This paper considers the behavior of the frequency and transient responses of the magnetic field created by currents in conducting bodies. It is assumed that the surrounding medium is an insulator. The relationship between the low-frequency part of the frequency spectrum and the late stage of the transient response depends on the type of conductor. These responses and the distribution of the spectrum poles differ for conductors having finite and infinite dimensions. The dependence of various components of the field on conductivity differs, which is important for understanding the resolving capabilities of the inductive methods.