We study the properties of an electromagnetically interacting medium in the presence of high concentration of electrons at extremely high temperatures and chemical potentials. We show that the electromagnetic properties of a medium such as the electric permittivity, magnetic permeability, magnetic moments and the propagation speed of electromagnetic waves as well as the corresponding particle processes depend on temperature and density of the medium. Electromagnetic properties of neutrinos are significantly modified due to their interactions with electrons when they propagate through such a medium of hot and dense electrons.