Introduction

Electromagnetism forms the basis of many technologies in our everyday lives. For example, magnetic resonance imaging enables precise diagnoses and therapies in medicine. Generators and transformers ensure the efficient generation, transmission and distribution of electrical energy. In computer technology, magnetic storage devices such as hard drives are indispensable for data processing and storage. However, the limits of their application areas have not yet been reached. Future technological developments such as quantum computers, wireless power supply and magnetic levitation will push these limits even further. A sound understanding of magnetic quantities is crucial for the further development and optimisation of existing and future technologies.

This chapter provides an introduction to electromagnetic effects and the associated magnetic quantities. First, the magnetic field is described, followed by an explanation of relevant quantities for the magnetic circuit, such as flux, magnetic flux and magnetic resistance. It then explains how the Lorentz force, induction and inductance work, followed by a calculation of the energy content in the magnetic field. The chapter concludes with a digression on the skin effect and Hall effect.

1 Magnetism

Magnetism is a physical phenomenon that manifests itself in the form of interacting forces between magnetised or magnetisable solids and moving electric charges. These forces are represented by a magnetic field. The most common forms of magnetism are electromagnetism and the magnetism of solids. Ferromagnetism is the best known and most important type of magnetised solid and describes the magnetic behaviour of some metallic bodies, known as ferromagnetic materials. As can be seen in Figure 1, a ferromagnetic material such as iron, cobalt or nickel consists of many small elementary magnets in so-called Weiss domains, which are separated from each other by Bloch walls. In a non-magnetised body, these Weiss domains are arranged randomly and are therefore not aligned. The body is not (or only slightly) magnetised on the outside, as the magnetisation directions of the individual domains largely cancel each other out. A strong external magnetic field (the required strength depends on temperature and material) can align the unordered elementary magnets in parallel. The uniform alignment of the Weiss domains causes the material itself to become magnetic.

2 Magnetic field

The orderly alignment of the Weiss domains creates a magnetic field that can be measured outside the body. Magnetic fields are vector fields that exert a force on magnetic materials in space. The strength of the magnetic field is described by the magnitude of the magnetic field strength \( \vec {H}\). This vector quantity assigns a corresponding direction with a specific magnetic strength to each point in space on which the magnetic field acts. Magnetic fields and the associated magnetic field strength are represented by field lines. Magnetic field lines have characteristic properties:

• Magnetic field lines are always closed (source-free).
• Outside the magnet, they run from the north pole to the south pole.
• They always exit or enter the magnetic surface perpendicularly.