Electromagnetism E-Book

I. S. Grant

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: The Manchester Physics Series
• Sprache: Englisch

Seitenzahl: 825

Veröffentlichungsjahr: 2013

Beschreibung

Electromagnetism Electromagnetism, Second Edition is suitable for a first course in electromagnetism, whilst also covering many topics frequently encountered in later courses. The material has been carefully arranged and allows for flexibility in its use for courses of different length and structure. A knowledge of calculus and an elementary knowledge of vectors is assumed, but the mathematical properties of the differential vector operators are described in sufficient detail for an introductory course, and their physical significance in the context of electromagnetism is emphasised. In this Second Edition the authors give a fuller treatment of circuit analysis and include a discussion of the dispersion of electromagnetic waves. Electromagnetism, Second Edition features: * The application of the laws of electromagnetism to practical problems such as the behaviour of antennas, transmission lines and transformers. * Sets of problems at the end of each chapter to help student understanding, with hints and solutions to the problems given at the end of the book. * Optional "starred" sections containing more specialised and advanced material for the more ambitious reader. * An Appendix with a thorough discussion of electromagnetic standards and units. Recommended by many institutions. Electromagnetism. Second Edition has also been adopted by the Open University as the course book for its third level course on electromagnetism. The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw the Physics of Stars Second Edition A. C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett.

Leseprobe

Contents

Flow Diagram

CHAPTER 1 Force and energy in electrostatics

1.1 ELECTRIC CHARGE

1.2 THE ELECTRIC FIELD

1.3 ELECTRIC FIELDS IN MATTER

1.4 GAUSS’ LAW

1.5 ELECTROSTATIC ENERGY

PROBLEMS 1

CHAPTER 2 Dielectrics

2.1 POLARIZATION

2.2 RELATIVE PERMITTIVITY AND ELECTRIC SUSCEPTIBILITY

2.3 MACROSCOPIC FIELDS IN DIELECTRICS

2.4 ENERGY IN THE PRESENCE OF DIELECTRICS

PROBLEMS 2

CHAPTER 3 Electrostatic field calculations

3.1 POISSON’S EQUATION AND LAPLACE’S EQUATION

3.2 BOUNDARIES BETWEEN DIFFERENT REGIONS

3.3 BOUNDARY CONDITIONS AND FIELD PATTERNS

3.4 ELECTROSTATIC LENSES

3.5 NUMERICAL SOLUTIONS OF POISSON’S EQUATION

3.6 SUMMARY OF ELECTROSTATICS

PROBLEMS 3

CHAPTER 4 Steady currents and magnetic fields

4.1 ELECTROMOTIVE FORCE AND CONDUCTION

4.2 THE MAGNETIC FIELD

4.3 THE MAGNETIC DIPOLE

4.4 AMPÈRE’S LAW

4.5 THE DIFFERENTIAL FORM OF AMPÈRE’S LAW

4.6 FORCES AND TORQUES ON COILS

4.7 THE MOTION OF CHARGED PARTICLES IN ELECTRIC AND MAGNETIC FIELDS

PROBLEMS 4

CHAPTER 5 Magnetic materials

5.1 MAGNETIZATION

5.2 THE MACROSCOPIC MAGNETIC FIELD INSIDE MEDIA

5.3 THE FIELD VECTOR H

5.4 MAGNETS

5.5 SUMMARY OF MAGNETOSTATICS

PROBLEMS 5

CHAPTER 6 Electromagnetic induction and magnetic energy

6.1 ELECTROMAGNETIC INDUCTION

6.2 SELF-INDUCTANCE AND MUTUAL INDUCTANCE

6.3 ENERGY AND FORCES IN MAGNETIC FIELDS

6.4 THE MEASUREMENT OF MAGNETIC FIELDS AND SUSCEPTIBILITIES

PROBLEMS 6

CHAPTER 7 Alternating currents and transients

7.1 ALTERNATING CURRENT GENERATORS

7.2 AMPLITUDE, PHASE AND PERIOD

7.3 RESISTANCE, CAPACITANCE AND INDUCTANCE IN A.C. CIRCUITS

7.4 THE PHASOR DIAGRAM AND COMPLEX IMPEDANCE

7.5 POWER IN A.C. CIRCUITS

7.6 RESONANCE

7.7 TRANSIENTS

PROBLEMS 7

CHAPTER 8 Linear circuits

8.1 NETWORKS

8.2 AUDIO-FREQUENCY BRIDGES

8.3 IMPEDANCE AND ADMITTANCE

8.4 FILTERS

8.5 TRANSFORMERS

PROBLEMS 8

CHAPTER 9 Transmission lines

9.1 PROPAGATION OF SIGNALS IN A LOSSLESS TRANSMISSION LINE

9.2 PRACTICAL TYPES OF TRANSMISSION LINE

9.3 REFLECTIONS

9.4 THE INPUT IMPEDANCE OF A MISMATCHED LINE

9.5 LOSSY LINES

PROBLEMS 9

CHAPTER 10 Maxwell’s equations

10.1 THE EQUATION OF CONTINUITY

10.2 DISPLACEMENT CURRENT

10.3 MAXWELL’S EQUATIONS

10.4 ELECTROMAGNETIC RADIATION

10.5 THE MICROSCOPIC FIELD EQUATIONS

PROBLEMS 10

CHAPTER 11 Electromagnetic waves

11.1 ELECTROMAGNETIC WAVES IN FREE SPACE

11.2 PLANE WAVES AND POLARIZATION

11.3 DISPERSION

11.4 ENERGY IN ELECTROMAGNETIC WAVES

11.5 THE ABSORPTION OF PLANE WAVES IN CONDUCTORS AND THE SKIN EFFECT

11.6 THE REFLECTION AND TRANSMISSION OF ELECTROMAGNETIC WAVES

11.7 ELECTROMAGNETIC WAVES AND PHOTONS

PROBLEMS 11

CHAPTER 12 Waveguides

12.1 THE PROPAGATION OF WAVES BETWEEN CONDUCTING PLATES

12.2 RECTANGULAR WAVEGUIDES

12.3 CAVITIES

PROBLEMS 12

CHAPTER 13 The generation of electromagnetic waves

13.1 THE RETARDED POTENTIALS

13.2 THE HERTZIAN DIPOLE

13.3 ANTENNAS

PROBLEMS 13

CHAPTER 14 Electromagnetism and special relativity

14.1 INTRODUCTORY REMARKS

14.2 THE LORENTZ TRANSFORMATION

14.3 CHARGES AND FIELDS AS SEEN BY DIFFERENT OBSERVERS

14.4 FOUR-VECTORS

14.5 MAXWELL’S EQUATIONS IN FOUR-VECTOR FORM

14.6 TRANSFORMATION OF THE FIELDS

14.7 MAGNETISM AS A RELATIVISTIC PHENOMENON

14.8 RETARDED POTENTIALS FROM THE RELATIVISTIC STANDPOINT

PROBLEMS 14

APPENDIX A Units

A.1 ELECTRICAL UNITS AND STANDARDS

A.2 GAUSSIAN UNITS

A.3 CONVERSION BETWEEN SI AND GAUSSIAN UNITS

APPENDIX B Fields and differential operators

B.1 THE OPERATORS DIV, GRAD AND CURL

B.2 FORMULAE IN DIFFERENT COORDINATE SYSTEMS

B.3 IDENTITIES

APPENDIX C The derivation of the Biot-Savart law

Solutions to Problems

Further Reading

Physical Constants

Index

The Manchester Physics Series

General Editors

D. J. SANDIFORD: F. MANDL: A. C. PHILLIPS

Department of Physics and Astronomy, Faculty of Science,University of Manchester

Properties of Matter:

B. H. Flowers and E. Mendoza

Optics:

Second Edition

F. G. Smith and J. H. Thomson

Statistical Physics:

Second Edition

F. Mandl

Electromagnetism:

Second Edition

I. S. Grant and W. R. Phillips

Statistics:

R. J. Barlow

Solid State Physics:

Second Edition

J. R. Hook and H. E. Hall

Quantum Mechanics:

F. Mandl

Particle Physics:

Second Edition

B. R. Martin and G. Shaw

The Physics of Stars:

Second Edition

A. C. Phillips

Computing for Scientists:

R. J. Barlow and A. R. Barnett

Copyright © 1975, 1990 by John Wiley & Sons, Ltd, The Atrium, Southern Gate,Chichester, West Sussex P019 8SQ, EnglandTelephone ([phone]

Email (for orders and customer service enquiries): [email protected] March 2003, January 2004, December 2004, April 2006, February 2007, March 2008,March 2010, March 2011

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Library of Congress Cataloging-in-Publication Data:

Grant, I. S. (Ian S.)Electromagnetism / I. S. Grant, W. R. Phillips.—2nd ed.p. cm.—(The Manchester physics series)ISBN 978 0 471 92711 2—ISBN 978 0 471 92712 9 (pbk.)1. Electromagnetism. I. Phillips, W. R. (William Robert)II. Title. III. Series.QC760.G76 1990537—dc20 90–35818CIP

British Library Cataloguing in Publication Data:

Grant, I. S.Electromagnetism.—2nd ed.1. ElectromagnetismI. Title II. Phillips, W. R. III. Series537

ISBN 978 0 471 92711 2 (hbk)ISBN 978 0 471 92712 9 (pbk)

Editors’ preface to the Manchester Physics Series

The Manchester Physics Series is a series of textbooks at first degree level. It grew out of our experience at the Department of Physics and Astronomy at Manchester University, widely shared elsewhere, that many textbooks contain much more material than can be accommodated in a typical undergraduate course; and that this material is only rarely so arranged as to allow the definition of a shorter self-contained course. In planning these books we have had two objectives. One was to produce short books: so that lecturers should find them attractive for undergraduate courses; so that students should not be frightened off by their encyclopaedic size or their price. To achieve this, we have been very selective in the choice of topics, with the emphasis on the basic physics together with some instructive, stimulating and useful applications. Our second objective was to produce books which allow courses of different lengths and difficulty to be selected, with emphasis on different applications. To achieve such flexibility we have encouraged authors to use flow diagrams showing the logical connections between different chapters and to put some topics in starred sections. These cover more advanced and alternative material which is not required for the understanding of latter parts of each volume.

Although these books were conceived as a series, each of them is self-contained and can be used independently of the others. Several of them are suitable for wider use in other sciences. Each Author’s Preface gives details about the level, prerequisites, etc., of his volume.

The Manchester Physics Series has been very successful with total sales of more than a quarter of a million copies. We are extremely grateful to the many students and colleagues, at Manchester and elsewhere, for helpful criticisms and stimulating comments. Our particular thanks go to the authors for all the work they have done, for the many new ideas they have contributed, and for discussing patiently, and often accepting, the suggestions of the editors.

Finally, we would like to thank our publishers, John Wiley & Sons Ltd, for their enthusiastic and continued commitment to the Manchester Physics Series.

D. J. SandifordF. MandlA. C. PhillipsFebruary 1997

Preface to the Second Edition

The basic content of undergraduate courses in electromagnetism does not change rapidly, and the range of topics covered in the second edition of this book is almost the same as in the first edition. We have made a few additions, for example by giving a fuller treatment of circuit analysis and by discussing the dispersion of electromagnetic waves. Some material which now seems outdated has been removed, and illustrative examples have been modernized.

We have made many small changes in presentation which we hope will make the argument clearer to readers. We gratefully acknowledge the help of all those who have suggested ways of improving the text. We are particularly indebted to Dr. R. Mackintosh and his colleagues at the Open University for a host of detailed suggestions. The adoption of this book as the text for the new ‘third-level’ Open University course on electricity and magnetism led to a careful scrutiny of the first edition by the course team. This has resulted, we believe, in changes which make the book more useful for students. Any errors or obscurities which remain are our responsibility.

ManchesterJanuary, 1990

I. S. GRANTW. R. PHILLIPS

Preface to the First Edition

This book is based on lectures on classical electromagnetism given at Manchester University. The level of difficulty is suitable for honours physics students at a British University or physics majors at an American University. A-level or high school physics and calculus are assumed, and the reader is expected to have some elementary knowledge of vectors. Electromagnetism is often one of the first branches of physics in which students find that they really need to make use of vector calculus. Until one is used to them, vectors are difficult, and we have accordingly treated them rather cautiously to begin with. Brief descriptions of the properties of the differential vector operators are given at their first appearance. These descriptions are not intended to be a substitute for a proper mathematical text, but to remind the reader what div, grad and curl are all about, and to set them in the context of electromagnetism. The distinction between macroscopic and microscopic electric and magnetic fields is fully discussed at an early stage in the book. It is our experience that students do get confused about the fields E and D, or B and H. We think that the best way to help them overcome their difficulties is to give a proper explanation of the origin of these fields in terms of microscopic charge distributions or circulating currents.

The logical arrangement of the chapters is summarized in a flow diagram on the inside of the front cover. Provided that one is prepared to accept Kirchhoff’s rules and the expressions for the e.m.f.s across components before discussing the laws on which they are based, the A.C. theory in Chapters 7 and 8 does not require any prior knowledge of the earlier chapters. Chapters 7 and 8 can therefore be used at the beginning of a course on electromagnetism. Sections of the book which are starred may be omitted at a first reading, since they do not contain material needed in order to understand later chapters.

We should like to thank the many colleagues and students who have helped with suggestions and criticisms during the preparation of this book; any errors which remain are our own responsibility. It is also a pleasure to thank Mrs Margaret King and Miss Elizabeth Rich for their rapid and accurate typing of the manuscript.

May, 1974Manchester, England.

I. S. GRANTW. R. PHILLIPS

FLOW DIAGRAM

This flow diagram shows the main logical connections between chapters. Any specific chapter can be understood if all the chapters above it which are connected by a line have been covered. Chapters 7 and 8 on A. C. Theory may be tackled before the earlier chapters provided that Kirchhoff’s rules are assumed. Strictly speaking Kirchhoff’s rules depend on earlier material, this is indicated by the dotted line joining Chapters 6 and 7.

CHAPTER 1

Force and energy in electrostatics

The only laws of force which are known with great precision are the two laws describing the gravitational forces between different masses and the electrical forces between different charges. When two masses or two charges are stationary, then in either case the force between them is inversely proportional to the square of their separation. These inverse square laws were discovered long ago: Newton’s law of gravitation was proposed in 1665, and Coulomb’s law of electrostatics in 1785. This chapter is concerned with the application of Coulomb’s law to systems containing any number of stationary charges. Before studying this topic in detail, it is worth pausing for a moment to consider the consequences of the law in the whole of physics.

In order to make full use of our knowledge of a law of force, we must have a theory of mechanics, that is to say, a theory which describes the behaviour of an object under the action of a known force. Large objects which are moving at speeds small compared to the speed of light obey very closely the laws of classical Newtonian mechanics. For example, these laws and the gravitational force law together lead to accurate predictions of planetary motion. But classical mechanics does not apply at all to observations made on particles of atomic scale or on very fast-moving objects. Their behaviour can only be understood in terms of the ideas of quantum theory and of the special theory of relativity. These two theories have changed the framework of discussion in physics, and have made possible the spectacular advances of the twentieth century.

It is remarkable that while mechanics has undergone drastic amendment, Coulomb’s law has stood unchanged. Although the behaviour of atoms does not fit the framework of the old mechanics, when the Coulomb force is used with the theories of relativity and quantum mechanics, atomic interactions are explained with great precision in every instance when an accurate comparison has been made between experiment and theory. In principle, atomic physics and solid state physics, and for that matter the whole of chemistry, can be derived from Coulomb’s law. It is not feasible to derive everything in this way, but it should be borne in mind that atoms make up the world around us, and that its rich variety and complexity are governed by electrical forces.

1.1 ELECTRIC CHARGE

Most of this book applies electromagnetism to large-scale objects, where the atomic origin of the electrical forces is not immediately apparent. However, to emphasize this origin, we shall begin by consideration of atomic systems. The simplest atom of all is the hydrogen atom, which consists of a single proton with a single electron moving around it. The hydrogen atom is stable because the proton and the electron attract one another. In contrast, two electrons repel one another, and tend to fly apart, and similarly the force between two protons is repulsive*. These phenomena are described by saying that there are two different kinds of electric charge, and that like charges repel one another, whereas unlike charges are attracted together. The charge carried by the proton is called positive, and the charge carried by the electron negative.

The magnitude and direction of the force between two stationary particles, each carrying electric charge, is given by Coulomb’s law. The law summarizes four facts:

(i) Like charges repel, unlike charges attract.

(ii) The force acts along the line joining the two particles.

(iii) The force is proportional to the magnitude of each charge.

(iv) The force is inversely proportional to the square of the distance between the particles.

The mathematical statement of Coulomb’s law is:

(1.1)

The vector F21 in Figure 1.1 represents the force on particle 1 (carrying a charge q1) exerted by the particle 2 (carrying charge q2). The line from q2 to q1 is represented by the vector r21, of length r21: since the unit vector along the direction r21 can be written r21/r21, Equation (1.1) is an inverse square law of force, although appears in the denominator. Notice that the equation automatically accounts for the attractive or repulsive character of the force if q1 and q2 include the sign of the charge. When the charges q1 and q2 are both positive or both negative, the force on q1 is along r21, i.e. it is repulsive. On the other hand, when one charge is positive and the other negative, the force is in the direction opposite to r21, i.e. it is attractive.

Figure 1.1. The force between two charges.

To complete the statement of the force law, we must decide what units to use, and hence determine the constant of proportionality in Equation (1.1). We shall use SI (Systeme International) units, which are favoured by most physicists and engineers applying electromagnetism to problems involving large-scale objects. A different system of units, called the Gaussian system, is frequently used in atomic physics and solid state physics, and it is an unfortunate necessity for students to become reasonably familiar with both systems. (The two systems of units are discussed in Appendix A.) In SI units, Coulomb’s law is written as

(1.2)

where

q1 and q2 are measured in coulombs,

r21 is measured in metres

and

F21 is measured in newtons.

The magnitude of the unit of charge, which is called the coulomb, is actually defined in terms of magnetic forces, and we shall leave discussion of the definition until Chapter 4. The factor 4π in the constant of proportionality in Coulomb’s law is introduced in order to simplify some important equations which we shall meet later. The constant ε0, which is called the permittivity of free space, has the value

Figure 1.2. How electrostatic forces are added when there are more than two charges.

The value of ε0 is not determined experimentally, but has been defined in a way which makes the SI system of units self-consistent: the relation between electrical units and other units is discussed in Appendix A.