Published online by Cambridge University Press: 16 October 2026
This appendix derives the momentum carried by electromagnetic fields and rewrites the Lorentz force law as a conservation law for total momentum in matter plus fields. Starting from the volume integral of ρE + J × B, it uses Maxwell’s equations to express the mechanical momentum change in terms of the fields alone, identifying a field momentum density ε0 E × B and introducing the Maxwell stress tensor as the flux of electromagnetic momentum through a surface. The resulting continuity equation states that changes in mechanical plus field momentum inside a volume are balanced by stress-tensor fluxes across its boundary. The appendix interprets this structure in terms of forces exerted on material bodies and the momentum carried by light, connecting the momentum density to the Poynting vector via g = S/c2.
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