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ELECTROMAGNETIC FIELD THEORY
Bo Thidé
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Also available
ELECTROMAGNETIC FIELD THEORY
EXERCISES
by
Tobia Carozzi, Anders Eriksson, Bengt Lundborg,
Bo Thidé and Mattias Waldenvik
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Electromagnetic
Field Theory
Bo Thidé
Swedish Institute of Space Physics
and
Department of Astronomy and Space Physics
Uppsala University, Sweden
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This book was typeset in LATEX 2ε
on an HP9000/700 series workstation
and printed on an HP LaserJet 5000GN printer.
Copyright ©1997, 1998, 1999, 2000 and 2001 by
Bo Thidé
Uppsala, Sweden
All rights reserved.
Electromagnetic Field Theory
ISBN X-XXX-XXXXX-X
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Contents
Preface
xi
1 Classical Electrodynamics
1
1.1 Electrostatics
. . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1.1 Coulomb’s law . . . . . . . . . . . . . . . . . . . . .
2
1.1.2
The electrostatic field . . . . . . . . . . . . . . . . . .
2
1.2 Magnetostatics
. . . . . . . . . . . . . . . . . . . . . . . . .
5
1.2.1 Ampère’s law . . . . . . . . . . . . . . . . . . . . . .
5
1.2.2
The magnetostatic field . . . . . . . . . . . . . . . . .
6
1.3 Electrodynamics
. . . . . . . . . . . . . . . . . . . . . . . .
8
1.3.1
Equation of continuity for electric charge . . . . . . .
9
1.3.2 Maxwell’s displacement current . . . . . . . . . . . .
9
1.3.3
Electromotive force . . . . . . . . . . . . . . . . . . .
10
1.3.4
Faraday’s law of induction . . . . . . . . . . . . . . .
11
1.3.5 Maxwell’s microscopic equations
. . . . . . . . . . .
14
1.3.6 Maxwell’s macroscopic equations . . . . . . . . . . .
14
1.4 Electromagnetic Duality
. . . . . . . . . . . . . . . . . . . .
15
Example 1.1 Faraday’s law as a consequence of conserva-
tion of magnetic charge
. . . . . . . . . . . .
16
Example 1.2 Duality of the electromagnetodynamic equations 18
Example 1.3 Dirac’s symmetrised Maxwell equations for a
fixed mixing angle . . . . . . . . . . . . . . .
18
Example 1.4 The complex field six-vector
. . . .