New model of the capturing vortices in the HTc superconductors is presented, describing their electromagnetic properties, such as the critical current of these materials. Critical current of the superconductors, such as HTc tapes is dependent on the magnitude of the interaction magnetic vortices with pinning centers. This is in fact quantum effect since the magnetic flux in vortices is quantized. Capturing the vortices on the normal state nano-sized inclusions should lead to the modification of the flux distribution in the vortex core depending on the vortex position in the respect to the pinning center edge. These effects are considered in the paper and their influence on the critical current of the HTc materials, basing on the new model of the pinning interaction.