  The interplay among the spectrum, geometry and magnetic field in tubular
neighbourhoods of curves in Euclidean spaces is investigated in the limit when
the cross section shrinks to a point. Proving a norm resolvent convergence, we
derive effective, lower-dimensional models which depend on the intensity of the
magnetic field and curvatures. The results are used to establish complete
asymptotic expansions for eigenvalues. Spectral stability properties based on
Hardy-type inequalities induced by magnetic fields are also analysed.
