Introduction to Electromagnetism

From Coulomb to Maxwell

Martin J N Sibley

• Publisher: CRC Press
• Year: 2021
• ISBN:
  9781000352399
• Edition: 2
• Topic: Technik & Maschinenbau
• Subtopic: Elektrotechnik & Telekommunikation

This edition aims to expand on the first edition and take the reader through to the wave equation on coaxial cable and free-space by using Maxwell's equations. The new chapters include time varying signals and fundamentals of Maxwell's equations. This book will introduce and discuss electromagnetic fields in an accessible manner. The author explains electroconductive fields and develops ideas relating to signal propagation and develops Maxwell's equations and applies them to propagation in a planar optical waveguide. The first of the new chapters introduces the idea of a travelling wave by considering the variation of voltage along a coaxial line. This concept will be used in the second new chapter which solves Maxwell's equations in free-space and then applies them to a planar optical waveguide in the third new chapter. As this is an area that most students find difficult, it links back to the earlier chapters to aid understanding. This book is intended for first- and second-year electrical and electronic undergraduates and can also be used for undergraduates in mechanical engineering, computing and physics. The book includes examples and homework problems.

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• Introduces and examines electrostatic fields in an accessible manner

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• Explains electroconductive fields

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• Develops ideas relating to signal propagation

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• Examines Maxwell's equations and relates them to propagation in a planar optical waveguide

Martin Sibley recently retired after 33 years of teaching at the University of Huddersfield. He has a PhD from Huddersfield Polytechnic in Preamplifier Design for Optical Receivers. He started his career in academia in 1986 having spent 3 years as a postgraduate student and then 2 years as a British Telecom-funded research fellow. His research work had a strong bias to the practical implementation of research, and he taught electromagnetism and communications at all levels since 1986. Dr. Sibley finished his academic career as a Reader in Communications, School of Computing and Engineering, University of Huddersfield. He has authored five books and published over 80 research papers.

1 Introduction

This book is concerned with the study of electrostatic, electromagnetic and electroconductive fields – sometimes referred to as field theory or, more simply, electromagnetism. A knowledge of this subject can help us to explain why a circuit refuses to behave as designed, why components sometimes break down and what happens in high-frequency circuits. In studying this area, life is made a lot easier if we can think in three dimensions. This is usually a case of drawing adequate diagrams and practicing.

Readers used to circuit theory may wonder why they should study such a discipline. Well, field theory is the study of some of the fundamental laws of Nature. Indeed, electromagnetism was the first theory to unite the sciences of electricity and magnetism. The search is now on to find a Grand Unified Theory that unites all the basic forces of Nature, and that should be of interest to us.

As we progress with our studies, we will meet some names that have become famous in the field of electrical engineering. Some of these people have had units named after them, and so will be more familiar than others. Before we begin our studies in earnest, let us take a moment to pay our respect to some of the researchers who contributed to electrical engineering as we know it today.

1.1 Historical Background

Electromagnetic field theory is really the result of the union of three distinct sciences. The oldest of these is electrostatics, which was first studied by the Greeks. They discovered that if they rubbed certain substances, they were able to attract lighter bodies to them. One of these substances was amber, whose Greek name is electron – this is where we get the name ‘electricity’. It was in 1785 that French physicist, Charles Augustin de Coulomb (1736–1806), showed that electrically charged materials sometimes attract and sometimes repel each other. This was the first indication that there were two types of charge – positive and negative.

In the late 1700s, two Italians were working on the new science of current electricity. One, Luigi Galvani (1737–1798), was a physiologist and physician who thought that animal tissues generate electricity. Although he was later proved wrong, his experiments stimulated Count Alessandro Volta (1745–1827) to invent the first electric battery in 1800. Most of the early experiments in current electricity were performed on frog’s legs – this was a result of Galvani’s work.

Later, a favourite party trick was to get a group of people to hold hands and then connect them to a voltaic cell (a battery). The cell produced quite a large voltage, which then caused current to flow through the guests. This made them jump uncontrollably! It wasn’t until 1833 that the British experimenter Michael Faraday (1791–1867) showed that the current electricity of Volta and Galvani was the same as the electrostatic electricity of Coulomb. Rather than linking these two phenomena, it was shown that the current and electrostatic electricity were one and the same thing. (Faraday’s contribution is all the more remarkable when it is realized that his theories were formulated by direct experimentation and not by manipulating mathematics!)

Although the ancient Greeks also knew about magnetism in the form of lodestone, the Chinese invented the magnetic compass, and in 1600, William Gilbert of Gloucester laid down some fundamentals. However, it was not until 1785 that Coulomb formulated his law relating the strengths of two magnetic poles to the force between them. Magnetism may have been laid to rest here if it wasn’t for the Danish physicist Hans Christian Oersted (1777–1851). It was Oersted who demonstrated to a group of students that a current-carrying wire produces a magnetic field. This was the first sign that electricity and magnetism could be interlinked. This link was strengthened in 1831 by the work of Faraday who showed that a changing magnetic field could induce a current into a wire. It was a French physicist André Marie Ampère who first formulated the idea that the field of a permanent magnet could be due to currents in the material. (We now accept that electrons orbiting the nucleus constitute a current, and this produces the magnetic field.)

We owe our present view of ‘field theory’ to Faraday who performed many experiments on electricity and magnetism. Although Faraday preferred to work without mathematics, he did introduce the idea of fields in free-space. This greatly influenced later workers, and it was in the mid-1800s that the British physicist James Clerk Maxwell (1831–1879) formalized Faraday’s results using mathematics. Among other things, Maxwell was able to predict the existence of electromagnetic waves. This work inspired others in the field, such as Oliver Heaviside (1850–1925) who worked on the first transatlantic telegraph cable as well as predicting the existence of the ionosphere.

The rest, as they say, is history. Due to the work of the German physicist Heinrich Rudolf Hertz (1857–1894) and the Italian engineer Guglielmo Marconi (1874–1937), we are now able to communicate over vast distances. We can also use electrical machinery to make our lives more comfortable. In fact, we owe our current way of life to the hard work of a number of researchers who continually questioned and experimented, carefully recording their results and observations.

1.2 Atomic Structure

When we learn to drive a car, we do not necessarily need to know exactly how the car works. However, if we do understand how the engine works and why the wheels turn, it can help us to be better drivers. A similar situation occurs with electricity and magnetism – when we use electricity and magnetism, we seldom have to worry about exactly how the effects are produced. However, it can make us better engineers if we have an adequate model of what electricity and magnetism are. This is where we have to study the structure of the atom.

Figure 1.1 shows the basic structure of the simplest atom, the hydrogen atom. This atom has one electron that orbits the nucleus containing a single proton. The charge on the electron is equal and opposite to the charge on the proton and has the value

FIGURE 1.1 Basic structure of a hydrogen atom.

$e=-1.6\times {10}^{-19}\text{C}(1.1)$

with units of coulomb, symbol C.

More complex materials, such as amber for instance, have many atoms held in a crystalline structure. If we rub amber, the friction removes electrons, so leaving the material positively charged. This is the basis of electrostatic electricity. In some materials, the electrons are very tightly bound to the nucleus and considerable energy must be expended to remove an electron. These are insulators...