Permeability (electromagnetism)

In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. 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 opposite of magnetic permeability is magnetic reluctance.

In SI units, permeability is measured in henries per meter (H/m or H·m⁻¹), 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. The magnetic constant has the exact (defined) value (µ₀ = 4π × 10⁻⁷ H·m⁻¹ ≈ 1.2566370614…×10⁻⁶ H·m⁻¹ or N·A⁻²).

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.

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