$$\require{cancel}$$

# 12.1: Introduction

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.