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A new experimental set-up which consists of a pulse magnetic field system has been developed to capture the different phases of expanding plasma plume across the transverse magnetic field, varying from 0 to 0.57 T. Two internally synchronized ICCD cameras mounted in the orthogonal direction have been used to record the two directional projections (across and along the magnetic field directions) of the plasma plume. The plume takes the conventional ellipsoidal shape in the absence of a magnetic field. Well-defined cavity-like structures have been observed in a plane perpendicular to the field direction, which are dominant at the early stage of the plasma and comparatively lower magnetic fields. As the time evolves, the cavity changes to jet/cone-like structures which in turn change to slab-like structures with a further increase in time delay. On the other hand, well separated intensity columns (striation-like structures) appeared in a plane parallel to the magnetic field direction, which are more apparent at a higher magnetic field. Based on the projections of plume images in two perpendicular planes, the three dimensional structure of the plasma plume is modeled as an elliptical cylinder-like structure. The time dependence of dynamics and geometry of the plasma plume in the presence of a magnetic field are correlated with the expansion in diamagnetic and non-diamagnetic regimes. The validity of plasma instability, which is responsible for observed striation-like structures, is also discussed.