Magnetism

Abstract

In this chapter we extend magnetostatics to include matter in general, where previously we have considered the magnetic fields arising from electrons in a vacuum or free electrons in metals. We use Gauss’s law for magnetic flux

$$ \int_s {B \cdot dS = 0} $$

Ampère’s circulation law for steady currents

$$ \oint_c {B \cdot ds = \mathop \mu \nolimits_0 } \int_s {j \cdot dS} $$

and we consider induced currents from Faraday’s law

$$ \oint_c {E \cdot ds = - \int_s {\frac{{\partial B}}{{\partial t}}} } \cdot dS $$

All states of matter will be considered: gases, liquids and solids, especially materials like iron with unusual magnetic properties. We first discuss the microscopic nature of magnetism, then define magnetization M, the magnetizing field H and find the boundary conditions for B and H between two media. We continue with an introduction to each of the commonest types of magnetism, dia-, para- and ferromagnetism, and conclude by discussing the production of both permanent and powerful magnetic fields.