Chapter 13: Magnetostatics – Magnetic Fields & Currents

Magnetostatics – Magnetic Fields & Currents on Magnetostatics introduces the fundamental concepts of the magnetic field (B), starting with the definition of the Lorentz force, which describes the total force acting on a moving charged particle. This force is the sum of the electric force and the velocity-dependent magnetic force. The magnetic force component is always perpendicular to the particle's velocity, meaning it performs no work. The text then transitions to describing electric currents, defining the current density (j) as the flow of charge per unit time and area, and introduces the critical principle of the conservation of charge. This principle relates the current density to the change in charge density (rho) over time. For steady currents, charge flow must occur in closed loops. A key distinction in magnetostatics is established: magnetic field lines never terminate, leading to the condition that the divergence of B is zero, which means there is no magnetic counterpart to electric charge (no magnetic monopoles). The foundational law for calculating magnetic fields produced by steady currents, Ampere’s law, is derived and applied to solve for the field surrounding a long straight wire and the uniform field found inside a solenoid. Most profoundly, the chapter demonstrates that the magnetic field is not an independent entity but is instead a relativistic manifestation of the electric field. By comparing observations across different inertial reference frames (one where a current-carrying wire is stationary and one where the moving charge is at rest), the text explicitly shows that the magnetic force observed in one frame transforms into a purely electric force in the other frame, illustrating that electricity and magnetism are unified phenomena linked by Special Relativity. This connection is formalized through the discussion that charge density (rho) and current density (j) combine to form a four-vector under relativistic transformations. The chapter concludes by affirming the principle of superposition for magnetic fields and detailing the use of the right-hand rule, clarifying that the magnetic field B is mathematically classified as a pseudo-vector (axial vector).