Exploring Covariant Electrodynamics Through Solved Problems
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Exploring Covariant Electrodynamics Through Solved Problems
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Author : Salvatore Capozziello
language : en
Publisher: Springer
Release Date : 2016-08-06
Exploring Covariant Electrodynamics Through Solved Problems written by Salvatore Capozziello and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-06 with Science categories.
This book introduces the reader to modern covariant electrodynamics by means of solved problems and exercises relating to the motion of charged particles and the generation, propagation, and confinement of radiation. The exercises are intended as a tool to bridge the gap between analytic theories and physical phenomena and will assist the young researcher in developing her/his understanding of the real world. The choice of representative examples has been carefully made with a view to enabling the reader to progress easily from a single example toward more general classes of phenomena. At the start of each chapter the principal required mathematical tools are listed, providing an insight into the technical difficulties to be confronted in that chapter. Particular emphasis is placed on discussion of fundamental experiments and phenomena confirming special relativity, such as the Wilson-Wilson experiment and the Stewart-Tolman, Sagnac, Compton, and Mössbauer effects. Throughout, the book aims to highlight the practical applications of electrodynamics. It will be ideal for master and graduate students in both Physics and Engineering.
Solved Problems In Classical Electrodynamics And Theory Of Relativity
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Author : Daniel Radu
language : en
Publisher: CRC Press
Release Date : 2023-11-23
Solved Problems In Classical Electrodynamics And Theory Of Relativity written by Daniel Radu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-23 with Science categories.
This book is intended for undergraduate and graduate students in physics, engineering, astronomy, applied mathematics and for researchers working in related subjects. It is an excellent study tool for those students who would like to work independently on more electrodynamics problems in order to deepen their understanding and problem solving skills. The book discusses main concepts and techniques related to Maxwell's equations, potentials and fields (including Liénard-Wiechert potentials), electromagnetic waves, and the interaction and dynamics of charged point particles. It also includes content on magnetohydrodynamics and plasma, radiation and antennas, special relativity, relativistic kinematics, relativistic dynamics and relativistic-covariant dynamics and general theory of relativity. It contains a wide range of problems, ranging from electrostatics and magnetostatics to the study of the stability of dynamical systems, field theories and black hole orbiting. The book even contains interdisciplinary problems from the fields of electronics, elementary particle theory, antenna design. Detailed, step-by step calculations are presented, meeting the need for a thorough understanding of the reasoning and steps of the calculations by all students, regardless of their level of training. Additionally, numerical solutions are also proposed and accompanied by adjacent graphical representations and even multiple methods of solving the same problem. It is structured in a coherent and unified way, having a deep didactic character, being thus oriented towards a university environment, where the transmission of knowledge in a logical, unified and coherent way is essential. It teaches students how to think about and how to approach solving electrodynamics problems. - Contains a wide range of problems and applications from the fields of electrodynamics and the theory of special relativity. - Presents numerical solutions to problems involving nonlinearities. - Details command lines specific to Mathematica software dedicated to both analytical and numerical calculations, which allows readers to obtain the numerical solutions as well as the related graphical representations.
Covariant Electrodynamics
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Author : John M. Charap
language : en
Publisher: JHU Press
Release Date : 2011-06-01
Covariant Electrodynamics written by John M. Charap and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-01 with Science categories.
A notoriously difficult subject, covariant electrodynamics is nonetheless vital for understanding relativistic field theory. John M. Charap’s classroom-tested introduction to the mathematical foundations of the topic presents the material in an approachable manner. Charap begins with a historical overview of electrodynamics and a discussion of the preliminary mathematics one needs in order to grasp the advanced and abstract concepts underlying the theory. He walks the reader through Maxwell’s four equations, explaining how they were developed and demonstrating how they are applied. From there, Charap moves through the other components of electrodynamics, such as Lorentz transformations, tensors, and charged particle behavior. At each point, he carefully works through the mathematics, applies the concepts to simple physical systems, and provides historical context that makes clear the connections among the theories and the mathematicians responsible for developing them. A concluding chapter reviews the history of electrodynamics and points the way for independent testing of the theory. Thorough, evenly paced, and intuitive, this friendly introduction to high-level covariant electrodynamics is a handy and helpful addition to any physicist’s toolkit.
Directed Quantities In Electrodynamics
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Author : Bernard Jancewicz
language : en
Publisher: Birkhäuser
Release Date : 2022-03-04
Directed Quantities In Electrodynamics written by Bernard Jancewicz and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-04 with Mathematics categories.
This monograph explores classical electrodynamics from a geometrical perspective with a clear visual presentation throughout. Featuring over 200 figures, readers will delve into the definitions, properties, and uses of directed quantities in classical field theory. With an emphasis on both mathematical and electrodynamic concepts, the author’s illustrative approach will help readers understand the critical role directed quantities play in physics and mathematics. Chapters are organized so that they gradually scale in complexity, and carefully guide readers through important topics. The first three chapters introduce directed quantities in three dimensions with and without the metric, as well as the development of the algebra and analysis of directed quantities. Chapters four through seven then focus on electrodynamics without the metric, such as the premetric case, waves, and fully covariant four-dimensional electrodynamics. Complementing the book’s careful structure, exercises are included throughout for readers seeking further opportunities to practice the material. Directed Quantities in Electrodynamics will appeal to students, lecturers, and researchers of electromagnetism. It is particularly suitable as a supplement to standard textbooks on electrodynamics.
Solved Problems In Classical Electromagnetism
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Author : J. Pierrus
language : en
Publisher: Oxford University Press
Release Date : 2018-08-02
Solved Problems In Classical Electromagnetism written by J. Pierrus and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-02 with Science categories.
Classical electromagnetism - one of the fundamental pillars of physics - is an important topic for all types of physicists from the theoretical to the applied. The subject is widely recognized to be one of the most challenging areas of the physics curriculum, both for students to learn and for lecturers to teach. Although textbooks on electromagnetism are plentiful, hardly any are written in the question-and-answer style format adopted in this book. It contains nearly 300 worked questions and solutions in classical electromagnetism, and is based on material usually encountered during the course of a standard university physics degree. Topics covered include some of the background mathematical techniques, electrostatics, magnetostatics, elementary circuit theory, electrodynamics, electromagnetic waves and electromagnetic radiation. For the most part the book deals with the microscopic theory, although we also introduce the important subject of macroscopic electromagnetism as well. Nearly all questions end with a series of comments whose purpose is to stimulate inductive reasoning and reach various important conclusions arising from the problem. Occasionally, points of historical interest are also mentioned. Both analytical and numerical techniques are used in obtaining and analyzing solutions. All computer calculations are performed with MathematicaCO® and the relevant code is provided in a notebook; either in the solution or the comments.
Core Electrodynamics
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Author : Sandra Chapman
language : en
Publisher:
Release Date : 2021
Core Electrodynamics written by Sandra Chapman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This book is intended to engage the students in the elegance of electrodynamics and special relativity, whilst giving them the tools to begin graduate study. Here, from the basis of experiment, the authors first derive the Maxwell equations and special relativity. Introducing the mathematical framework of generalized tensors, the laws of mechanics, Lorentz force and the Maxwell equations are then cast in manifestly covariant form. This provides the basis for graduate study in field theory, high energy astrophysics, general relativity and quantum electrodynamics. As the title suggests, this book is "electrodynamics lite". The journey through electrodynamics is kept as brief as possible, with minimal diversion into details, so that the elegance of the theory can be appreciated in a holistic way. It is written in an informal style and has few prerequisites; the derivation of the Maxwell equations and their consequences is dealt with in the first chapter. Chapter 2 is devoted to conservation equations in tensor formulation; here, Cartesian tensors are introduced. Special relativity and its consequences for electrodynamics are introduced in Chapter 3 and cast in four-vector form, and here, the authors introduce generalized tensors. Finally, in Chapter 4, Lorentz frame invariant electrodynamics is developed. Supplementary material and examples are provided by the two sets of problems. The first is revision of undergraduate electromagnetism, to expand on the material in the first chapter. The second is more advanced corresponding to the remaining chapters, and its purpose is twofold: to expand on points that are important, but not essential, to derivation of manifestly covariant electrodynamics, and to provide examples of manipulation of cartesian and generalized tensors. As these problems introduce material not covered in the text, they are accompanied by full worked solutions. The philosophy here is to facilitate learning by problem solving, as well as by studying the text. Extensive appendices for vector relations, unit conversion and so forth are given with graduate study in mind. .
Quantum Physics
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Author : Florian Scheck
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-07-08
Quantum Physics written by Florian Scheck and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Science categories.
Scheck’s Quantum Physics presents a comprehensive introductory treatment, ideally suited for a two-semester course. Part One covers the basic principles and prime applications of quantum mechanics, from the uncertainty relations to many-body systems. Part Two introduces to relativistic quantum field theory and ranges from symmetries in quantum physics to electroweak interactions. Numerous worked-out examples as well as exercises, with solutions or hints, enables the book’s use as an accompanying text for courses, and also for independent study. For both parts, the necessary mathematical framework is treated in adequate form and detail. The book ends with appendices covering mathematical fundamentals and enrichment topics, plus selected biographical notes on pioneers of quantum mechanics and quantum field theory. The new edition was thoroughly revised and now includes new sections on quantization using the path integral method and on deriving generalized path integrals for bosonic and fermionic fields.
Classical Covariant Fields
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Author : Mark Burgess
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-31
Classical Covariant Fields written by Mark Burgess and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-31 with Science categories.
This 2002 book is for graduate students and researchers working on field theory, group theory and dynamical systems.
Exploring Physics With Geometric Algebra
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Author : Peeter Joot
language : en
Publisher: Peeter Joot
Release Date :
Exploring Physics With Geometric Algebra written by Peeter Joot and has been published by Peeter Joot this book supported file pdf, txt, epub, kindle and other format this book has been release on with Science categories.
This is an exploratory collection of notes containing worked examples of a number of applications of Geometric Algebra (GA), also known as Clifford Algebra. This writing is focused on undergraduate level physics concepts, with a target audience of somebody with an undergraduate engineering background (i.e. me at the time of writing.) These notes are more journal than book. You'll find lots of duplication, since I reworked some topics from scratch a number of times. In many places I was attempting to learn both the basic physics concepts as well as playing with how to express many of those concepts using GA formalisms. The page count proves that I did a very poor job of weeding out all the duplication. These notes are (dis)organized into the following chapters * Basics and Geometry. This chapter covers a hodge-podge collection of topics, including GA forms for traditional vector identities, Quaterions, Cauchy equations, Legendre polynomials, wedge product representation of a plane, bivector and trivector geometry, torque and more. A couple attempts at producing an introduction to GA concepts are included (none of which I was ever happy with.) * Projection. Here the concept of reciprocal frame vectors, using GA and traditional matrix formalisms is developed. Projection, rejection and Moore-Penrose (generalized inverse) operations are discussed. * Rotation. GA Rotors, Euler angles, spherical coordinates, blade exponentials, rotation generators, and infinitesimal rotations are all examined from a GA point of view. * Calculus. Here GA equivalents for a number of vector calculus relations are developed, spherical and hyperspherical volume parameterizations are derived, some questions about the structure of divergence and curl are examined, and tangent planes and normals in 3 and 4 dimensions are examined. Wrapping up this chapter is a complete GA formulation of the general Stokes theorem for curvilinear coordinates in Euclidean or non-Euclidean spaces is developed. * General Physics. This chapter introduces a bivector form of angular momentum (instead of a cross product), examines the components of radial velocity and acceleration, kinetic energy, symplectic structure, Newton's method, and a center of mass problem for a toroidal segment. * Relativity. This is a fairly incoherent chapter, including an attempt to develop the Lorentz transformation by requiring wave equation invariance, Lorentz transformation of the four-vector (STA) gradient, and a look at the relativistic doppler equation. * Electrodynamics. The GA formulation of Maxwell's equation (singular in GA) is developed here. Various basic topics of electrodynamics are examined using the GA toolbox, including the Biot-Savart law, the covariant form for Maxwell's equation (Space Time Algebra, or STA), four vectors and potentials, gauge invariance, TEM waves, and some Lienard-Wiechert problems. * Lorentz Force. Here the GA form of the Lorentz force equation and its relation to the usual vectorial representation is explored. This includes some application of boosts to the force equation to examine how it transforms under observe dependent conditions. * Electrodynamic stress energy. This chapter explores concepts of electrodynamic energy and momentum density and the GA representation of the Poynting vector and the stress-energy tensors. * Quantum Mechanics. This chapter includes a look at the Dirac Lagrangian, and how this can be cast into GA form. Properties of the Pauli and Dirac bases are explored, and how various matrix operations map onto their GA equivalents. A bivector form for the angular momentum operator is examined. A multivector form for the first few spherical harmonic eigenfunctions is developed. A multivector factorization of the three and four dimensional Laplacian and the angular momentum operators are derived. * Fourier treatments. Solutions to various PDE equations are attempted using Fourier series and transforms. Much of this chapter was exploring Fourier solutions to the GA form of Maxwell's equation, but a few other non-geometric algebra Fourier problems were also tackled.
Electrodynamics
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Author : Carolina C. Ilie
language : en
Publisher:
Release Date : 2018
Electrodynamics written by Carolina C. Ilie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with SCIENCE categories.
This book of problems and solutions is a natural continuation of Ilie and Schrecengost's first book Electromagnetism: Problems and Solutions. Aimed towards students who would like to work independently on more electrodynamics problems in order to deepen their understanding and problem-solving skills, this book discusses main concepts and techniques related to Maxwell's equations, conservation laws, electromagnetic waves, potentials and fields, and radiation.