An exact analytic solution is derived for the perturbation of a magnetic field while exposed to an immersed, axisymmetric, azimuthal, steady current source of arbitrary distribution in the presence of a slender, electrically conducting, independently permeated, compressible jet threading the axis of symmetry, subject to an equilibrium pressure balance. A further influence is the enclosure of the magnetic field by a coaxial cylindrical wall. The steady-state result invariably exhibits an infinite discrete superposition of axially decaying terms. In addition, there arise two admissible alternatives involving a fluid parameter λ (dependent on the flow speed, sound speed and both Alfvén speeds pertaining to the jet) together with a scale parameter χ(0) (equal to twice the ratio of the cross-sectional area of the jet to that of its externally enveloping field). Provided that λ exceeds χ(0), each element constituting the current distribution induces a stationary-wave contribution confined, as a consequence of an applied radiation condition, to the upstream domain, corresponding to an upstream-directed group velocity. However, if λ is exceeded by χ(0), this upstream wave is replaced by another decaying term, acting on both sides of every current constituent, like all other decaying terms.