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 F′=I×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 (Idssinθ)/r2 and we called the constant of proportionality μ/(4π) where μ 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 μ, 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/μ.
In an isotropic medium, the vectors B and H are parallel, and the permeability is a scalar quantity. In an anisotropic crystal, B and H are not necessarily parallel, and the permeability is a tensor.
Some people see an analogy between the equation between the equation B=μH and the equation D=ϵE 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=ϵE and H=B/μ.
For example, consider a long solenoid, in the inside of which are two different magnetic materials in series, the first of permeability μ1 and the second of greater permeability μ2. The H-field everywhere inside the solenoid is just nI, regardless of what is inside it. Like D, the component of H perpendicular to the boundary between two media is continuous, whereas the perpendicular component of 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 B parallel to the boundary between the media is continuous, and the parallel component of 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.