Trajectories of paramagnetic particles in regular infinite rectangular and rhombic lattices of parallel magnetized fibers have been calculated. The mathematical model for this analysis accounts for both the collective magnetic and the collective fluid effects of all the fibers in the lattice in the potential flow regime. The viscous force on the particles is taken to be the Stokes force, and diffusion and particle inertia are assumed to be negligible. The particle capture cross section for a fiber in a lattice is found to be significantly different from the isolated fiber cross section for closely packed fibers. However, they become equal as the filter porosity approaches unity. It is seen that channels form, allowing particles to pass through the filter. These channels persist for arbitrarily large porosity, but can be made as narrow as desired by increasing the ratio of magnetic to viscous forces.