Foundations of Classical Electromagnetism


Polat A. B.

Efe Academy Press, İstanbul, 2019

  • Basım Tarihi: 2019
  • Yayınevi: Efe Academy Press
  • Basıldığı Şehir: İstanbul

Özet

Foundations of Classical Electromagnetism is the first volume of the series Lectures in Electromagnetic Theory. The content of the present volume is integrated to the following volumes, which are also planned to be released soon:

Vol.2 Electromagnetic Fields and Waves

Vol.3 Singularities in Classical Electromagnetism

Vol.4 Hertzian Electrodynamics

Vol.5 Electromagnetic Scattering by Moving Bodies

The present volume is a reflection of my personal outlook on physics centered around original contributions to mathematical foundations, principles and applications of classical electromagnetic field theory. It is not designed as a typical textbook covering all topics in the curriculum with plenty of solved problems but should rather be considered as a supplementary source for readers ranging from undergraduate students with little background on electromagnetic theory to graduates and researchers of Electrical Engineering and Basic Sciences who are specializing on this field.

The first part of the present book focuses on axiomatic foundations and principles of electromagnetic theory from a deductive perspective. It involves discussions of the postulates and laws that constitute the field theory, along with various principles, theorems and relations which they reveal.

In the second part static electric and magnetic fields in stationary media are studied in the space of continuous functions to be able to appeal to sophomore students as well. This comes at the cost of a severely restricted analytical freedom that hinders legitimate derivations of certain relations. However, I shall compensate for all missing proofs in Volume 3, where discontinuities and singularities in electromagnetic field theory are treated systematically accompanied by a thorough review of required topics from Analysis in Lebesgue and Schwartz-Sobolev Spaces. 

I also devoted an Appendix to customary approaches and various discussions from literature along with my commentaries and pedagogical solutions to a number of issues in the teaching of Vector Calculus. Unity holds for all mathematical and physical symbols and abbreviations in the series, while MKSA units are adopted as they are rather focused on engineering applications. Semicolon (;) is used to distinguish between variables of different units in arguments of functions as  or . I adopted informal and plain language to create a classroom environment at the expense of falling into repetitions, while frequently referring to footnotes for extra information and italicization in order to emphasize terms and concepts.

Main contributions of the present volume to literature can be outlined as follows:

-         Original approaches to modeling and interpretation of electromagnetic phenomena

-         Alternative representations for Maxwell’s Equations with emphasis on Duality Transformations.

-         Proper descriptions of work and energy in static electric and magnetic fields

-         Proper definitions for Perfect Electric and Magnetic Conductors

-         Introduction of Principle of Conservation of Energy and Power in moving media

-         New physical concepts and quantities associated with Duality Principle and Conservation of Energy and Power in moving media

The structure and design of these volumes are reflections of my worldview that the laws of macroscopic electromagnetism - as described by Maxwell’s Equations of stationary media - are frame indifferent and recognize all frame indifferent (complementary) axioms, postulates, principles and laws of other disciplines that constitute Newtonian Continuum Mechanics in Euclidean Space. In the spirit of Natural Philosophy I draw criticism for the attempts to integrate (contradicting) alternative theories for moving bodies (especially Special and General Theories of Relativity) into the areas of study of Electrical Engineering. If a relativistic improvement for Maxwell’s Equations will ever be required on cosmological scale, then I believe it is bound to be constructed in a way as to yield the frame indifferent Hertz-Heaviside Equations exactly in the nonrelativistic limiting cases.

The volumes themselves are much better suited for citation purposes since they involve a considerable number of corrections and advances over my published papers.