  In the framework of three-dimensional Born-Infeld Electrodynamics, we pursue
an investigation of the consequences of the space-time dimensionality on the
existence of magnetostatic fields generated by electric charges at rest in an
inertial frame, which are present in its four-dimensional version. Our analysis
reveals interesting features of the model. In fact, a magnetostatic field
associated with an electric charge at rest does not appear in this case.
Interestingly, the addition of the topological term (Chern-Simons) to
Born-Infeld Electrodynamics yields the appearance of the magnetostatic field.
We also contemplate the fields associated to the would-be-magnetic monopole in
three dimensions.
