  We present a gauge and Lorentz invariant effective field theory model for the
interaction of a charged scalar matter field with a magnetic monopole source,
described by an external magnetic current. The quantum fluctuations of the
monopole field are described effectively by a strongly-coupled ``dual'' $U_{\rm
d}(1)$ gauge field, which is independent of the electromagnetic $U_{\rm em}(1)$
gauge field. The effective interactions of the charged matter with the monopole
source are described by a gauge invariant mixed Chern-Simons-like
(Pontryagin-density) term between the two $U(1)$ gauge fields. The latter
interaction coupling is left free, and a Lattice study of the system is
performed with the aim of determining the phase structure of this effective
theory. Our study shows that, in the spontaneously-broken-symmetry phase, the
monopole source triggers, via the mixed Chern-Simons term, which is non-trivial
in its presence, the generation of a dynamical singular configuration
(magnetic-monopole-like) for the respective gauge fields. The scalar field also
behaves in the broken phase in a way similar to that of the scalar sector of
the `t Hooft-Polyakov monopole.
