Derivation of the Coulomb Force in the AG-CEM Constitutive Sector

Derivation of the Coulomb Forcein the AG-CEM Constitutive Sector Valentin Ionescu Companion note to the corrected manuscript of 30 October 2026 This manuscript presents a variational derivation of electrostatic interactions within AG Constitutive Electromagnetism (AG-CEM), using the P-EM electromagnetic action of the Integral Corpus of AMC Theory and the explicit coupling to electric sources specified in Addendum III-EM. Its aim is to establish how the electrostatic field equation, the point-charge potential and the force on a test charge follow from this framework in Euclidean reference space, without introducing a gravitational metric. The analysis proceeds from the action with sources to the constitutive relations and the generalized Poisson equation. For a positive, static and spatially homogeneous background, the isolated point-charge problem is solved with a specified boundary condition. Gauss’s flux law fixes the normalization, and a uniqueness argument identifies the solution of the stated problem. Varying the test-charge trajectory then yields the electromagnetic force rather than assuming the force law independently. On this homogeneous background, the reference force retains the Coulomb inverse-square form. Its coefficient is multiplied by the constant scaling factor Λ0, not divided by it, and the classical expression is recovered at Λ0 = 1. The calculation also derives the interaction energy and checks agreement with the Coulomb term in the ideal atomic Hamiltonian used in the Corpus. These are internal consistency results; the reference force is distinguished from acceleration and from a local instrument reading. The manuscript further treats spatially varying backgrounds. It retains the background-gradient contribution in the field equation and supplies an exact radial solution for the special case in which the background is spherically symmetric about the charge. It explains why substituting a position-dependent scaling factor directly into the homogeneous potential is not generally valid, and how boundary conditions enter the potential. The result is a derivation within the proposed P-EM/AG-CEM constitutive branch. It does not claim a microscopic origin of electric charge from the Cold Big Bang Model (CBBM), an identification of charge signs with CBBM chirality, or experimental validation of the complete model. The source coupling, test-particle approximation and prescribed background remain explicit premises. The study is offered for independent examination of the derivation, its normalization and its physical interpretation. Keywords: AG-CEM; Coulomb force; electrostatics; variational principle; constitutive electromagnetism; P-EM; CBBM.