Contribution à l'étude des formulations de calcul de la force magnétique en magnétostatique

Download Contribution à l'étude des formulations de calcul de la force magnétique en magnétostatique PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.:/5 (491 download)

DOWNLOAD NOW!


Book Synopsis Contribution à l'étude des formulations de calcul de la force magnétique en magnétostatique by : Olivier Barré

Download or read book Contribution à l'étude des formulations de calcul de la force magnétique en magnétostatique written by Olivier Barré and published by . This book was released on 2003 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ce mémoire présente une étude des méthodes de calcul de la force engendrée par les champs magnétiques sur les matériaux linéaires en magnétostatique et se propose d'en comparer les performances sur les matériaux de faibles perméabilité. Les démonstrations de ces méthodes sont abordées et les hypothèses mises en évidence. Pour discriminer les formulations, courants équivalents, masses magnétiques équivalentes, tenseur de Maxwell, dérivée de l'énergie, une expérience et les mesures associées sont conçues par calcul de champ. Un matériau spécifique, de faible module d'élasticité est également synthétisé. Plongé dans un champ magnétique, un volume de test de ce matériau se déforme. Chaque formulation permet d'obtenir une répartition des contraintes sur le volume. Pour chaque répartition, la déformation du volume est calculée. Chaque déformation est comparée à celle qui est obtenue expérimentalement. Il apparaît que les méthodes énergétiques sont les plus précises.

Développement de formulations intégrales de volume en magnétostatique

Download Développement de formulations intégrales de volume en magnétostatique PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (94 download)

DOWNLOAD NOW!


Book Synopsis Développement de formulations intégrales de volume en magnétostatique by : Vinh Le Van

Download or read book Développement de formulations intégrales de volume en magnétostatique written by Vinh Le Van and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ces dernières années, la Méthode Intégrale de Volume (MIV) a reçu une attention particulière pour lamodélisation des problèmes électromagnétiques en basse fréquence. Son intérêt principal est l'absencedu maillage de la région air, ce qui rend la méthode légère et rapide. Associée aux méthodes decompression matricielle la MIV devient aujourd'hui une alternative compétitive à la méthode deséléments finis pour la modélisation de dispositifs électromagnétiques ayant un volume d'airprépondérant.Ce rapport porte sur le développement de deux formulations intégrales de volume pour la résolution deproblèmes magnétostatiques avec prise en compte des matériaux non linéaires, des aimants, desbobines, des circuits magnétiques avec ou sans entrefer et des régions minces magnétiques. Lapremière est une formulation en flux de mailles indépendantes basée sur l'interpolation par éléments defacette. La deuxième est une formulation en potentiel vecteur magnétique basée sur l'interpolation paréléments d'arête. L'application de ces formulations permet d'une part d'obtenir des résultats précismême en présence d'un faible maillage et d'autre part de résoudre aisément des problèmes nonlinéaires. Des méthodes de calcul de la force magnétique globale ainsi que du flux magnétique dansles bobines ont été également mises en oeuvre. Les développements informatiques ont été réalisés dansla plateforme MIPSE et ont été validés sur des problèmes académiques ainsi que sur quelquesdispositifs industriels.

Contribution à la modélisation numérique des phénomènes couples magneto-élastiques

Download Contribution à la modélisation numérique des phénomènes couples magneto-élastiques PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.:/5 (49 download)

DOWNLOAD NOW!


Book Synopsis Contribution à la modélisation numérique des phénomènes couples magneto-élastiques by : Mondher Besbes

Download or read book Contribution à la modélisation numérique des phénomènes couples magneto-élastiques written by Mondher Besbes and published by . This book was released on 1995 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Les travaux présentés dans ce mémoire traitent de la modélisation numérique dans l'hypothèse bidimensionnelle des phénomènes couples magneto-elastiques dans les dispositifs electromagnetiques. L'objectif est particulièrement cible a l'étude théorique et expérimentale des vibrations d'origine magnétique dans les machines a reluctance variable a double saillance. Dans le but de quantifier la réponse vibratoire d'une telle machine, nous avons introduit dans un code de calcul du champ magnétique, base sur la méthode des éléments finis, un module qui permet la détermination de la répartition des forces magnétiques locales pour calculer les déformations mécaniques résultantes. Le choix de la méthode de calcul de force magnétique, qui se base sur l'application locale du principe des travaux virtuels, a été justifie par la précision de cette méthode, sa generalite (milieux satures) et sa souplesse de mise en ouvre. L'analyse spectrale des forces magnétiques nous a permis de prédire quelles sont les modes de vibrations qui vont être excites. Le calcul du spectre des vibrations a été réalise en cherchant la solution de l'équation d'équilibre relative a chaque harmonique de force. Une analyse modale a été aussi effectuée pour déterminer les fréquences de résonance et les modes de vibrations associées. Parallèlement a cette approche numérique, nous avons analyse expérimentalement, en se basant sur des mesures accelerometriques, le comportement vibratoire de la machine. Grâce a cette analyse, nous avons pu valider le code de calcul des vibrations ainsi développe. L'ensemble de ces travaux a montre que la source principale du bruit acoustique, ou des vibrations qui le produisent, dans la machine d'étude réside sur l'action des forces magnétiques radiales d'attraction des dents statoriques et rotoriques en particulier lorsque celles-ci sont en conjonction. A la fin de ce mémoire, nous avons mis au point un modèle de couplage fort qui permet la résolution simultanée des problèmes couples magneto-elastiques. Ce type de modèle trouve son importance dans le cas ou les propriétés magnétiques et élastiques sont en forte interaction. Nous avons spécialement évoque dans cette partie le calcul des déformations des matériaux fortement magnétostrictifs et la résolution des problèmes de grandes déformations élastiques

The Finite Element Method for Electromagnetic Modeling

Download The Finite Element Method for Electromagnetic Modeling PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 0470393807
Total Pages : 618 pages
Book Rating : 4.4/5 (73 download)

DOWNLOAD NOW!


Book Synopsis The Finite Element Method for Electromagnetic Modeling by : Gérard Meunier

Download or read book The Finite Element Method for Electromagnetic Modeling written by Gérard Meunier and published by John Wiley & Sons. This book was released on 2010-01-05 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by specialists of modeling in electromagnetism, this book provides a comprehensive review of the finite element method for low frequency applications. Fundamentals of the method as well as new advances in the field are described in detail. Chapters 1 to 4 present general 2D and 3D static and dynamic formulations by the use of scalar and vector unknowns and adapted interpolations for the fields (nodal, edge, face or volume). Chapter 5 is dedicated to the presentation of different macroscopic behavior laws of materials and their implementation in a finite element context: anisotropy and hysteretic properties for magnetic sheets, iron losses, non-linear permanent magnets and superconductors. More specific formulations are then proposed: the modeling of thin regions when finite elements become misfit (Chapter 6), infinite domains by using geometrical transformations (Chapter 7), the coupling of 2D and 3D formulations with circuit equations (Chapter 8), taking into account the movement, particularly in the presence of Eddy currents (Chapter 9) and an original approach for the treatment of geometrical symmetries when the sources are not symmetric (Chapter 10). Chapters 11 to 13 are devoted to coupled problems: magneto-thermal coupling for induction heating, magneto-mechanical coupling by introducing the notion of strong and weak coupling and magneto-hydrodynamical coupling focusing on electromagnetic instabilities in fluid conductors. Chapter 14 presents different meshing methods in the context of electromagnetism (presence of air) and introduces self-adaptive mesh refinement procedures. Optimization techniques are then covered in Chapter 15, with the adaptation of deterministic and probabilistic methods to the numerical finite element environment. Chapter 16 presents a variational approach of electromagnetism, showing how Maxwell equations are derived from thermodynamic principles.

Mathematical Models for Eddy Currents and Magnetostatics

Download Mathematical Models for Eddy Currents and Magnetostatics PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9400702027
Total Pages : 309 pages
Book Rating : 4.4/5 (7 download)

DOWNLOAD NOW!


Book Synopsis Mathematical Models for Eddy Currents and Magnetostatics by : Rachid Touzani

Download or read book Mathematical Models for Eddy Currents and Magnetostatics written by Rachid Touzani and published by Springer Science & Business Media. This book was released on 2013-10-01 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies, i.e. magnetostatic and eddy current problems which are rarely presented in the applied mathematics literature. In the first part, the authors introduce the mathematical models in a realistic context in view of their use for industrial applications. Several geometric configurations of electric conductors leading to different mathematical models are carefully derived and analyzed, and numerical methods for the solution of the obtained problems are given. Related issues such as convergence of the approximations and error estimates are discussed. The second part of the monograph presents various coupled problems that involve eddy current or magnetostatic problems, in particular magneto-hydrodynamic problems and magnetic shaping problems concerning the melt flow of electrically conducting metals, induction heating processes, inductively coupled plasmas and ferromagnetic screening modeling. The presentation of each model comes with numerical illustration from industrial applications.

An Introduction to Differential Manifolds

Download An Introduction to Differential Manifolds PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3319207350
Total Pages : 408 pages
Book Rating : 4.3/5 (192 download)

DOWNLOAD NOW!


Book Synopsis An Introduction to Differential Manifolds by : Jacques Lafontaine

Download or read book An Introduction to Differential Manifolds written by Jacques Lafontaine and published by Springer. This book was released on 2015-07-29 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of “abstract” notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory. The original French text Introduction aux variétés différentielles has been a best-seller in its category in France for many years. Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.

Aeronomy

Download Aeronomy PDF Online Free

Author :
Publisher : Elsevier
ISBN 13 : 1483260666
Total Pages : 445 pages
Book Rating : 4.4/5 (832 download)

DOWNLOAD NOW!


Book Synopsis Aeronomy by : P. M. Banks

Download or read book Aeronomy written by P. M. Banks and published by Elsevier. This book was released on 2013-09-24 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aeronomy, Part A is an attempt to make a comprehensive exposition of the processes in aeronomy, the study of composition, movement, and thermal balance of the upper regions of the planetary atmosphere. The text covers topics such as atmospheric regions and atmospheric density, the temperature and molecular mass of the atmosphere; the permanent constituents and the molecular and isotonic composition of the homosphere; and the transition from the homosphere to the heterosphere. Also covered are topics such as the temperature gradient and energies in the thermosphere, conditions at 200km and above 250km, solar radiation and ionization, and aeronomic reactions. The book is recommended for scientists, especially natural physicists, who would like to know more about the field of aeronomy and its advances.

The Philosophy of Physical Science

Download The Philosophy of Physical Science PDF Online Free

Author :
Publisher : BoD – Books on Demand
ISBN 13 : 3734792207
Total Pages : 198 pages
Book Rating : 4.7/5 (347 download)

DOWNLOAD NOW!


Book Synopsis The Philosophy of Physical Science by : Sir Arthur Eddington

Download or read book The Philosophy of Physical Science written by Sir Arthur Eddington and published by BoD – Books on Demand. This book was released on 2021-03-17 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is often said that there is no "philosophy of science", but only the philosophies of certain scientists. But in so far as we recognize an authoritative body of opinion which decides what is and what is not accepted as present-day physics, there is an ascertainable present-day philosophy of physical science. It is the philosophy to which those who follow the accepted practice of science stand committed by their practice. This book contains the substance of the course of lectures which the author Eddington delivered as Tarner Lecturer of Trinity College Cambridge in the Easter Term 1938. The lectures have afforded him an opportunity of developing more fully than in his earlier books the principles of philosophic thought associated with the modern advances of physical science.

Infrastructure Design, Signalling and Security in Railway

Download Infrastructure Design, Signalling and Security in Railway PDF Online Free

Author :
Publisher : BoD – Books on Demand
ISBN 13 : 9535104489
Total Pages : 537 pages
Book Rating : 4.5/5 (351 download)

DOWNLOAD NOW!


Book Synopsis Infrastructure Design, Signalling and Security in Railway by : Xavier Perpinya

Download or read book Infrastructure Design, Signalling and Security in Railway written by Xavier Perpinya and published by BoD – Books on Demand. This book was released on 2012-04-04 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Railway transportation has become one of the main technological advances of our society. Since the first railway used to carry coal from a mine in Shropshire (England, 1600), a lot of efforts have been made to improve this transportation concept. One of its milestones was the invention and development of the steam locomotive, but commercial rail travels became practical two hundred years later. From these first attempts, railway infrastructures, signalling and security have evolved and become more complex than those performed in its earlier stages. This book will provide readers a comprehensive technical guide, covering these topics and presenting a brief overview of selected railway systems in the world. The objective of the book is to serve as a valuable reference for students, educators, scientists, faculty members, researchers, and engineers.

Local Approximation Techniques in Signal and Image Processing

Download Local Approximation Techniques in Signal and Image Processing PDF Online Free

Author :
Publisher : SPIE-International Society for Optical Engineering
ISBN 13 :
Total Pages : 584 pages
Book Rating : 4.3/5 (91 download)

DOWNLOAD NOW!


Book Synopsis Local Approximation Techniques in Signal and Image Processing by : Vladimir I︠A︡kovlevich Katkovnik

Download or read book Local Approximation Techniques in Signal and Image Processing written by Vladimir I︠A︡kovlevich Katkovnik and published by SPIE-International Society for Optical Engineering. This book was released on 2006 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with a wide class of novel and efficient adaptive signal processing techniques developed to restore signals from noisy and degraded observations. These signals include those acquired from still or video cameras, electron microscopes, radar, X-rays, or ultrasound devices, and are used for various purposes, including entertainment, medical, business, industrial, military, civil, security, and scientific. In many cases useful information and high quality must be extracted from the imaging. However, often raw signals are not directly suitable for this purpose and must be processed in some way. Such processing is called signal reconstruction. This book is devoted to a recent and original approach to signal reconstruction based on combining two independent ideas: local polynomial approximation and the intersection of confidence interval rule.

Radioactive Aerosols

Download Radioactive Aerosols PDF Online Free

Author :
Publisher : Elsevier
ISBN 13 : 0080555985
Total Pages : 187 pages
Book Rating : 4.0/5 (85 download)

DOWNLOAD NOW!


Book Synopsis Radioactive Aerosols by : Constantin Papastefanou

Download or read book Radioactive Aerosols written by Constantin Papastefanou and published by Elsevier. This book was released on 2011-07-28 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whenever radioactivity is released to the atmosphere, for example by the detonation of nuclear weapons or the testing of nuclear weapons or from nuclear reactor accidents that fraction of it which remains airborne for more than a few hours is liable to be attached to aerosol particles. The resulting radioactive aerosols are carried by atmospheric mixing processes until they settle out or are scavenged by precipitation. The radiation exposure pathway of maximum concern to humans is by inhalation of aerosols and their deposition in the respiratory tract. In this context, it is important to note that radioactive aerosols are commonly of natural origin alos. In particular, the associated radionuclides can be of natural terrestrial origin, such as the decay products of radon gas, or they can e cosmogenic, such as beryllium-7. The exposure of miners of uranium and other ores and minerals to radon and its aerosol-borne decay products is of major significance. The book describes the formation of aerosols, their aerodynamic size distribution, their atmospheric residence time, their sampling and measurement, the range of radioactive aerosols found and studied thus far, including man-made nuclides and radon decay products and their interaction with man, including deposition in the lung and subsequent health effects. Advanced level science handbook for researchers, scientists and academics Covers all aspects of radiation exposure in humans, including subsequent health implications Presents the latest findings and analysis in this highly topical area

Signal Processing for Communications

Download Signal Processing for Communications PDF Online Free

Author :
Publisher : Collection Savoir suisse
ISBN 13 : 2940222207
Total Pages : 392 pages
Book Rating : 4.9/5 (42 download)

DOWNLOAD NOW!


Book Synopsis Signal Processing for Communications by : Paolo Prandoni

Download or read book Signal Processing for Communications written by Paolo Prandoni and published by Collection Savoir suisse. This book was released on 2008-06-17 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a novel, less classical approach to the subject, the authors have written a book with the conviction that signal processing should be taught to be fun. The treatment is therefore less focused on the mathematics and more on the conceptual aspects, the idea being to allow the readers to think about the subject at a higher conceptual level, thus building the foundations for more advanced topics. The book remains an engineering text, with the goal of helping students solve real-world problems. In this vein, the last chapter pulls together the individual topics as discussed throughout the book into an in-depth look at the development of an end-to-end communication system, namely, a modem for communicating digital information over an analog channel.

Classical and Modern Numerical Analysis

Download Classical and Modern Numerical Analysis PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 1420091581
Total Pages : 628 pages
Book Rating : 4.4/5 (2 download)

DOWNLOAD NOW!


Book Synopsis Classical and Modern Numerical Analysis by : Azmy S. Ackleh

Download or read book Classical and Modern Numerical Analysis written by Azmy S. Ackleh and published by CRC Press. This book was released on 2009-07-20 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis.The text covers the main areas o

Minimum competence in scientific English

Download Minimum competence in scientific English PDF Online Free

Author :
Publisher : L'Editeur : EDP Sciences
ISBN 13 : 9782868835888
Total Pages : 264 pages
Book Rating : 4.8/5 (358 download)

DOWNLOAD NOW!


Book Synopsis Minimum competence in scientific English by : Sue Blattes

Download or read book Minimum competence in scientific English written by Sue Blattes and published by L'Editeur : EDP Sciences. This book was released on 2003 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cet ouvrage, devenu célèbre sous son sigle MCSE, a déjà été utilisé par plus de 50 000 étudiants, chercheurs, professionnels. L'objectif est de lire et écrire des textes en anglais scientifique avec facilité et pertinence. L'ouvrage est conçu pour que l'apprenant devienne un véritable utilisateur de l'anglais. La méthode originale repose sur l'analyse des fonctions et structures nécessaires : measurement, frequency, comparison, modification, link words, time, cause and consequence, hypothesis, modality, purpose and process, impersonal forms, compound nouns and adjectives. Dans chaque unit, des tests d'auto-évaluation permettent de se situer et de construire son parcours de formation, d'abord en définissant ses objectifs à l'aide des key points et du lexis, puis, de façon plus personnalisée, en puisant dans les examples in context, checkpoints (back to basics, word web), web search, FAQs... MCSE est l'outil de base d'une méthode qui comprend aussi d'autres outils dans la même collection (Listening Comprehension for Scientiflc English et Speaking Skills in Scientitic English). L'ouvrage est destiné à tout apprenant de niveau baccalauréat qui désire acquérir une réelle compétence dans l'écriture et la lecture de textes en anglais scientifique.

Optimization and Inverse Problems in Electromagnetism

Download Optimization and Inverse Problems in Electromagnetism PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9401724946
Total Pages : 348 pages
Book Rating : 4.4/5 (17 download)

DOWNLOAD NOW!


Book Synopsis Optimization and Inverse Problems in Electromagnetism by : Marek Rudnicki

Download or read book Optimization and Inverse Problems in Electromagnetism written by Marek Rudnicki and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: From 12 to 14 September 2002, the Academy of Humanities and Economics (AHE) hosted the workshop "Optimization and Inverse Problems in Electromagnetism". After this bi-annual event, a large number of papers were assembled and combined in this book. During the workshop recent developments and applications in optimization and inverse methodologies for electromagnetic fields were discussed. The contributions selected for the present volume cover a wide spectrum of inverse and optimal electromagnetic methodologies, ranging from theoretical to practical applications. A number of new optimal and inverse methodologies were proposed. There are contributions related to dedicated software. Optimization and Inverse Problems in Electromagnetism consists of three thematic chapters, covering: -General papers (survey of specific aspects of optimization and inverse problems in electromagnetism), -Methodologies, -Industrial Applications. The book can be useful to students of electrical and electronics engineering, computer science, applied mathematics (PhD level) and to researchers interested in the topic.

Popular Astronomy

Download Popular Astronomy PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 732 pages
Book Rating : 4.A/5 ( download)

DOWNLOAD NOW!


Book Synopsis Popular Astronomy by : Camille Flammarion

Download or read book Popular Astronomy written by Camille Flammarion and published by . This book was released on 1894 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Magnetic Fields, Special Relativity and Potential Theory

Download Magnetic Fields, Special Relativity and Potential Theory PDF Online Free

Author :
Publisher : Elsevier
ISBN 13 : 148313931X
Total Pages : 253 pages
Book Rating : 4.4/5 (831 download)

DOWNLOAD NOW!


Book Synopsis Magnetic Fields, Special Relativity and Potential Theory by : B. H. Chirgwin

Download or read book Magnetic Fields, Special Relativity and Potential Theory written by B. H. Chirgwin and published by Elsevier. This book was released on 2013-10-22 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Magnetic Fields, Special Relativity and Potential Theory is an introduction to electromagnetism, special relativity, and potential theory, with emphasis on the magnetic field of steady currents (magnetostatics). Topics covered range from the origin of the magnetic field and the magnetostatic scalar potential to magnetization, electromagnetic induction and magnetic energy, and the displacement current and Maxwell's equations. This volume is comprised of five chapters and begins with an overview of magnetostatics, followed by a chapter on the methods of solving potential problems drawn from electrostatics, magnetism, current flow, and gravitation. Relaxing the constraint of stationary steady currents, the next chapter considers electromagnetic induction when the current strengths in closed circuits vary or when the circuits move. This leads to the necessity of assessing the breakdown of Newtonian ideas and the introduction of special relativity. When the constraint of closed circuits is further relaxed and the motion of charges in open circuits is taken into account, the discussion turns to displacement current because of the relativistic theory already set up, leading to Maxwell's equations. This book will be a valuable resource for undergraduate students of physics.