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2020 | Book

Potential and Current Density Distribution Read chapter Read first chapter

Maxwell´s Equations

From Current Density Distribution to the Radiation Field of the Hertzian Dipole

Author: Prof. Jürgen Donnevert

Publisher: Springer Fachmedien Wiesbaden

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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About this book

This book focuses on the derivation and solution of Maxwell’s equations. The stations along the way include the laws of potential and current density distribution, as well as the laws of electrostatics and stationary magnetic fields. The book is chiefly intended for students of electrical engineering, information technology, and physics; the goal is to prepare them for courses on Electromagnetic Field Theory (EFT). Building on what they have learned in advanced physics and mathematics courses at secondary school or technical college, it is intended to accompany university-level EFT courses. Particular importance is attached to detailed explanations in text form, combined with a wealth of illustrations. All formulas are derived step by step.

Table of Contents

Frontmatter
Chapter 1. Potential and Current Density Distribution
Abstract
The subject of the first chapter is the electric field accompanying a current that is constant in time. The terms current density, potential and electric field strength are explained. The gradient of a scalar field and the differential operator Nabla or ∇ are introduced and the formulas for cartesian, cylindrical and spherical coordinates are derived. Kirchhoff's laws for the field of electric current densities are explained and the ohmic law for this field. Finally, the energy required to move a charge in the electric field is calculated.
Jürgen Donnevert
Chapter 2. Electrostatics
Abstract
Subject of the second chapter is the static electric field, which is generated by static electric charges and charge distributions. Using a test arrangement, the formula for the force exerted on a charge in an electric field is determined. The value of absolute permeability is calculated on the basis of a charging process of a capacitor. Spatial charge distributions are treated and the relationship between flux density and charge density is given. The vector operator divergence is introduced and the formulas for Cartesian, cylindrical and spherical coordinates are derived. The Gaussian integral theorem is derived and the potential equation of the electrical scalar potential. In this context the Laplace operator is introduced. Finally, the formula for energy density of the electric field is derived.
Jürgen Donnevert
Chapter 3. The Stationary Magnetic Field
Abstract
Chapter 3 deals with temporally constant magnetic fields. A parameter of this field is the magnetic flux density. In the first step, the relationship between magnetic flux density and the force exerted on a conductor through which current flows is derived. Furthermore, it is shown that a voltage will be generated at the ends of a conductor loop moving in a magnetic field in such a way that the concatenated magnetic flux changes in time. The differential form of the law of Ampère is introduced and the vector operator rotation. For Cartesian, cylindrical and spherical coordinate systems the calculation formulas are derived. The magnetic vector potential is introduced and finally the law of Biot-Savart.
Jürgen Donnevert
Chapter 4. Time-Varying Electric and Magnetic Fields
Abstract
The chapter 4 deals with time-varying electric and magnetic fields, which will generate electromagnetic waves that propagate in space. At first is discussed the switch-on process of an inductor and then derived the equation for the energy density of the magnetic field. Next, the focus is on the law of induction, the second Maxwell’s equation, respectively. The continuity equation is formulated. Then displacement current, which leads to the first Maxwell’s equation, will be discussed. The introduction of the displacement current was necessary, because without the displacement current Ampére’s law for an open alternating current circuit has no validity.
Jürgen Donnevert
Chapter 5. Wave Propagation
Abstract
The propagation in free space is determined by the type of excitation by the transmitter and its transmitting antenna. In chapter 5 of this book the solutions of Maxwell’s equations are discussed in detail. For simplicity, the wave propagation in free space was chosen with wave excitation by a Hertzian dipole. The formulas for calculating the near field and the far field are derived and the energy flux in these field areas are calculated. The procedure for calculating the field lines is given. Finally, the essential characteristic values of antennas are derived.
Jürgen Donnevert
Chapter 6. Appendix: Verification of the Calculation Rules for Vector Analysis
Abstract
Verification of the Calculation Rules for Vector Analysis.
Jürgen Donnevert
Backmatter
Metadata
Title
Maxwell´s Equations
Author
Prof. Jürgen Donnevert
Copyright Year
2020
Electronic ISBN
978-3-658-29376-5
Print ISBN
978-3-658-29375-8
DOI
https://doi.org/10.1007/978-3-658-29376-5