Maxwells Equations

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Maxwell S Equations

Author : Paul G. Huray
ISBN : 9780470549902
Genre : Science
File Size : 89.56 MB
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An authoritative view of Maxwell's Equations that takes theory to practice Maxwell's Equations is a practical guide to one of the most remarkable sets of equations ever devised. Professor Paul Huray presents techniques that show the reader how to obtain analytic solutions for Maxwell's equations for ideal materials and boundary conditions. These solutions are then used as a benchmark for solving real-world problems. Coverage includes: An historical overview of electromagnetic concepts before Maxwell and how we define fundamental units and universal constants today A review of vector analysis and vector operations of scalar, vector, and tensor products Electrostatic fields and the interaction of those fields with dielectric materials and good conductors A method for solving electrostatic problems through the use of Poisson's and Laplace's equations and Green's function Electrical resistance and power dissipation; superconductivity from an experimental perspective; and the equation of continuity An introduction to magnetism from the experimental inverse square of the Biot-Savart law so that Maxwell's magnetic flux equations can be deduced Maxwell's Equations serves as an ideal textbook for undergraduate students in junior/senior electromagnetics courses and graduate students, as well as a resource for electrical engineers.
Category: Science

A Student S Guide To Maxwell S Equations

Author : Daniel Fleisch
ISBN : 1139468472
Genre : Science
File Size : 70.98 MB
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Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere–Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.
Category: Science

Maxwell S Equations And The Principles Of Electromagnetism

Author : Richard Fitzpatrick
ISBN : 9781934015209
Genre : Science
File Size : 81.2 MB
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Designed for upper division electromagnetism courses or as a reference for electrical engineers and scientists, this book introduces Maxwell’s equations and electromagnetic waves as soon as possible (i.e., in the first third of the book), and then goes on to discuss electrostatics, magnetostatics, induction, etc., in the light of those equations. The book also provides a thorough discussion of vector field theory which emphasizes the rotational invariance of the dot and cross products, together with div, grad, and curl, and thus gives a clear physical motivation for the use of those constructs to describe electric and magnetic fields. Unlike many competing books, Maxwell’s Equations & the Principles of Electromagnetism covers topics such as advanced potentials, retarded fields, forces on dielectric liquids, antenna theory, and Faraday rotations.
Category: Science

Symmetries Of Maxwell S Equations

Author : W.I. Fushchich
ISBN : 9789400937291
Genre : Science
File Size : 28.54 MB
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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the fina\ question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu\ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Category: Science

Finite Element Methods For Maxwell S Equations

Author : Peter Monk
ISBN : 0198508883
Genre : Mathematics
File Size : 70.33 MB
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The emphasis in on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book.
Category: Mathematics

Numerical Solution Of Maxwell S Equations On Transformed Coordinates For Non Rectangular Electromagnetic Applications

Author : Vishal Sharma
ISBN : OCLC:1176275242
Genre : Electronic dissertations
File Size : 79.34 MB
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The utilization of a fourth-order Modified Runge-Kutta (MRK) scheme on a transformed coordinate system for simulating electromagnetic applications that involve non-rectangular domains are presented. The model equations were obtained by writing the governing Maxwell’s equations in the curvilinear coordinate system. Therefore, by transforming the arbitrary-shaped structures to a uniform rectangular grid, numerical schemes and boundary conditions can be easily implemented. The time advancement of fields in the computational space is performed by leapfrogging the stages of explicit fourth-order MRK method. The one-dimensional traveling wave simulation results indicate that the leapfrogging of MRK stages reduces the dissipation errors associated with the MRK solution of wave propagation. The computer algorithms based on this technique have been developed for near-field and far-field scattering applications. Several classes of problems have been investigated in the dissertation. In the initial stage, accuracy of the scheme has been established by simulating two standing wave problems and comparing MRK results with the existing exact solution. The results for both cases are found to be in good agreement. In the second stage, the total field-scattered field (TF-SF) formulation is incorporated in the algorithm for the simulation of far-field scattering. The two-dimensional and three-dimensional computer codes developed based on this algorithm are used to perform qualitative analysis using planes waves and cylindrical waves as source. The diffraction and penetration of the waves are studied in the presence of dielectric or conducting materials having linear, non-dispersive, and homogeneous properties. The results are compared with the results from the benchmark method and indicates good agreement. The grid independence investigations revealed the dependence on the Courant number to obtain accurate results. Subsequently, scattering investigations are carried out on non-rectangular geometries with the clustered grid points. Finally, computer algorithm is modified to include the modeling of dispersive (frequency-dependent) material, and the absorption and reflection of electromagnetic waves by biological tissues is studied in one-dimension. The predicted reflection coefficient for two separate studies indicate excellent agreement with the exact reflection coefficients for a wideband frequency range.
Category: Electronic dissertations

Boundary Value Problems For Maxwell S Equations

Author : K. S. Yee
ISBN : UCAL:C3521148
Genre :
File Size : 70.80 MB
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This report contains the proofs of the uniqueness and existence theorems for an electromagnetic field when the normal component of both the electric and magnetic fields are given on a smooth surface. The truth of the above theorems was suggested by V. Rumsey. The results are obtained for an exterior domain. However, the same method can be used for the interior problems. Whereas one synthesizes an electromagnetic field by a surface current when either the tangential electric or magnetic field is given, we synthesize our electromagnetic field by means of the electric and magnetic surface charges. We also show that solutions to Maxwell's equations can be expressed in terms of solutions to a second order partial differential equation in certain coordinate systems when the parameters E and mu are allowed to have a certain anisotropic property. This result represents an extension of those obtained by C. Mueller and by P. Friedman.

Approximations And Numerical Methods For The Solution Of Maxwell S Equations

Author : Institute for Mathematics and Its Applications
ISBN : STANFORD:36105023150324
Genre : Science
File Size : 59.38 MB
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This book was written in response to the increasing interest in the high frequency numerical solution of Maxwell's equations. Research activity in this area has been stimulated by requirements for greater precision in radar cross-section calculations, particularly for geometries with lowobservability; however there are also a growing number of applications in bio-electromagnetism and electromagnetic compatibility. It is hoped that these proceedings will be of interest both to specialists in this area as well as to others simply looking for a guide to recent developments.
Category: Science


Author : Wenhua Yu
ISBN : 1580537316
Genre : Computers
File Size : 45.82 MB
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Here's a powerful, full three-dimensional Maxwell's equations solver that serves as a fast and accurate tool for modeling a wide variety of antenna and arrays, waveguides, cavities, microwave circuits, as well as a useful resource for Radar Cross Section analysis. This cutting-edge CFDTD software package combines visual languages and advanced techniques in computational electromagnetics to simulate the behaviors of complex microwave systems. Designed to handle 220 x 220 x 220 nodes, the software is well-equipped for large-size and high-frequency problems.
Category: Computers

Electricity And Magnetism For Mathematicians

Author : Thomas A. Garrity
ISBN : 9781107435162
Genre : Mathematics
File Size : 45.45 MB
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Maxwell's equations have led to many important mathematical discoveries. This text introduces mathematics students to some of their wonders.
Category: Mathematics

A Treatise On Electricity And Magnetism

Author : James Clerk Maxwell
ISBN : 0486606376
Genre : Science
File Size : 43.11 MB
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Volume 2 of the great physicist and mathematician's final elaboration of the theory of electromagnetism covers the study of solenoids and shells, magnetic induction, methods of observation, and terrestrial magnetism. Additional topics include the mutual action of electric currents, dimensions of electric units, and much more. 1891 edition.
Category: Science

Introduction To Electromagnetism

Author : Martin J N Sibley
ISBN : 9781000352375
Genre : Science
File Size : 23.9 MB
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This edition aims to expand on the first edition and take the reader through to the wave equation on coaxial cable and free-space by using Maxwell’s equations. The new chapters include time varying signals and fundamentals of Maxwell's equations. This book will introduce and discuss electromagnetic fields in an accessible manner. The author explains electroconductive fields and develops ideas relating to signal propagation and develops Maxwell’s equations and applies them to propagation in a planar optical waveguide. The first of the new chapters introduces the idea of a travelling wave by considering the variation of voltage along a coaxial line. This concept will be used in the second new chapter which solves Maxwell’s equations in free-space and then applies them to a planar optical waveguide in the third new chapter. As this is an area that most students find difficult, it links back to the earlier chapters to aid understanding. This book is intended for first- and second-year electrical and electronic undergraduates and can also be used for undergraduates in mechanical engineering, computing and physics. The book includes examples and homework problems. Introduces and examines electrostatic fields in an accessible manner Explains electroconductive fields Develops ideas relating to signal propagation Examines Maxwell’s equations and relates them to propagation in a planar optical waveguide Martin Sibley recently retired after 33 years of teaching at the University of Huddersfield. He has a PhD from Huddersfield Polytechnic in Preamplifier Design for Optical Receivers. He started his career in academia in 1986 having spent 3 years as a postgraduate student and then 2 years as a British Telecom-funded research fellow. His research work had a strong bias to the practical implementation of research, and he taught electromagnetism and communications at all levels since 1986. Dr. Sibley finished his academic career as a Reader in Communications, School of Computing and Engineering, University of Huddersfield. He has authored five books and published over 80 research papers.
Category: Science

Field Force Energy And Momentum In Classical Electrodynamics Revised Edition

Author : Masud Mansuripur
ISBN : 9781681085562
Genre : Science
File Size : 62.71 MB
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The classical theory of electrodynamics is based on Maxwell's equations and the Lorentz law of force. This book begins with a detailed analysis of these equations, and proceeds to examine their far-reaching consequences. The traditional approach to electrodynamics treats the ‘microscopic’ equations of Maxwell as fundamental, with electric charge and electric current as the sole sources of the electric and magnetic fields. Subsequently, polarization and magnetization are introduced into Maxwell's equations to account for the observed behavior of material media. The augmented equations, known as Maxwell's ‘macroscopic’ equations, are considered useful for practical applications, but are also ultimately reducible to the more fundamental ‘microscopic’ equations. In contrast, this textbook treats Maxwell's ‘macroscopic’ equations as the foundation of classical electrodynamics, and treats electrical charge, electrical current, polarization, and magnetization as the basic constituents of material media. The laws that govern the distribution of electromagnetic energy and momentum in space-time are also introduced in an early chapter, then discussed in great detail in subsequent chapters. The text presents several examples that demonstrate the solution of Maxwell's equations in diverse situations, aiming to enhance the reader’s understanding of the flow of energy and momentum as well as the distribution of force and torque throughout the matter-field systems under consideration. This revised edition of Field, Force, Energy and Momentum in Classical Electrodynamics features revised chapters, some of which include expanded discussions of fundamental concepts or alternative derivations of important formulas. The new edition also features three additional chapters covering Maxwell’s equations in spherical coordinates (Chapter 10), the author’s recent discussion (and streamlined proof) of the Optical Theorem (Chapter 13), and the fascinating connections between electromagnetism and Einstein’s special theory of relativity (Chapter 15). A new appendix covers the SI system of units that has been used throughout the book. The book is a useful textbook for physics majors studying classical electrodynamics. It also serves as a reference for industry professionals and academic faculty in the fields of optics and advanced electronics.
Category: Science

Essays On The Formal Aspects Of Electromagnetic Theory

Author : Akhlesh Lakhtakia
ISBN : 9789814505840
Genre : Technology
File Size : 81.81 MB
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The book deals with formal aspects of electromagnetic theory from the classical, the semiclassical and the quantum viewpoints in essays written by internationally distinguished scholars from several countries. The fundamental basis of electromagnetic theory is examined in order to elucidate Maxwell's equations, identify problematic aspects as well as outstanding problems, suggest ways and means of overcoming the obstacles, and review existing literature.This book will be especially valuable for those who wish to go in depth, rather than simply use Maxwell's equations for the solution of engineering problems. Graduate students will find it rich in dissertation topics, and advanced researchers will relish the controversial and detailed arguments and models.
Category: Technology

Classical Field Theory

Author : Florian Scheck
ISBN : 9783642279850
Genre : Science
File Size : 84.69 MB
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The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity (perihelion precession of Mercury, and light deflection by the sun). ------ Textbook features: detailed figures, worked examples, problems and solutions, boxed inserts, highlighted special topics, highlighted important math etc., helpful summaries, appendix, index.
Category: Science


Author : Engineer Engineer
ISBN : 9798629051633
Genre :
File Size : 35.5 MB
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