Permeability (electromagnetism)

In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself, otherwise known as distributed inductance in transmission line theory. Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the (italicized) Greek letter μ. The term was coined in September 1885 by Oliver Heaviside. The reciprocal of magnetic permeability is magnetic reluctivity. In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself, otherwise known as distributed inductance in transmission line theory. Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the (italicized) Greek letter μ. The term was coined in September 1885 by Oliver Heaviside. The reciprocal of magnetic permeability is magnetic reluctivity. In SI units, permeability is measured in henries per meter (H/m), or equivalently in newtons per ampere squared (N⋅A−2). The permeability constant μ0, 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. Until 20 May 2019, the magnetic constant had the exact (defined) value μ0 = 4π × 10−7 H/m ≈ 12.57×10−7 H/m. On 20 May 2019 a revision to the SI system has gone into effect, making the vacuum permeability no longer a constant but rather a value that needs to be determined experimentally; 4π × 1.00000000082(20)×10−7 H⋅m−1 is a recently measured value in the new system. It is proportional to the dimensionless fine-structure constant with no other dependencies. 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. In electromagnetism, the auxiliary magnetic field H represents how a magnetic field B influences the organization of magnetic dipoles in a given medium, including dipole migration and magnetic dipole reorientation. Its relation to permeability is where the permeability, μ, is a scalar if the medium is isotropic or a second rank tensor for an anisotropic medium. In general, permeability is not a constant, as it can vary with the position in the medium, the frequency of the field applied, humidity, temperature, and other parameters. In a nonlinear medium, the permeability can depend on the strength of the magnetic field. Permeability as a function of frequency can take on real or complex values. In ferromagnetic materials, the relationship between B and H exhibits both non-linearity and hysteresis: B is not a single-valued function of H, but depends also on the history of the material. For these materials, it is sometimes useful to consider the incremental permeability defined as This definition is useful in local linearizations of non-linear material behaviour, for example in a Newton–Raphson iterative solution scheme that computes the changing saturation of a magnetic circuit. Permeability is the inductance per unit length. In SI units, permeability is measured in henries per metre (H⋅m−1 = J/(A2⋅m) = N⋅A−2). The auxiliary magnetic field H has dimensions current per unit length and is measured in units of amperes per metre (A⋅m−1). The product μH thus has dimensions inductance times current per unit area (H⋅A/m2). But inductance is magnetic flux per unit current, so the product has dimensions magnetic flux per unit area, that is, magnetic flux density. This is the magnetic field B, which is measured in webers (volt-seconds) per square-metre (V⋅s/m2), or teslas (T).