  In this paper a formulation of the field equation for moving media is
developed by the generalization of an axiomatic geometric formulation of the
electromagnetism in vacuum (Ivezi\'{c} T 2005 Found. Phys. Lett. 18 401. First,
the field equations with bivectors F(x) and \mathcal{M}(x) are presented and
then these equations are written with vectors E(x), B(x), P(x) and M(x). The
latter ones contain both the velocity vector u of a moving medium and the
velocity vector v of the observers who measure E and B fields. They do not
appear in the entire previous literature. All these equations are written in
the standard basis and compared with Maxwell's equations with 3-vectors. In
this approach the Amp\`{e}r-Maxwell law and Gauss's law are inseparably
connected in one law and the same happens with Faraday's law and the law that
expresses the absence of magnetic charge. It is shown that Maxwell's equations
with 3-vectors and our field equations with 4D geometric quantities are not
equivalent in the 4D spacetime.
