Di Barba / Savini / Wiak Field Models in Electricity and Magnetism

1. Auflage 2008
ISBN: 978-1-4020-6843-0
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 174 Seiten, eBook

The subject of computation in electricity and magnetism has so advanced in the past 40 years, since the advent of digital computers and thanks to the development of numerical methods, that today it urges and deserves adequate collocation also in curricula for electrical engineering. However, the time allotted to the subject in generalisnotverylargeinundergraduatestudies,wheremoreemphasisisstillusually attributed to circuits and systems than to ?elds. Moreover, ?eld models are generally not very popular among students, who are by far more familiar with circuit models. Even if one considers the quasi-static case, however, not only is electromagnetism fundamentalforpeopledealingwithelectricandmagneticdevices,butitprovidesthe basisfor,e.g.semiconductordevicedesign,bioengineeringapplicationsandsoforth. In the authors’opinion, therefore, time has come to present ?eld models in el- tricity and magnetism, in the frame of an introductory textbook to be used by senior undergraduateorgraduatestudentsintheareaofelectricalandcomputerengineering. Elementary electromagnetism, basic vector analysis and fundamentals of numerical analysis are assumed to be known subjects. Havingthisinmind,theauthorshavecollectedtheexperiencetheyhaveaccu- lated in teaching electromagnetic theory at various levels and in different countries; theyintendtoofferabookonappliedelectricityandmagnetism,describingthepr- lemsofcalculatingelectromagnetic?eldsandtheintegralparametersconnectedwith them in suf?ciently clear and short form. The aim is that of writing a textbook containing the necessary background, i.e. laws explaining electromagnetic phenomena, mathematical operators and equations as well as methods for electromagnetic ?eld calculation. The latter include both analytical and numericalmethods applied to the analysis as well as to the synthesis of electromagnetic devices.

Zielgruppe

Research

Autoren/Hrsg.

Di Barba, Paolo

Savini, Antonio

Wiak, Slawomir

Inhaltsverzeichnis

1 Introduction2 Vector fields2.1 Basic operators and equations2.1.1 Vector fields and operators2.1.2 Definition of a vector field2.1.3 Decomposition of a field2.1.4 Scalar and vector potentials2.1.5 Green’s theorem2.1.6 Green’s formula2.2 Electrostatic field2.2.1 Maxwell’s equations for electrostatics2.2.2 Electrostatic potentials2.2.3 Electrostatic energy2.2.4 Field of a charged plane (rectangular domain)2.2.5 Field of a point charge in R3 (spherical domain)2.2.6 Field of a dipole of moment d q p = in R32.2.7 Field of a line charge in R3 (cylindrical domain)2.2.8 Field of a surface charge on a sphere of radius a with density s2.2.9 Energy and forces in the electrostatic field2.2.10 Force between the plates of a capacitor2.2.11 Force at the interface between two dielectric materials2.3 Magnetostatic field2.3.1 Maxwell’s equations for magnetostatics2.3.2 Magnetostatic potentials2.3.3 Magnetostatic energy2.3.4 Field of a line current in R32.3.5 Energy and forces in the magnetostatic field2.3.6 Force on an electromagnet2.3.7 Test problems2.4 Steady conduction field2.4.1 Maxwell’s equations for conduction field2.4.2 Potentials2.4.3 Power loss2.4.4 Analytic functions of complex variable2.4.5 Field of a cylindrical conductor in R33 Analytical methods of solving boundary value problems3.1 Method of Green’s functions3.1.1 Green’s formula for electrostatics3.1.2 Field of a point charge q surrounded by a sphere of radius a with U = 03.1.3 Field of a point charge q surrounded by a sphere of radius a with U = k3.1.4 Field of a surface dipole distributed on a sphere of radius a with dipole densityt3.1.5 Green’s formula for two-dimensional magnetostatics3.2 Method of images3.2.1 Magnetic field of a line current in a slot3.2.2 Magnetic field of an AC line current over a conducting half-space3.3 Method of separation of variables3.3.1 Magnetic field of a current uniformly distributed in a slot4 Numerical methods of solving boundary value problems4.1 Variational formulation in magnetostatics4.2 Finite elements for two-dimensional magnetostatics4.2.1 Discretization of energy functional4.2.2 Local shape functions4.2.3 Coefficient matrix and source vector4.2.4 From potential to field4.2.5 Magnetic field in a slot solved by the finite element method4.3 Finite elements for three-dimensional magnetostatics5 Time-varying electromagnetic field5.1 Maxwell’s equations in differential form5.2 Poynting’s vector5.3 Maxwell’s equations in frequency domain5.4 Plane waves in an infinite domain5.5 Wave and diffusion equations in terms of vectors E and H5.6 Wave and diffusion equations in terms of scalar and vector potentials5.7 Electromagnetic field radiated by an oscillating dipole5.8 Diffusion equations in terms of dual potentials5.9 Weak eddy current in a conducting plane under a.c. conditions5.10 Strong eddy current in a conducting plane under a.c. conditions5.11 Eddy current in a cylindrical conductor under step excitation5.12 Electromagnetic field equations in different reference frames6 Inverse problems6.1 Direct and inverse problems6.2 Well-posed and ill-posed problems6.3 Fredholm’s integral equation of the first kind6.4 Case study: synthesis of magnetic field sources6.5 Under- and over-determined systems of equations6.6 Least-squaressolution6.7 Classification of inverse problems7 Optimization7.1 Solution of inverse problems by the minimization of a functional7.2 Constrained optimization7.3 Gradient–free and gradient-based methods7.4 Deterministic vs non-deterministic search7.5 A deterministic algorithm of lowest order: simplex method7.6 A non-deterministic algorithm of lowest order: evolution strategy7.7 Numerical case studies7.7.1 Identification of B-H curve of the iron region of a magnetic pole7.7.2 Shape design of a magnetic pole (static optimisation)7.7.3 Shape design of a magnetic pole (dynamic optimisation)7.7.4 A multiobjective approach to the shape design of a magnetic pole