For finite systems boundaries can introduce remarkable novel features. A well known example is the Casimir effect [1, 2] that is observed in quantum electrodynamic systems. In classical systems too novel effects associated with finite boundaries have been observed, for example the surface plasmon mode  that appears when the plasma has a finite extension. In this work a novel instability associated with the finite transverse size of a beam owing through a plasma system has been shown to exist. This instability leads to distinct characteristic features of the associated magnetic field that gets generated. For example, in contrast to the well known unstable Weibel mode of a beam plasma system which generates magnetic field at the skin depth scale, this instability generates magnetic field at the scales length of the transverse beam dimension . The existence of this new instability is demonstrated by analytical arguments and by simulations conducted with the help of a variety of Particle - In - Cell (PIC) codes (e.g. OSIRIS, EPOCH, PICPSI). Two fluid simulations have also been conducted which confirm the observations. Furthermore, laboratory experiments on laser plasma system also provides evidence of such an instability mechanism at work.