We present a set of equations modelling a low-pressure plasma column sustained by a travelling electromagnetic wave in the dipolar mode in the presence of a constant external magnetic field. It is shown that, from a practical point of view, only the m = 1 mode (the right-hand-polarized wave) can sustain plasma columns in a wide region of gas-discharge conditions: plasma radius R, wave frequency omega, magnetic field B0 and low pressures, irrespective of the nature of the gas. We have examined two gas-discharge regimes: free-fall/diffusion and recombination respectively. For a given gas-discharge regime the axial column structure and wave-field characteristics are specified by two numerical parameters: sigma = omegaR/c and OMEGA = omega(c)/omega, where c is the speed of light and omega(c) the electron-cyclotron frequency. The main result of our study is that the magnetic field-makes it possible to sustain a plasma column for values of sigma smaller than sigma(cr) = 0.3726, below which, in the absence of a magnetic field, the dipolar wave cannot produce a plasma. Moreover, at a fixed wave power, the magnetic field - in contrast with the case of plasma columns sustained by azimuthally symmetric waves - increases the plasma density and its axial gradient. The limit of an infinite external magnetic field (OMEGA --> infinity) is also considered. A three-dimensional wave structure is obtained, and it indicates that the wave can be a generalized surface mode, a pure surface or a pseudosurface one.