  In this work, we investigate a Maxwell-scalar model that couples the scalar
and gauge fields through the electric permittivity and another model, in which
the scalar field lives in the presence of impurity. By considering a single
spatial dimension, we determine the conditions under which the model with
impurity can be seen as an effective model for the Maxwell-scalar system,
having similar solutions. This correspondence shows that the impurity can be
used to describe the presence of a charge density, and we use it to verify that
the impurity-free case, which supports minimum energy configurations, is
related to the case of point charges. We also investigate a class of impurities
which modifies the core of the scalar field, and find the corresponding
nontrivial charge densities and electric fields. In particular, the asymptotic
behavior in terms of the impurity is also studied, leading to solutions
exhibiting long-range or quasi-compact profile.
