  We consider a regular and bounded dielectric body moving at a speed $|V|$,
following a constant vector field $V$, with respect to a reference frame. In
this frame, the special relativity implies that the Maxwell system is derived
through the constitutive equations linking the moving speed $|V|$ and the speed
of light $c$ in the background medium (as the vacuum for instance). Based on
this model, we derive the well-poseness of the related forward scattering
problem in the natural regime where $\frac{|V|}{c}\leq C_{te}$ with an
appropriate constant $C_{te} <1$ that we estimate. In particular, we show the
invertibility of the related Lippmann-Schwinger system in this regime and state
the corresponding Born series in terms of the ratio $\frac{|V|}{c}$. As an
application, we state and show the unique identifiability of the inverse
problem of detecting the dielectric body, without knowing the moving speed
$|V|$ or $V$, by illuminating it with incident electromagnetic waves
propagating at the speed $c$. Such identifiability result makes sense in the
regime under consideration.
