# 12.1: Introduction

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This chapter is likely to be a short one, not least because it is a subject in which my own knowledge is, to put it charitably, a little limited. A thorough understanding of why some materials are magnetic requires a full course in the physics of the solid state, a course that I could not possibly give. Nevertheless, there are a few basic concepts and ideas concerned with magnetic materials which everyone who is interested in electromagnetism should know, and it is the aim of this chapter to describe them in a very introductory way.

It may be worthwhile to remind ourselves of the ways in which we have defined the magnetic fields \(B\) and \(H\). To define \(B\), we noted that an electric current situated in a magnetic field experiences a force at right angles to the current, the magnitude and direction of this force depending on the direction of the current. We accordingly defined \(B\) as being equal to the maximum force per unit length experienced per unit current, the defining equation being \(\textbf{F}^\prime = \textbf{I} \times \textbf{B}\).

Later, we asked ourselves about the strength of the magnetic field in the vicinity of an electric current. We introduced the Biot-Savart law, which says that the contribution to the magnetic field from an element \(ds\) of a circuit carrying a current \(I\) is proportional to \((I\,ds\, \sin \theta )/r^2\) and we called the constant of proportionality \(\mu/(4\pi)\) where \(\mu\) is the *permeability* of the material surrounding the current. We might equally well have approached it from another angle. For example, we might have noted that the magnetic field inside a solenoid is proportional to \(nI\), and we could have denoted the constant of proportionality \(\mu\), the permeability of the material inside the solenoid.

We then defined \(H\) as being an alternative measure of the magnetic field, given by \(H = B/\mu\).

In an isotropic medium*,* the vectors \(\textbf{B}\) and \(\textbf{H}\) are parallel, and the permeability is a scalar quantity. In an anisotropic crystal, \(\textbf{B}\) and \(\textbf{H}\) are not necessarily parallel, and the permeability is a tensor.

Some people see an analogy between the equation between the equation \(B = \mu H\) and the equation \(D=\epsilon E\) of electric fields. With our approach, however, I think most readers will see that, to the extent that there may be an analogy, the analogy is between \(D = \epsilon E\) and \(H = B/\mu \).

For example, consider a long solenoid, in the inside of which are two different magnetic materials in series, the first of permeability \(\mu_1\) and the second of greater permeability \(\mu_2\). The \(H\)-field everywhere inside the solenoid is just \(nI\), regardless of what is inside it. Like \(\textbf{D}\), the component of \(\textbf{H}\) perpendicular to the boundary between two media is continuous, whereas the perpendicular component of \(\textbf{B}\) is greater inside the material with the larger permeability. Likewise, if you were to consider, for example, two different media lying side-by-side in parallel, between the poles, for example, of a horseshoe magnet, the component of \(\textbf{B}\) parallel to the boundary between the media is continuous, and the parallel component of \(\textbf{H}\) is less in the medium of greater permeability.

In this chapter, we shall introduce a few new words, such as *permeance* and *magnetization*. We shall describe in a rather simple and introductory way five types of magnetism exhibited by various materials: *diamagnetism, paramagnetism, ferromagnetism, antiferromagnetism and ferrimagnetism.* And we shall discuss the phenomenon of *hysteresis.*