Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

=== Faraday’s law in integral form, ===

∮CE⋅dℓ=−ddt∫ΣCB⋅dS,\oint_{\mathcal C} \mathbf{E}\cdot d\mathbf{\ell} = -\frac{d}{dt}\int_{\Sigma_{\mathcal C}}\mathbf{B}\cdot d\mathbf{S},∮CE⋅dℓ=−dtd∫ΣCB⋅dS,
applies to any loop C\mathcal CC on the spherical surface. On Sr02S^2_{r_0}Sr02, if localized currents j∥\mathbf{j}_\parallelj∥ flow or if surface charge distribution σ\sigmaσ changes, the magnetic flux through a patch Σ\SigmaΣ will change; Faraday’s law then produces an EMF around the patch which drives surface currents (feedback). Concretely:
* an absorption event that changes σ\sigmaσ locally typically implies local changes to B\mathbf{B}B and hence an induced tangential E\mathbf{E}E around loops that modifies j∥\mathbf{j}_\parallelj∥;
* conversely, time-varying surface currents radiate into the bulk (Maxwell retarded potentials), producing the spherical emission event of QAT.

This is the boundary version of Faraday induction and shows how microscopic absorption/emission events produce EM cascades along the shell and into the bulk.

Historically: Faraday’s lines of force are the intuitive picture behind these local, surface-driven field changes — surface currents change the topology and flux of field lines; that is the physical core of QAT’s exchange process.