Chapter 1: Electromagnetism – Forces & Fields

The first chapter of Volume II introduces the core principles of electromagnetism, beginning with a comparison of electrical and gravitational forces, noting that while both follow an inverse square law relationship, electrical forces are vastly stronger. Electrical interactions arise from two types of fundamental charge, positive and negative, which govern attraction between unlike charges and repulsion between like charges. Matter typically appears electrically neutral because these opposing charges are balanced in an intimate mixture, but the minute residual electrical forces are responsible for all chemical bonding, molecular structures, and the strength of ordinary matter. The fundamental unified nature of these phenomena is captured by the electromagnetic force law, known as the Lorentz force, which describes the total force acting on a moving charge due to the presence of both an electric field and a magnetic field. This formulation defines the electric and magnetic fields as vector fields that exist everywhere in space and vary with time. These fields adhere to the principle of superposition, meaning the total field at any point is simply the vector sum of all fields produced by individual charges. To analyze these vector fields, the concepts of flux (representing the flow of the field outward through a surface) and circulation (representing the integral of the field's tangential component around a closed curve) are introduced as essential mathematical tools. Using these concepts, the foundational laws of electromagnetism are detailed: Gauss's Law for the electric field relates electric flux to the net enclosed charge; Gauss's Law for the magnetic field states that magnetic flux through any closed surface is zero; Faraday's Law connects the circulation of the electric field to the time rate of change of magnetic flux; and the corrected Ampère's law (including Maxwell's displacement current term) relates the circulation of the magnetic field to both electrical currents and the time rate of change of electric flux. This chapter stresses that the magnetic force is fundamentally a relativistic effect of the electric force observed when charges are in motion, making the study of electromagnetism inseparable from the principles of relativity. The laws of electrodynamics, particularly as codified by Maxwell, represent one of the most profound and significant scientific achievements in history, underpinning all modern electrical technology.