  We study the properties of magnetised cylindrical polytropes as models for
interstellar filamentary clouds, extending the analysis presented in a
companion paper (Toci & Galli 2014a). We formulate the general problem of
magnetostatic equilibrium in the presence of a helical magnetic field, with the
aim of determining the degree of support or compression resulting from the
magnetisation of the cloud. We derive scale-free solutions appropriate to
describe the properties of the envelopes of filaments at radii larger than the
flat-density region. In these solutions, the polytropic exponent determines the
radial profiles of the density and the magnetic field. The latter decreases
with radius less steeply than the density, and field lines are helices twisted
over cylindrical surfaces. A soft equation of state supports magnetic
configurations that preferentially compress and confine the filament, whereas
in the isothermal limit the field provides support. For each value of the
polytropic exponent, the Lorentz force is directed outward or inward depending
on whether the pitch angle is below or above some critical value which is a
function of the polytropic exponent only.
