- Title Pages
- Preface
- Contents
- 1 Some essential mathematics
- 2 Static electric fields in vacuum
- 3 The electrostatics of conductors
- 4 Static magnetic fields in vacuum
- 5 Quasi-static electric and magnetic fields in vacuum
- 6 Ohm’s law and electric circuits
- 7 Electromagnetic fields and waves in vacuum
- 8 The electromagnetic potentials
- 9 Static electric and magnetic fields in matter
- 10 Some applications of Maxwell’s equations in matter
- 11 Electromagnetic radiation
- 12 Electromagnetism and special relativity
- Appendix A Vectors and Cartesian tensors
- Appendix A Vectors and Cartesian tensors
- Appendix B Cartesian coordinates
- Appendix C Spherical polar coordinates
- Appendix D Cylindrical polar coordinates
- Appendix E The Dirac delta function
- Appendix E The Dirac delta function
- Appendix F Legendre polynomials
- Appendix F Legendre polynomials
- Appendix G Bessel functions
- Appendix G Bessel functions
- Appendix H Parametric representation of a surface
- Appendix H Parametric representation of a surface
- Appendix I The Cauchy–Riemann equations
- Appendix I The Cauchy–Riemann equations
- Appendix J Questions involving computational work
- Glossary of symbols
- Index

# Quasi-static electric and magnetic fields in vacuum

# Quasi-static electric and magnetic fields in vacuum

- Chapter:
- (p.249) 5 Quasi-static electric and magnetic fields in vacuum
- Source:
- Solved Problems in Classical Electromagnetism
- Author(s):
### J. Pierrus

- Publisher:
- Oxford University Press

In this chapter, the transition from time-independent to time-dependent source densities and fields is made. It is here that Faraday’s famous nineteenth-century experiments on electromagnetic induction are first encountered. This important phenomenon—whereby a changing magnetic field produces an induced electric field (whose curl is now no longer zero)—forms the basis of most of the questions and solutions which follow. Some new and interesting examples—not usually found in other textbooks—are introduced. These are treated both from an analytical and numerical point of view. Also considered here is the standard yet important topic (at least from a practical standpoint) of mutual and self-inductance. Several questions deal with this concept.

*Keywords:*
quasi-static currents quasi-static fields, electromotive force induced emf, electromagnetic induction Faraday’s law, Lenz’s law magnetic flux, self-inductance mutual inductance

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- Title Pages
- Preface
- Contents
- 1 Some essential mathematics
- 2 Static electric fields in vacuum
- 3 The electrostatics of conductors
- 4 Static magnetic fields in vacuum
- 5 Quasi-static electric and magnetic fields in vacuum
- 6 Ohm’s law and electric circuits
- 7 Electromagnetic fields and waves in vacuum
- 8 The electromagnetic potentials
- 9 Static electric and magnetic fields in matter
- 10 Some applications of Maxwell’s equations in matter
- 11 Electromagnetic radiation
- 12 Electromagnetism and special relativity
- Appendix A Vectors and Cartesian tensors
- Appendix A Vectors and Cartesian tensors
- Appendix B Cartesian coordinates
- Appendix C Spherical polar coordinates
- Appendix D Cylindrical polar coordinates
- Appendix E The Dirac delta function
- Appendix E The Dirac delta function
- Appendix F Legendre polynomials
- Appendix F Legendre polynomials
- Appendix G Bessel functions
- Appendix G Bessel functions
- Appendix H Parametric representation of a surface
- Appendix H Parametric representation of a surface
- Appendix I The Cauchy–Riemann equations
- Appendix I The Cauchy–Riemann equations
- Appendix J Questions involving computational work
- Glossary of symbols
- Index