# Permeability – Relative Permeability

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 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 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 the 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, a dimensionless proportionality factor that indicates the degree of magnetization of a material in response to an applied magnetic field.

Neither μr nor χ is 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 can 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 are of real practical use. Ferromagnetic, ferrimagnetic, or antiferromagnetic materials possess permanent magnetization without an external magnetic field and do not have a well-defined zero-field susceptibility.

References:
Materials Science:
1. U.S. Department of Energy, Material Science. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
2. U.S. Department of Energy, Material Science. DOE Fundamentals Handbook, Volume 2 and 2. January 1993.
3. William D. Callister, David G. Rethwisch. Materials Science and Engineering: An Introduction 9th Edition, Wiley; 9 edition (December 4, 2013), ISBN-13: 978-1118324578.
4. Eberhart, Mark (2003). Why Things Break: Understanding the World by the Way It Comes Apart. Harmony. ISBN 978-1-4000-4760-4.
5. Gaskell, David R. (1995). Introduction to the Thermodynamics of Materials (4th ed.). Taylor and Francis Publishing. ISBN 978-1-56032-992-3.
6. González-Viñas, W. & Mancini, H.L. (2004). An Introduction to Materials Science. Princeton University Press. ISBN 978-0-691-07097-1.
7. Ashby, Michael; Hugh Shercliff; David Cebon (2007). Materials: engineering, science, processing, and design (1st ed.). Butterworth-Heinemann. ISBN 978-0-7506-8391-3.
8. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.

## See above:

Magnetic Properties