has been recently shown that center vortices, when transformed to the Coulomb gauge, indeed reside on the Gribov horizon [@goz].

The curvature of the Gribov region contributes to matrix elements via the functional measure determined by the determinant of the Faddeev-Popov operator. This determinant prevents analytical calculations of functional integrals, however it has been shown that its effect can be approximated by imposing appropriate boundary conditions on the gluon wave functional [@as4; @hr]. This wave functional is in turn constrained by minimizing the expectation value of the energy density which leads to a set of coupled self-consistent Dyson equations [@as1; @sw]. Once the wave functional is determined it is possible to calculate the distribution of the chromo-electric field in the system. This is the main subject of this paper.

In the following we study the chromo-electric field in the presence of the static quark-antiquark and three-quark systems, prototypes for a meson and a baryon respectively. Recent lattice computations indicate that the gluonic field near the static $Q-{\bar Q}$ state forms flux tubes. There are also indications that for the $QQQ$ state the fields arrange in the so called “Y”-shape [@tak; @latY], although some work supports the “$\Delta$”-shape [@latD]. String-like behavior 