Basic Books in Science Book 10 More Physics: electric charges and fields - electromagnetism Roy McWeeny BASIC BOOKS IN SCIENCE – a Series of books that start at the beginning Book 10 More Physics: electric charges and fields – electromagnetism Roy McWeeny Professore Emerito di Chimica Teorica, Universit`adi Pisa, Pisa (Italy) The Series is maintained, with regular updating and improvement, at http://www.learndev.org/ScienceWorkBooks.html and the books may be downloaded entirely free of charge This book is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License. (Last updated 24 November 2011) BASIC BOOKS IN SCIENCE Acknowledgements In a world increasingly driven by information technology no educational experiment can hope to make a significant impact without effective bridges to the ‘user community’ – the students and their teachers. In the case of “Basic Books in Science” (for brevity, “the Series”), these bridges have been provided as a result of the enthusiasm and good will of Dr. David Peat (The Pari Center for New Learning), who first offered to host the Series on his website, and of Dr. Jan Visser (The Learning Development Institute), who set up a parallel channel for further development of the project. The credit for setting up and maintaining the bridgeheads, and for promoting the project in general, must go entirely to them. Education is a global enterprise with no boundaries and, as such, is sure to meet linguistic difficulties: these will be reduced by providing translations into some of the world’s most widely used languages. Dr. Angel S. Sanz (Madrid) is preparing Spanish versions of the books and his initiative is most warmly appreciated. We appreciate the interest shown by universities in Sub-Saharan Africa (e.g. University of the Western Cape and Kenyatta University), where trainee teachers are making use of the Series; and that shown by the Illinois Mathematics and Science Academy (IMSA) where material from the Series is being used in teaching groups of refugee children from many parts of the world. All who have contributed to the Series in any way are warmly thanked: they have given freely of their time and energy ‘for the love of Science’. Pisa, 30 August 2009 Roy McWeeny (Series Editor) i BASIC BOOKS IN SCIENCE About this book This book, like the others in the Series1, is written in simple English – the language most widely used in science and technology. It builds on the foundations laid in Books 1-4, which covered many parts of Mathematics and Physics, and on some parts of Book 5, which refers to the structure and properties of matter in general. The present book takes up the story from Book 4, which introduced the science of Me- chanics and showed how it could account for the motion of objects ranging from particles to planets. Things move under the action of applied forces (like ‘pushes’ and ‘pulls’). But some forces, like the one due to ‘gravity’, arise from the attraction between massive objects. You can feel the force due to gravity, which makes a body fall to the ground even when nothing is touching it, but you can’t see it. We say there is a field of force at any point in space and it is proportional to the mass m of the body on which it acts. Besides having a mass m, a body may carry an electric charge q; and another kind of force may act on the body when it is placed in an electric field. If you double the quantity of charge q the force is also doubled; so the electric field felt by a charge is proportional to the charge. The electric field is so similar to the gravitational field that you’ll be able to take over from Book 4 many things you know about already. In Book 5 you learnt that electric charge is carried by elementary particles such as the electron and the proton; and that their charges are of two kinds, negative and positive respectively. So you’re already well on the way to understanding electricity. Much of this book is about fields. Electricity plays an important part in everyday life: think of electric lights, power stations where electricity is generated in dynamos, and electric motors, which use electricity to drive the machines in our factories; think of radios and the telephone, through which we can communicate with people all over the world – and even beyond, in space! When you speak into the telephone, the sound of your voice sets up vibrations and these are used to make electrons move along wires; the currents produced can be used to send radio signals through space; and these can be picked up by a radio receiver millions of miles away and converted back into sounds! By the end of this book you’ll be ready to start understanding how all this is possible. 1The aims of the Series are described elsewhere, e.g. in Book 1. i Looking ahead – In Book 4, when you started on Physics, we said “Physics is a big subject and you’ll need more than one book”. Here is the next one! Book 4 was mainly about particles, the ways they move when forces act on them, and how the same ‘laws of motion’ still hold good for objects built up from particles – however big. In Book 10 we’ll be more interested in the fields that govern the interactions between particles. The only field we knew about in Book 4 was that ‘due to gravity’, which acts on the mass of a particle and makes it fall, but now we’ll be thinking about the fields which act on particles that carry an electric charge. Chapter 1 explains how two kinds of electric charge, positive and negative, can • be defined in terms of the forces between particles that carry charge. The force law 2 (F = q1q2/r ) is so similar to that for masses that you can still use most of what you already know, provided you put in the + or signs and take a positive force as a repulsion, tending to increase the separation (−r) of the particles, and a negative one as an attraction, tending to decrease the separation. It’s as simple as that! And it all links up with Book 5, where you first met the electron and the proton – the basic negative and positive charges that are found in Nature. In this chapter the charges are at rest: we’re talking about electrostatics. You’ll learn about machines for making ‘static’ electricity and about how it can be stored in condensers and used to make sparks. And you’ll learn how all of electrostatics can be understood in terms of a single basic principle – Gauss’s law. In Chapter 2 you’ll be thinking about charges in motion, which produce electric • curents. The currents are carried through conductors – materials which allow charges, usually electrons, to flow through them. Other materials, which don’t allow charge to pass, are called insulators; and in between there are resistances, which allow some charge to pass but are not very good at it! Long thin copper wires are good conductors and are used in all electrical gad- gets. You’ll study some simple electric circuits, in which ‘circuit elements’ like condensers and resistances are connected by wires so that current can flow between them. Finally, we’ll make a connection with Chemistry (Book 5). Batteries make a plentiful supply of electricity from certain chemical reactions which depend on the transfer of electrons between the atoms taking part. Chapter 3 again starts from discoveries made over 3000 years ago! – that certain • heavy stones could attract small pieces of iron, and that the iron itself could be given the same property by stroking the stone with it. The property is called magnetism and a piece of iron with this property is a magnet. When a magnet is free to move, one end of it always points the same way – towards the ‘North pole’ of the axis around which the Earth turns; so magnets were first used in steering ships at sea. ii From such simple beginnings the whole theory of the magnetic field was built up over the centuries. The magnetic field (B), like the electric field (E), is a vector; but unlike the electric field it acts only on a moving charge, pushing it away from the direction of motion. As a moving charge is an electric current, magnetism and electricity are closely related: you’ll discover how an electric current can produce a magnetic field; and how a magnetic field can exert a force on a current-carrying wire. You’re now ready to put all these ideas together and look at Maxwell’s equa- • tions – one of those great breakthroughs that happen perhaps only once in a hun- dred years. In Chapter 4 you’ll find how the fields E and B, and the electric charges and currents that produce them, can all be related through just four equations, set up by Maxwell about 130 years ago. This is difficult stuff, but if you’ve got so far you’re ready to make the last step into electromagnetism. You’re going to need many of the ideas you’ve picked up about fields, that vary from point to point in space (and in time!), and the differential equations that they obey. You don’t have to solve them at this point; it’s enough just to understand what they mean. Then, in the rest of the book, you’ll find they tell you how to build electric power stations, electric motors, radio transmitters, and many other things that can be found ready-made nowadays – thanks to the work of all the other people who’ve made the rest of the journey from the principles to the practice.