Permeability (electromagnetism)
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In electromagnetism, permeability is the measure of magnetization that a material obtains in response to
an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter μ. The term
was coined by William Thomson, 1st Baron Kelvin in 1872,[1] and used alongside permittivity by Oliver
Heaviside in 1885. The reciprocal of permeability is magnetic reluctivity.
In SI units, permeability is measured in henries per meter (H/m), or equivalently
in newtons per ampere squared (N/A2). The permeability constant μ0, also known as the magnetic
constant or the permeability of free space, is the proportionality between magnetic induction and
magnetizing force when forming a magnetic field in a classical vacuum.
A closely related property of materials is magnetic susceptibility, which is
a dimensionless proportionality factor that indicates the degree of magnetization of a material in
response to an applied magnetic field.
Explanation [edit]
In the macroscopic formulation of electromagnetism, there appears two different kinds of magnetic field:
the magnetizing field H which is generated around electric currents and displacement currents, and
also emanates from the poles of magnets. The SI units of H are amperes/meter.
the magnetic flux density B which acts back on the electrical domain, by curving the motion of
charges and causing electromagnetic induction. The SI units of B are volt-seconds/square meter (teslas).
The concept of permeability arises since in many materials (and in vacuum), there is a simple
relationship between H and B at any location or time, in that the two fields are precisely proportional to
each other:[2]
,
where the proportionality factor μ is the permeability, which depends on the material. The permeability of
vacuum (also known as permeability of free space) is a physical constant, denoted μ0. The SI units
of μ are volt-seconds/ampere-meter, equivalently henry/meter. Typically μ would be a scalar, but for an
anisotropic material, μ could be a second rank tensor.
However, inside strong magnetic materials (such as iron, or permanent magnets), there is typically no
simple relationship between H and B. The concept of permeability is then nonsensical or at least only
applicable to special cases such as unsaturated magnetic cores. Not only do these materials have
nonlinear magnetic behaviour, but often there is significant magnetic hysteresis, so there is not even a
single-valued functional relationship between B and H. However, considering starting at a given value
of B and H and slightly changing the fields, it is still possible to define an incremental permeability as:[2]
.
assuming B and H are parallel.
In the microscopic formulation of electromagnetism, where there is no concept of an H field, the vacuum
permeability μ0 appears directly (in the SI Maxwell's equations) as a factor that relates total electric
, currents and time-varying electric fields to the B field they generate. In order to represent the magnetic
response of a linear material with permeability μ, this instead appears as a magnetization M that arises in
response to the B field: . The magnetization in turn is a contribution to the total electric current
—the magnetization current.
Relative permeability and magnetic susceptibility [edit]
Relative permeability, denoted by the symbol , is the ratio of the permeability of a specific
medium to the permeability of free space μ0:
where 4π × 10−7 H/m is the magnetic permeability of free space.[3] In terms of relative
permeability, the magnetic susceptibility is
The number χm is a dimensionless quantity, sometimes called volumetric or bulk susceptibility, to
distinguish it from χp (magnetic mass or specific susceptibility) and χM (molar or molar
mass susceptibility).
Diamagnetism [edit]
Main article: Diamagnetism
Diamagnetism is the property of an object which causes it to create a magnetic field in opposition of an
externally applied magnetic field, thus causing a repulsive effect. Specifically, an external magnetic field
alters the orbital velocity of electrons around their atom's nuclei, thus changing the magnetic dipole
moment in the direction opposing the external field. Diamagnets are materials with a magnetic
permeability less than μ0 (a relative permeability less than 1).
Consequently, diamagnetism is a form of magnetism that a substance exhibits only in the presence of an
externally applied magnetic field. It is generally a quite weak effect in most materials,
although superconductors exhibit a strong effect.
Paramagnetism [edit]
Main article: Paramagnetism
Paramagnetism is a form of magnetism which occurs only in the presence of an externally applied
magnetic field. Paramagnetic materials are attracted to magnetic fields, hence have a relative magnetic
permeability greater than one (or, equivalently, a positive magnetic susceptibility).
The magnetic moment induced by the applied field is linear in the field strength, and it is rather weak. It
typically requires a sensitive analytical balance to detect the effect. Unlike ferromagnets, paramagnets
do not retain any magnetization in the absence of an externally applied magnetic field, because thermal
motion causes the spins to become randomly oriented without it. Thus the total magnetization will drop
to zero when the applied field is removed. Even in the presence of the field, there is only a
small induced magnetization because only a small fraction of the spins will be oriented by the field. This
Jump to navigationJump to search
In electromagnetism, permeability is the measure of magnetization that a material obtains in response to
an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter μ. The term
was coined by William Thomson, 1st Baron Kelvin in 1872,[1] and used alongside permittivity by Oliver
Heaviside in 1885. The reciprocal of permeability is magnetic reluctivity.
In SI units, permeability is measured in henries per meter (H/m), or equivalently
in newtons per ampere squared (N/A2). The permeability constant μ0, also known as the magnetic
constant or the permeability of free space, is the proportionality between magnetic induction and
magnetizing force when forming a magnetic field in a classical vacuum.
A closely related property of materials is magnetic susceptibility, which is
a dimensionless proportionality factor that indicates the degree of magnetization of a material in
response to an applied magnetic field.
Explanation [edit]
In the macroscopic formulation of electromagnetism, there appears two different kinds of magnetic field:
the magnetizing field H which is generated around electric currents and displacement currents, and
also emanates from the poles of magnets. The SI units of H are amperes/meter.
the magnetic flux density B which acts back on the electrical domain, by curving the motion of
charges and causing electromagnetic induction. The SI units of B are volt-seconds/square meter (teslas).
The concept of permeability arises since in many materials (and in vacuum), there is a simple
relationship between H and B at any location or time, in that the two fields are precisely proportional to
each other:[2]
,
where the proportionality factor μ is the permeability, which depends on the material. The permeability of
vacuum (also known as permeability of free space) is a physical constant, denoted μ0. The SI units
of μ are volt-seconds/ampere-meter, equivalently henry/meter. Typically μ would be a scalar, but for an
anisotropic material, μ could be a second rank tensor.
However, inside strong magnetic materials (such as iron, or permanent magnets), there is typically no
simple relationship between H and B. The concept of permeability is then nonsensical or at least only
applicable to special cases such as unsaturated magnetic cores. Not only do these materials have
nonlinear magnetic behaviour, but often there is significant magnetic hysteresis, so there is not even a
single-valued functional relationship between B and H. However, considering starting at a given value
of B and H and slightly changing the fields, it is still possible to define an incremental permeability as:[2]
.
assuming B and H are parallel.
In the microscopic formulation of electromagnetism, where there is no concept of an H field, the vacuum
permeability μ0 appears directly (in the SI Maxwell's equations) as a factor that relates total electric
, currents and time-varying electric fields to the B field they generate. In order to represent the magnetic
response of a linear material with permeability μ, this instead appears as a magnetization M that arises in
response to the B field: . The magnetization in turn is a contribution to the total electric current
—the magnetization current.
Relative permeability and magnetic susceptibility [edit]
Relative permeability, denoted by the symbol , is the ratio of the permeability of a specific
medium to the permeability of free space μ0:
where 4π × 10−7 H/m is the magnetic permeability of free space.[3] In terms of relative
permeability, the magnetic susceptibility is
The number χm is a dimensionless quantity, sometimes called volumetric or bulk susceptibility, to
distinguish it from χp (magnetic mass or specific susceptibility) and χM (molar or molar
mass susceptibility).
Diamagnetism [edit]
Main article: Diamagnetism
Diamagnetism is the property of an object which causes it to create a magnetic field in opposition of an
externally applied magnetic field, thus causing a repulsive effect. Specifically, an external magnetic field
alters the orbital velocity of electrons around their atom's nuclei, thus changing the magnetic dipole
moment in the direction opposing the external field. Diamagnets are materials with a magnetic
permeability less than μ0 (a relative permeability less than 1).
Consequently, diamagnetism is a form of magnetism that a substance exhibits only in the presence of an
externally applied magnetic field. It is generally a quite weak effect in most materials,
although superconductors exhibit a strong effect.
Paramagnetism [edit]
Main article: Paramagnetism
Paramagnetism is a form of magnetism which occurs only in the presence of an externally applied
magnetic field. Paramagnetic materials are attracted to magnetic fields, hence have a relative magnetic
permeability greater than one (or, equivalently, a positive magnetic susceptibility).
The magnetic moment induced by the applied field is linear in the field strength, and it is rather weak. It
typically requires a sensitive analytical balance to detect the effect. Unlike ferromagnets, paramagnets
do not retain any magnetization in the absence of an externally applied magnetic field, because thermal
motion causes the spins to become randomly oriented without it. Thus the total magnetization will drop
to zero when the applied field is removed. Even in the presence of the field, there is only a
small induced magnetization because only a small fraction of the spins will be oriented by the field. This
