The use of magnetic fields is quite common in low-pressure, low-temperature, gas-discharge devices for industrial applications. However, transport in such devices is still not very well clarified, mainly due to the presence of walls playing a crucial role and to the variety of configurations studied. The latter often obstruct the underlying basic physical phenomena and make the different studies valid only for very specific configurations. This work presents a numerical study of particle transport in low-pressure (0.3 Pa) plasmas across a localized transverse magnetic field (magnetic barrier) by means of the 2D3V particle-in-cell with Monte Carlo collisions method. The problem is treated as generally as possible while trying to reveal the basic physics, using very simplified chemistry and considering a simple rectangular configuration. The conditions chosen for the magnetic field are common to many applications—magnetized electrons and almost unmagnetized ions. Two basic configurations with different magnetic field directions are analyzed in detail: magnetic field perpendicular to the simulation plane and along the simulation plane. An extensive parametric study is carried out in order to obtain the main trends and scaling laws for particle transport with respect to different parameters: plasma density, magnetic barrier size and magnetic field magnitude. The total current of electrons crossing the barrier is found to scale linearly with the plasma density, which extends the validity of the obtained results to a wide range of plasma density values.