Geometry of Electromagnetic Systems (Monographs in Electrical & Electronic Engineering)

This book examines the close relationship between the physical phenomena of electromagnetism and the geometry of space and time. It starts with the Faraday-Maxwell insight that in electromagnetism exists an interconnected dynamical system in which space and time are closely linked with the physical phenomena. An appropriate mathematical basis is given by differential geometry to describe local relationships and topology to describe the system. These tools are introduced in the context of Maxwell's equations in the familiar vector notation, which are greatly simplified by the geometrical approach. Moreover, the geometrical idea of symmetry unifies the various conservation laws. Overall, the book clarifies the relationship between fields, potentials, and sources. Links between macroscopic and quantum phenomena are explored from a geometrical angle, and there is a simple discussion of superconductivity. This book is addressed to engineers, applied mathematicians, physicists, and students involved in the design and analysis of electromagnetic systems.