Generally speaking, a field generated by a current located on any surface depends on the shape of the surface and the current value and its distribution. The main idea discussed below is based on the existence of such surfaces for which a certain property of fields generated by currents distributed on these surfaces does not depend on the currents and is fully and soley determined by the surfaces. This is such a property that any complete system of functions generates an incomplete system of fields. This means that it is impossible not only to realize but even to approximate any given field by the generated field if the given field does not satisfy this condition. In this case, the corresponding inverse problem of the approximate current synthesis is not solvable. Practical results have been received for the horn construction, the determination of the scattering body shape and so on.