Published online by Cambridge University Press: 16 October 2026
This chapter develops a description of magnetic matter and shows how magnetizable media are incorporated into classical electromagnetism. It begins from the near field of localized magnetic dipoles, introduces the magnetic dipole moment and magnetization density (𝑟, 𝑡), and derives the near-field Maxwell equations in the presence of magnetic matter. Linear magnetic materials are then defined through constitutive relations among 𝐵, 𝐻, and 𝑀, with permeability, paramagnetism, and diamagnetism characterized in terms of microscopic dipole moments and their alignment with external fields. Next, the chapter derives magnetic energy density in linear materials and explains how inserting magnetic cores enhances inductance. It then analyzes forces and torques between current distributions, the energy required to assemble prescribed current configurations, and the relationship between these forces and the underlying dipole–dipole interaction. Finally, returning to Faraday’s law, it interprets inductors and their field energy in terms of an effective “electromagnetic mass” associated with the motion of charge carriers.
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