In-situ observations and modeling work have indicated the interaction between the solar wind and lunar crustal magnetic anomalies. This interaction will thus alter the near-surface plasma environment in the magnetic anomaly regions and may have effects on the formation of unusual albedo features, the ‘lunar swirls’ and possibly also on the production (or loss) of volatiles (e.g. hydroxyl). This interaction is complicated by the complex geometries of the lunar crustal magnetic fields. Here we present a series of laboratory investigations that we have done for understanding fundamental physical processes of the plasma interaction with magnetic dipole fields above an insulating surface. The dipole field was oriented parallel, oblique and normal to the surface. We investigated moderate strength magnetic fields in which the electrons were magnetized while the ions were unmagnetized. Complex potential distributions were shown with enhanced electric fields, as the electrons and ions interact with the magnetic field differently. Several interesting physical processes have been identified. When the dipole was parallel to the surface, the electrons were shielded away from the center, the surface was charged positively by the ions. When the dipole was normal to the surface, a large fraction of the electrons was reflected in the central cusp due to the magnetic mirror effect. When the dipole field obliquely intersected the surface, an asymmetric potential distribution developed. Non-monotonic sheaths were observed in all these cases. Our experimental results indicate that plasma environment near the lunar surface can be greatly modified in the magnetic anomaly regions. Further studies will include a flowing plasma and dusty surface.