  Orbital effects of a magnetic field in a proximitized semiconductor nanowire
are studied in the context of the spatial extent of Majorana bound states. We
develop analytical model that explains the impact of concurring effects of
paramagnetic coupling of the nanowire bands via the kinetic energy operator and
spin-orbit interaction on the Majorana modes. We find, that the perpendicular
field, so far considered as to be detrimental to the Majorana fermion
formation, is in fact helpful in establishing the topological zero-energy-modes
in a finite system due to significant decrease in the Majorana decay length.
