Schwab Field Theory Concepts

Electromagnetic Fields. Maxwell’s Equations grad, curl, div. etc. Finite-Element Method. Finite-Difference Method. Charge Simulation Method. Monte Carlo Method
Erscheinungsjahr 2012
ISBN: 978-3-642-48941-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 218 Seiten, Web PDF

Reihe: Mathematics and Statistics

"Field Theory Concepts" is a new approach to the teaching
and understanding of field theory. Exploiting formal analo-
gies of electric, magnetic, and conduction fields and
introducing generic concepts results in a transparently
structured electomagnetic field theory. Highly illustrative
terms alloweasyaccess to the concepts of curl and div which
generally are conceptually demanding. Emphasis is placed on
the static, quasistatic and dynamic nature of fields.
Eventually, numerical field calculation algorithms, e.g.
Finite Element method and Monte Carlo method, are presented
in a concise yet illustrative manner.

Zielgruppe

Research

Autoren/Hrsg.

Schwab, Adolf J.

Inhaltsverzeichnis

1 Elementary Concepts of Electric and Magnetic Fields.- 1.1 Flux and Flux Density of Vector Fields.- 1.2 Equations of Matter — Constitutive Relations.- 2 Types of Vector Fields.- 2.1 Electric Source Fields.- 2.2 Electric and Magnetic Vortex Fields.- 2.3 General Vector Fields.- 3 Field Theory Equations.- 3.1 Integral Form of Maxwells Equations.- 3.2 Law of Continuity in Integral Form Source Strength of Current Density Fields.- 3.3 Differential Form of Maxwell’s Equations.- 3.4 Law of Continuity in Differential Form Source Density of Current Density Fields.- 3.5 Maxwell’s Equations in Complex Notation.- 3.6 Integral Theorems of Stokes and Gauss.- 3.7 Network Model of Induction.- 4 Gradient, Potential, Potential Function.- 4.1 Gradient of a Scalar Field.- 4.2 Potential and Potential Function of Static Electric Fields.- 4.3 Development of the Potential Function from a Given Charge Distribution.- 4.4 Potential Equations.- 4.5 Electric Vector Potential.- 4.6 Vector Potential of the Conduction Field.- 5 Potential and Potential Function of Magnetostatic Fields.- 5.1 Magnetic Scalar Potential.- 5.2 Potential Equation for Magnetic Scalar Potentials.- 5.3 Magnetic Vector Potential.- 5.4 Potential Equation for Magnetic Vector Potentials.- 6 Classification of Electric and Magnetic Fields.- 6.1 Stationary Fields.- 6.2 Quasi-Stationary Fields (Steady-State) Fields.- 6.3 Nonstationary Fields, Electromagnetic Waves.- 7 Transmission-Line Equations.- 8 Typical Differential Equations of Electrodynamics and Mathematical Physics.- 8.1 Generalized Telegraphist’s Equation.- 8.2 Telegraphist’s Equation with a, b>0; c=0.- 8.3 Telegraphist’s Equation with a>0; b=0; c=0.- 8.4 Telegraphist’s Equation with b>0; a=0; c=0.- 8.5 Helmholtz Equation.- 8.6 Schroedinger Equation.- 8.7Lorentz’s Invariance of Maxwell’s Equations.- 9 Numerical Calculation of Potential Fields.- 9.1 Finite-Element Method.- 9.2 Finite-Difference Method.- 9.3 Charge Simulation Method.- 9.4 Monte Carlo Method.- 9.5 General Remarks on Numerical Field Calculation.- A1 Units.- A2 Scalar and Vector Integrals.- A3 Vector Operations in Special Coordinate Systems.- A5 Complex Notation of Harmonic Quantities.- Literature.