Peculiar solutions of Maxwell equations

Peculiar solutions examined herein are characterized by the fact that vectors corresponding to them and describing electromagnetic field are equal to zero in free space points, i.e. beyond restricted area V, occupied with a substance, at the same time electromagnetic potentials of the field are different from zero within the whole space. The paper demonstrates that Maxwell equation solutions will be peculiar if electric current density j, polarization P and magnetization J considered as electromagnetic field sources represent gradients of smooth finite functions in V domain, and also that variation of sources values in time instantly transferred to the field vectors, without delaying.