relationship to quantities such as permeability
Permeability (electromagnetism)
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...
and magnetization density
Magnetization
In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material...
, such as the relationship that defines the magnetic H-field in terms of the magnetic B-field. In real media, this relationship has the form:
where M is the magnetization density. In free space, M = 0.
Maxwell's laws show that speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
in a vacuum, c is related to the magnetic constant and the electric constant (vacuum permittivity), ε0, by the formula
See also
- Characteristic impedance of vacuum
- Electromagnetic wave equationElectromagnetic wave equationThe electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum...
- Sinusoidal plane-wave solutions of the electromagnetic wave equationSinusoidal plane-wave solutions of the electromagnetic wave equationSinusoidal plane-wave solutions are particular solutions to the electromagnetic wave equation.The general solution of the electromagnetic wave equation in homogeneous, linear, time-independent media can be written as a linear superposition of plane-waves of different frequencies and...
- Mathematical descriptions of the electromagnetic fieldMathematical descriptions of the electromagnetic fieldThere are various mathematical descriptions of the electromagnetic field that are used in the study of electromagnetism, one of the four fundamental forces of nature. In this article four approaches are discussed.-Vector field approach:...