  The conservation of the energy flux in turbulent jets which propagate in the
intergalactic medium (IGM) allows deducing the law of motion in the classical
and relativistic cases. Three types of IGM are considered: constant density,
hyperbolic and inverse power law decrease of density. An analytical law for the
evolution of the magnetic field along the radio-jets is deduced using a linear
relation between the magnetic pressure and the rest density. Astrophysical
applications are made to the centerline intensity of synchrotron emission in
NGC315 and to the magnetic field of 3C273.
