Interaction of high-intensity laser pulses with solid targets results in generation of large quantities of energetic electrons that are the origin of various effects such as intense x-ray emission, ion acceleration, and so on. Some of these electrons are escaping the target, leaving behind a significant positive electric charge and creating a strong electromagnetic pulse long after the end of the laser pulse. We propose here a detailed model of the target electric polarization induced by a short and intense laser pulse and an escaping electron bunch. A specially designed experiment provides direct measurements of the target polarization and the discharge current in the function of the laser energy, pulse duration, and target size. Large-scale numerical simulations describe the energetic electron generation and their emission from the target. The model, experiment, and numerical simulations demonstrate that the hot-electron ejection may continue long after the laser pulse ends, enhancing significantly the polarization charge.