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We present semiclassical and quantum mechanical results for the effects of astrong magnetic field in Quantum Wires in the presence of Rashba Spin Orbitcoupling. Analytical and numerical results show how the perturbation acts inthe presence of a transverse magnetic field in the ballistic regime and weassume a strong reduction of the backward scattering interaction which couldhave some consequences for the Tomonaga-Luttinger transport. We analyze thespin texture due to the action of Spin Orbit coupling and magnetic field oftenreferring to the semiclassical solutions that magnify the singular spinpolarization: results are obtained for free electrons in a twodimensionalelectron gas and for electrons in a Quantum Wire.  We propose the systems as possible devices for the spin filtering at variousregimes.Comment: 12 pages, 12 figures, to appear in Phys. Rev.

Rashba effect in two-dimensional mesoscopic systems with transverse magnetic field