  We construct the effective theory of electrically charged, spatially
extended, infinitely heavy objects at leading power. The theory may be viewed
as a generalization of NRQED for particles with a finite charge distribution
where the charge radius and higher moments of the charge distribution are
counted as $O(1)$ rather than $O(1/M)$. We show this is equivalent to a Wilson
line traced by the worldline of an extended charge distribution. Our canonical
use case is atomic nuclei with large charge $Z\gg 1$. The theory allows for the
insertion of external operators and is sufficiently general to allow a
treatment of both electromagnetic and weak mediated lepton-nucleus scattering
including charged-current processes. This provides a first step towards the
factorization of Coulomb regions, including structure dependence arising from a
finite charge distribution, for scattering with nuclei.
