  The hadron string dynamics (HSD) model is generalized to include the creation
and evolution of retarded electromagnetic fields as well as the influence of
the magnetic and electric fields on the quasiparticle propagation. The
time-space structure of the fields is analyzed in detail for non-central Au+Au
collisions at $\sqrt{s_{NN}}=$200 GeV. It is shown that the created magnetic
field is highly inhomogeneous but in the central region of the overlapping
nuclei it changes relatively weakly in the transverse direction. For the impact
parameter $b=$10 fm the maximal magnetic field - perpendicularly to the
reaction plane - is obtained of order $eB_y/m_\pi^2\sim$5 for a very short time
$\sim$ 0.2 fm/c, which roughly corresponds to the time of a maximal overlap of
the colliding nuclei. We find that at any time the location of the maximum in
the $eB_y$ distribution correlates with that of the energy density of the
created particles. In contrast, the electric field distribution, being also
highly inhomogeneous, has a minimum in the center of the overlap region.
Furthermore, the field characteristics are presented as a function of the
collision energy and the centrality of the collisions. To explore the effect of
the back reaction of the fields on hadronic observables a comparison of HSD
results with and without fields is exemplified. Our actual calculations show no
noticeable influence of the electromagnetic fields - created in heavy-ion
collisions - on the effect of the electric charge separation with respect to
the reaction plane.
