GRAVITATIONAL INSTABILITY OF AN INFINITELY EXTENDING LAYER OF FINITE THICKNESS SURROUNDED BY NON-CONDUCTING MATERIAL IN THE PRESENCE OF MAGNETIC FIELD AND ROTATION

Abstract

The present note deals with the study of gravitational instability of an infinite layer of finite thickness surrounded by a non-conducting material in the presence of magnetic field directed parallel to the interfaces and rotating uniformly about an axis perpendicular to the interfaces. The perturbations  considered here are more general than studied by Ognesyan in the case of non-rotating layerand by Chakraborty . in the case of rotating layer. as in these two investigations the perturbations  are taken symmetrical to the mid-plane of the conducting layer. In the absence of the surrounding non-conducting material the system is always overstable. In the presence of the surrounding material the system remains overstable in the presence of the magnetic field if the surrounding material is lighter than the  conducting material but when the surrounding material is heavier than the conducting material there exists a critical wave number k" for a given I, the wave number transverse to the magnetic field and the axis of rotation. such that when k < k" the system is unstable_ The rotating system in the absence of magnetic field is always unstable irrespective of the relative magnitudes of the densities of the conducting and nonconducting materials.