Essential Electromagnetism
Essential electromagnetic foundations for physics and engineering undergraduates.
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- • Master the essentials of electrostatics and magnetostatics in a single compact text.
- • Learn to solve Poisson’s and Laplace’s equations analytically and numerically.
- • Understand multipole expansions and how they approximate fields at large distances.
- • Connect dielectric polarization theory to boundary conditions on E, V, and D.
- • Build intuition for magnetism of materials, including H, susceptibility, and hysteresis.
الوصف
“Essential Electromagnetism” is designed as a compact, essentials-focused resource for students studying electromagnetism at undergraduate level in physics and engineering. It introduces the core ideas and standard methods behind electrostatics and magnetostatics, including Coulomb’s law, electric flux, Gauss’ law, and electrostatic potential, then develops Poisson’s and Laplace’s equations (with method of images, analytic solutions, and a finite-difference numerical approach). It proceeds to multipole expansions for localized charge distributions, macroscopic and microscopic dielectric theory with polarization and boundary conditions, and then magnetism: magnetic fields and forces, Biot–Savart law, vector potential, Ampère’s law, magnetic flux, and magnetization of materials, concluding with paramagnetism, ferromagnetism, and magnetic circuits.
فهرس المحتويات
Preface 1 Electrostatics 1.1 Electric charge, field and flux 1.2 The electrostatic potential 2 Poisson’s and Laplace’s equations 2.1 Poisson’s equation 2.2 Method of images 2.3 Laplace’s equation 2.4 Laplace’s equation in spherical coordinates 2.5 Finite-difference method for Laplace’s equation 3 Multipole expansion for localised charge distribution 3.1 Point charge on z axis 3.2 The monopole moment 3.3 The dipole moment 3.4 The quadrupole moment tensor 3.5 Electric dipoles 3.6 Multipole expansion in spherical coordinates 4 Macroscopic and microscopic dielectric theory 4.1 Dielectrics 4.2 Macroscopic dielectric theory 4.3 Gauss’ law and the electric displacement 4.4 Boundary conditions on V , E and D 4.5 Microscopic dielectric theory 5 Magnetic field and vector potential 5.1 Magnetism 5.2 The magnetic field and forces 5.3 The magnetic vector potential 5.4 Ampère’s law 5.5 Magnetic flux 5.6 Multipole expansion of vector potential 6 Magnetism of materials 6.1 Magnetic materials 6.2 Magnetisation field 6.3 Magnetisation currents and Ampère’s law 6.4 Ampère’s law in magnetised materials 6.5 Magnetic susceptibility and permeability 6.6 Paramagnetism 6.7 Ferromagnetism Bibliography Appendices A Vectors B Vector differential calculus C Vector integral calculus D Basics of index notation E Uniqueness of solutions of Poisson’s equation F Field line tracing as an initial value problem G Code for 2D finite-difference method for Laplace’s equation H Dipole term of multipole expansion of vector potential I Summary of vector calculus identities
معاينة
undergraduate studies in physics and engineering. Due to limited space available in this series,
it is not possible to go into the material in great depth, so I have attempted to encapsulate
what I consider to be the essentials. This book does not aim to replace existing textbooks
on these topics of which there are many excellent examples, several of which are listed in the
bibliography. Nevertheless, if appropriately supplemented, this book and “Essential Electrodynamics” could together serve as a textbook for 2nd and 3rd year electromagnetism courses
at Australian and British universities, or for junior/senior level electromagnetism courses at
American universities/colleges.
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