The transformer ensures the transmission of electrical power by electromagnetic induction between the first (11) and second (12) coils concentrically arranged on the first (7) and second (8) tubular parts respectively, which are made of a ferromagnetic material, and coaxially mounted in such a way that an outer surface (13a, 13b, 13c) of one part can rotate in relation to an inner surface (14a, 14b, 14c) of the other. These surfaces each consist of two straight cylindrical rotation surfaces (13a, 13c; 14a, 14c) of different diameters, each extending from one of the axial ends of the part (7; 8) to an intermediate radial shoulder (13b, 14b) for connecting these surfaces. The parts (7; 8) are arranged head-to-foot one inside the other so as to delimit, between the shoulders (13b; 14b), an annular space receiving the coils (11, 12), between two annular gaps each delimited by two (13a, 14a; 13b, 14b) of the facing cylindrical surfaces of the first (7) and second (8) parts. Each coil comprises at least one layer of a plurality of strip-like windings.