A Multi-physics numerical model was developed to investigate the influence of a steady magnetic field aligned perpendicular to the welding direction during partial penetration fiber laser beam welding of carbon steel(SCP1-S) in down hand position. Two-dimensional fluid dynamics including phase transition and electromagnetic field partial differential equations were successfully solved with the finite element differential equation solver COMSOL Multiphysic 3.5. The use of magnetic fields to influence weld bead shape and dilution in laser welding of SCP1-S alloys was recently suggested. However, the interaction mechanisms between the SCP1-S melt and the magnetic field are not understood in detail yet, and consequently, the selection of process parameters is so far purely empirical. In this paper, recent results of a study to elucidate interaction mechanisms between a laser-induced melt pool and a magnetic field will be reported and discussed. Based on analytical models for the main potential interaction mechanisms, the relevance to typical welding conditions was assessed. The flow pattern in the melt as well as the weld bead geometry was significantly changed by the induced Lorentz force distribution in the liquid metal. The governing mechanisms identified were implemented into a COMSOL model for laser welding and the effect of the magnetic field on the resulting melt flow was investigated. To validate the results, welding trials were performed on a model system allowing to easily visualizing the effect of melt flow on melt bead dynamics using optical microscopy.