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Understanding vectors & electrostatic fields
Understanding vectors and electrostatic fields
Electromagnetics is not an easy subject for students. The subject presents a number of challenges, such as: new math, new physics, new geometry, new insights and difficult problems. As a result, every aspect needs to be presented to students carefully, with thorough mathematics and strong physical insights and even alternative ways of viewing and formulating the subject. The theoretician James Clerk Maxwell and the experimentalist Michael Faraday, both shown on the cover, had high respect for physical insights. This book is written primarily as a text for an undergraduate course in electromagnetics, taken by junior and senior engineering and physics students. The book can also serve as a text for beginning graduate courses by including advanced subjects and problems. The book has been thoroughly class-tested for many years for a two-semester Electromagnetics course at Syracuse University for electrical engineering and physics students. It could also be used for a one-semester course, covering up through Chapter 8 and perhaps skipping Chapter 4 and some other parts. For a one-semester course with more emphasis on waves, the instructor could briefly cover basic materials from statics (mainly Chapters 2 and 6) and then cover Chapters 8 through 12.
1. Introduction to vectors -- 1.1 Introduction -- 1.1.1 Josiah Willard Gibbs (1839-1903) and the development of vector analysis -- 1.2 Vector algebra -- 1.2.1 Basic operations of vector algebra -- 1.2.2 Vector algebra in rectangular coordinates -- 1.2.3 Triple products -- 1.3 Coordinate systems -- 1.3.1 Coordinate system geometry -- 1.3.2 Differential elements of length, surface and volume -- 1.3.3 Coordinate transformations -- 1.3.4 Integrals of vector functions -- 1.4 Vector calculus -- 1.4.1 Definitions -- 1.4.2 Gradient -- 1.4.3 Divergence -- 1.4.5 The divergence theorem and Stokes' theorem - solenoidal and conservative fields -- 1.4.6 Vector identities -- 1.4.7 Higher order functions of vector calculus -- 1.5 Helmholtz's theorem --
2. Introduction to electrostatic fields and electromagnetic potentials -- 2.1 Introduction -- 2.2 Electric charge -- 2.3 The electric field in free space -- 2.4 Charles Augustin Coulomb (1736-1806) and the discovery of Coulomb's law -- 2.5 Gauss' law -- 2.6. The electric fields of arbitrary charge distributions -- 2.7. The scalar electric potential V -- 2.8. Potential of an arbitrary charge distribution -- 2.9. Conductors -- 2.10. The electric dipole.
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