Elements of Classical Electrodynamics and Special Relativity
Series: UNITEXT for Physics;
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Product details:
- Publisher Springer Nature Switzerland
- Date of Publication 9 September 2026
- ISBN 9783032298485
- Binding Hardback
- No. of pages473 pages
- Size 235x155 mm
- Language English
- Illustrations X, 473 p. 150 illus. in color. 700
Categories
Long description:
This book presents the fundamental aspects of classical electrodynamics and special relativity, focusing on the mathematical framework that underpins a coherent theory of electromagnetism. It prioritizes theoretical consistency while summarizing foundational and phenomenological aspects concisely, leaving more detailed discussions to introductory texts. The book provides a set of mathematical tools essential for addressing and solving common problems in the field.
It begins with a review of key mathematical techniques, including vector calculus, Green’s theorem, and Dirac delta functions. The discussion then moves to electrostatics, covering Poisson’s equation, Green’s functions, the method of images, and multipole expansions. Solutions to Laplace’s equation are explored in Cartesian, spherical, and cylindrical coordinates, both analytically and numerically. The treatment of electric currents and magnetostatics follows, introducing Ampère’s law, the vector potential, and magnetic multipoles.
Maxwell’s equations are then derived and applied to wave propagation, energy and momentum conservation, and gauge transformations. The final sections introduce special relativity, covering Lorentz transformations, four-vectors, and the covariant formulation of electrodynamics, concluding with an introduction to relativistic Lagrangian dynamics.
Each chapter includes exercises designed to reinforce students’ understanding. This book is intended for advanced undergraduate and graduate students in physics. Readers are expected to have prior knowledge of algebra and electromagnetism.
MoreTable of Contents:
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Mathematical tools.- Electrostatic interactions.- Conductors and electrostatic boundary value problems.- Series expansions of potential solutions.- Laplace s equation in spherical
coordinates.- Laplace’s equation in cylindrical.- Numerical solutions of Laplace s equation.- Multipole expansion of the electrostatic potential.- Electric currents.- Magnetic field.- Electric and magnetic fields in continuous media.- Electromagnetic induction and Maxwell s equations.- Electromagnetic waves.- Conservation laws in electrodynamics.- Special relativity.- Covariant Electrodynamics.- Relativistic Lagrangian dynamics.
