The basic effects of metallic electrodes on planar monolayers of electric dipoles are investigated. The electric dipoles are arranged along a grid (which is rhombic in the general case) and can rotate around the grid nodes in the monolayer plane. The electrode charge densities are properly approximated in order to define an approximate analytical expression for the electric field generated by each electrode. Interactions among dipoles, among dipoles and electrodes, and among electrodes are simplified. A set of equilibrium hysteresis cycles for the dipole monolayer that are due to a properly charged electrode are presented and discussed for different shapes of the rhombic grid. Then, the possibility of employing electrodes to measure a voltage representative of the polarization of the dipole lattice is explored. Two sets of equilibrium hysteresis cycles related to the polarization of the dipoles in the grid and to the output voltage are presented and discussed. The correspondence between the output electrode voltage and the polarization of the dipole monolayer points out the role of the electrodes both in controlling and in detecting transitions among stable equilibrium configurations of a dipole lattice.