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 www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

Designed for upper division electro- magnetism courses or as a reference for electrical engineers & scientists, this is an introduction to Maxwell's equations & electromagnetic waves. Further discusses electrostatics, magnetostatics, induction, etc., in the light of those equations. Discussion of vector field theory included.

Divergencies in quantum field theory referred to as OC infinite zero-point energyOCO have been a problem for 70 years. Renormalization has always been considered an unsatisfactory remedy. In 1985 it was found that Maxwell''s equations generally do not have solutions that satisfy the causality law. An additional term for magnetic dipole currents corrected this shortcoming. Rotating magnetic dipoles produce magnetic dipole currents, just as rotating electric dipoles in a material like barium titanate produce electric dipole currents. Electric dipole currents were always part of Maxwell''s equations. This book shows that the correction of Maxwell''s equations eliminates the infinite zero-point energy in quantum electrodynamics. In addition, it presents many more new results. Contents: Monopole, Dipole, and Multipole Currents; Hamiltonian Formalism; Quantization of the Pure Radiation Field; KleinOCoGordon Equation and Vacuum Constants. Readership: Senior undergraduates, graduate students, researchers and academics in quantum, atomic, theoretical, mathematical and nuclear physics."

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.

This volume collects longer articles on the analysis and numerics of Maxwell’s equations. The topics include functional analytic and Hilbert space methods, compact embeddings, solution theories and asymptotics, electromagnetostatics, time-harmonic Maxwell’s equations, time-dependent Maxwell’s equations, eddy current approximations, scattering and radiation problems, inverse problems, finite element methods, boundary element methods, and isogeometric analysis.

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 www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

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.

How can one determine the physical properties of the medium or the geometrical properties of the domain by observing electromagnetic waves? To answer this fundamental problem in mathematics and physics, this book leads the reader to the frontier of inverse scattering theory for electromagnetism.The first three chapters, written comprehensively, can be used as a textbook for undergraduate students. Beginning with elementary vector calculus, this book provides fundamental results for wave equations and Helmholtz equations, and summarizes the potential theory. It also explains the cohomology theory in an easy and straightforward way, which is an essential part of electromagnetism related to geometry. It then describes the scattering theory for the Maxwell equation by the time-dependent method and also by the stationary method in a concise, but almost self-contained manner. Based on these preliminary results, the book proceeds to the inverse problem for the Maxwell equation.The chapters for the potential theory and elementary cohomology theory are good introduction to graduate students. The results in the last chapter on the inverse scattering for the medium and the determination of Betti numbers are new, and will give a current scope for the inverse spectral problem on non-compact manifolds. It will be useful for young researchers who are interested in this field and trying to find new problems.

Provides a concise yet complete discussion of Maxwell's four equations of electrodynamics - the fundamental theory of electricity, magnetism, and light. Written for a general audience, it guides readers step-by-step through the vector calculus and development of each equation. Pictures and diagrams illustrate what the equations mean in basic terms.

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.