Book contents
- Frontmatter
- Contents
- Preface
- Units, constants, and formulae
- Glossary of symbols
- Mathematical prologue
- 1 Charges and currents
- 2 Electrostatics
- 3 Electric dipoles
- 4 Static magnetic fields
- 5 Time-dependent fields: Faraday's law and Maxwell's equations
- 6 Electromagnetic waves in a vacuum
- 7 The electrostatics of conductors
- 8 Steady currents in conductors
- 9 Magnetostatics
- 10 Insulators
- 11 Magnetic properties of materials
- 12 Time-dependent fields in insulators
- 13 Time-dependent fields in metals and plasmas
- 14 Superconductors
- 15 Surface electricity
- 16 Radiation
- 17 Applications of radiation theory
- 18 Transmission lines, wave guides, and optical fibres
- 19 The electromagnetic field and special relativity
- Appendix A Proof of Gauss's theorem
- Appendix B The uniqueness theorem
- Appendix C Fields at the interface between materials
- Appendix D Gaussian c.g.s. units
- Further reading
- Answers to problems
- Index
Mathematical prologue
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Units, constants, and formulae
- Glossary of symbols
- Mathematical prologue
- 1 Charges and currents
- 2 Electrostatics
- 3 Electric dipoles
- 4 Static magnetic fields
- 5 Time-dependent fields: Faraday's law and Maxwell's equations
- 6 Electromagnetic waves in a vacuum
- 7 The electrostatics of conductors
- 8 Steady currents in conductors
- 9 Magnetostatics
- 10 Insulators
- 11 Magnetic properties of materials
- 12 Time-dependent fields in insulators
- 13 Time-dependent fields in metals and plasmas
- 14 Superconductors
- 15 Surface electricity
- 16 Radiation
- 17 Applications of radiation theory
- 18 Transmission lines, wave guides, and optical fibres
- 19 The electromagnetic field and special relativity
- Appendix A Proof of Gauss's theorem
- Appendix B The uniqueness theorem
- Appendix C Fields at the interface between materials
- Appendix D Gaussian c.g.s. units
- Further reading
- Answers to problems
- Index
Summary
In the chapters which follow, we assume that you are already familiar with the basic mathematics of scalar and vector fields in three dimensions, the properties of the ∇ operator, the integral theorems which hold for these fields, and so forth. In this prologue, we remind you of some basic definitions, and outline (without proof) those mathematical theorems of which we shall make extensive use. We also establish our notation and sign conventions.
We envisage space filled with electromagnetic fields, and at any instant we describe these fields mathematically using functions which may be scalar functions of position (like the potential Φ(r)) or vector functions of position (like the electric field E(r)). We shall assume that the functions which appear in the theory are continuous, and have derivatives existing as required, except perhaps at special points or on special surfaces. Singularities in the mathematics will usually correspond to singularities in the physics. For example, the electrostatic potential of a point charge Q at the origin is Q/4πε0r, and this function satisfies our conditions except at r = 0, which is the position of the point charge.
We sometimes focus on these fields in limited regions of space, say inside a volume V enclosed by a surface S, or over a surface S(Γ) bounded by a curve Γ.
Volume integrals
Volume integrals will often arise naturally in the theory, for example when we calculate the total charge or total energy in some volume V of space.
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- Information
- Electricity and Magnetism , pp. 1 - 6Publisher: Cambridge University PressPrint publication year: 1991