Electromagnetic
Field Theory
BO THIDÉ
ϒ
UPSILON BOOKS
ELECTROMAGNETIC FIELD THEORY
Electromagnetic
Field Theory
BO THIDÉ
Swedish Institute of Space Physics
Uppsala, Sweden
and
Department of Astronomy and Space Physics
Uppsala University, Sweden
and
LOIS Space Centre
School of Mathematics and Systems Engineering
Växjö University, Sweden
ϒ
UPSILON BOOKS · UPPSALA · SWEDEN
Also available
ELECTROMAGNETIC FIELD THEORY
EXERCISES
by
Tobia Carozzi, Anders Eriksson, Bengt Lundborg,
Bo Thidé and Mattias Waldenvik
Freely downloadable from
www.plasma.uu.se/CED
This book was typeset in LATEX 2ε (based on TEX 3.141592 and Web2C 7.4.4) on an HP Visu-
alize 9000⁄3600 workstation running HP-UX 11.11.
Copyright©1997–2008 by
Bo Thidé
Uppsala, Sweden
All rights reserved.
Electromagnetic Field Theory
ISBN X-XXX-XXXXX-X
To the memory of professor
LEV MIKHAILOVICH ERUKHIMOV (1936–1997)
dear friend, great physicist, poet
and a truly remarkable man.
Downloaded from http://www.plasma.uu.se/CED/Book
Version released 16th February 2009 at 18:18.
CONTENTS
Contents
ix
List of Figures
xiii
Preface
xv
1 Classical Electrodynamics
1
1.1 Electrostatics
2
1.1.1 Coulomb’s law
2
1.1.2 The electrostatic field
3
1.2 Magnetostatics
6
1.2.1 Ampère’s law
6
1.2.2 The magnetostatic field
7
1.3 Electrodynamics
9
1.3.1 Equation of continuity for electric charge
10
1.3.2 Maxwell’s displacement current
10
1.3.3 Electromotive force
11
1.3.4
Faraday’s law of induction
12
1.3.5 Maxwell’s microscopic equations
15
1.3.6 Maxwell’s macroscopic equations
15
1.4 Electromagnetic duality
16
1.5 Bibliography
18
1.6 Examples
20
2 Electromagnetic Waves
25
2.1 The wave equations
26
2.1.1 The wave equation for E
26
2.1.2 The wave equation for B
27
2.1.3 The time-independent wave equation for E
27
ix
Contents
2.2 Plane waves
30
2.2.1 Telegrapher’s equation
31
2.2.2 Waves in conductive media
32
2.3 Observables and averages
33
2.4 Bibliography
35
2.5 Example
36
3 Electromagnetic Potentials
39
3.1 The electrostatic scalar potential
39
3.2 The magnetostatic vector potential
40
3.3