What is Permeability – Relative Permeability - Definition

In electromagnetism, permeability is the measure of the resistance of a substance against the formation of a magnetic field. This constant is very important, since one of important magnetic properties is the relative permeability (dimensionless), the ratio of the permeability in a material to the permeability in a vacuum.

In electromagnetism, permeability is the measure of the resistance of a substance against the formation of a magnetic field. The auxiliary magnetic field H represents how a magnetic field B influences the organization of magnetic dipoles in a given substance. The magnetic field strength and flux density are related according to:

In this equation, B represents the magnitude of the internal field strength within a substance that is subjected to an H field. The permeability has dimensions of webers per ampere-meter (Wb/A.m) or henries per meter (H/m). 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. This constant is very important, since one of important magnetic properties is the relative permeability (dimensionless), the ratio of the permeability in a material to the permeability in a vacuum.

According to the NIST reference on fundamental physical constants, the magnetic constant has the exact (defined) value

μ₀ = 4π × 10⁻⁷ H/m ≈ 12.57×10⁻⁷ H/m.

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.

Neither μ_r nor χ are constants, , as they can vary with the position in the medium. They depend not only on the material but also on the magnitude of the field, H, the frequency of the applied magnetic field, humidity, temperature, and other parameters. Nearly all materials respond to a magnetic field by becoming magnetized, but most are paramagnetic with a response so faint that it is of no practical use. A few, however, contain atoms that have large dipole moments and have the ability to spontaneously magnetize (i.e. to align their dipoles in parallel). These are called ferromagnetic and ferrimagnetic materials (the second one is called ferrites for short), and it is these that are of real practical use. Ferromagnetic, ferrimagnetic, or antiferromagnetic materials possess permanent magnetization even without external magnetic field and do not have a well defined zero-field susceptibility.

References:

Materials Science:

U.S. Department of Energy, Material Science. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
U.S. Department of Energy, Material Science. DOE Fundamentals Handbook, Volume 2 and 2. January 1993.
William D. Callister, David G. Rethwisch. Materials Science and Engineering: An Introduction 9th Edition, Wiley; 9 edition (December 4, 2013), ISBN-13: 978-1118324578.
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Gaskell, David R. (1995). Introduction to the Thermodynamics of Materials (4th ed.). Taylor and Francis Publishing. ISBN 978-1-56032-992-3.
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Ashby, Michael; Hugh Shercliff; David Cebon (2007). Materials: engineering, science, processing and design (1st ed.). Butterworth-Heinemann. ISBN 978-0-7506-8391-3.
J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.

See above:

Magnetic Properties

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