An Introduction to Electromagnetism

An Introduction to Electromagnetism incorporates critical elements of electromagnetism and electrodynamics, delving into foundational concepts while highlighting important lessons. The book opens with an introductory section on exterior calculus and its applications in electromagnetism that introduces increasingly popular mathematical tools at the heart of most vector calculus theorems. Sections cover electrostatics and magnetostatics, satisfying Curie’s principle and exploring how to use symmetry plane(s) of the charge and current distributions to facilitate problem-solving, explain Earnshaw’s electrostatic and magnetostatic instability theorems, and explore the Bohr-van Leewen theorem on the impossibility of a non-zero classical magnetic susceptibility.

The book further makes the case that electromagnetism can be more naturally expressed in terms of differential forms, making this novel geometric approach more accessible to a wider audience. The book has a unique and specialized focus on topics such as a discussion on the incompleteness of Maxwell’s equations, a dissection of Purcell’s thought experiment on the magnetic force from a current-carrying wire onto a free charge, and a review of the interpretation of dipole and multipole moments and how their properties contribute to the electric and magnetic phenomena.