  This paper is dedicated to the study of interactions between external sources
for the electromagnetic field in a model which exhibits Lorentz symmetry
breaking. We investigate such interactions in the CPT-even photon sector of the
Standard Model Extension (SME), where the Lorentz symmetry breaking is caused
by a background tensor $K_{(F)\alpha\beta\sigma\tau}$. Since the background
tensor is very tiny, we treat it perturbatively up to first order and we focus
on physical phenomena which have no counterpart in Maxwell electrodynamics. We
consider effects related to field sources describing point-like charges,
straight line currents and Dirac strings. We also investigate the so called
Aharonov-Bohm bound states in a Lorentz-symmetry breaking scenario. We use
atomic experimental data to verify if we could impose upper bounds to the
Lorentz-symmetry breaking parameters involved. We also use some overestimated
constrains for the Lorentz-symmetry breaking parameters in order to investigate
if the obtained results could be relevant for condensed matter systems.
