Abstract— The electrogravitational instability of a dielectric fluid cylinder surrounded by medium of negligible motion pervaded by varying transverse oscillating electric field has been investigated in the axisymmetric perturbation. The acting forces on the model are: self-gravitating, pressure gradient and electrodynamic forces. The model is governed by Mathieu second order integro-differential equation. Some limiting cases are recovering from the present general one. The electric field is only destabilizing in few states but it is strongly stabilizing in the remaining states. The self-gravitating force is destabilizing in the domain 0 1.0668 x < ≤ while it is stabilizing in the rest. The oscillating time-dependent electric has strong destabilizing effect. Index Terms— Hydrodynamic stability, Self-gravitating, Stability of laminar flows, Time-dependent electric field. I. INTRODUCTION The stability of self-gravitating fluid cylinder has been studied for first time by Chandrasekhar and Fermi (1953). Later on Chandrasekhar (1981) made several extensions as the fluid cylinder is acted by different forces. See also Reynolds (1965), Yih (1968) Nayyar & Murty (1960) and Baker (1983) as the cylinder subject to forces due to electric fields. The electrogravitational stability of a full fluid cylinder has developed by Radwan (1991). He (1991) considered that the fluids are penetrated by constant and uniform electric fields. Manuscript received April 19, 2008. Ahmed E. Radwan, Mathematics Department, Faculty of Science, Ain-Shams University, Cairo, Egypt Tel.: +20 0106163011 ( e-mail : ahmed16853@yahoo.com) Alfaisal A. Hasan, Engineering Physics and Mathematics Department, Faculty of Engineering (Mataria), Helwan University, Cairo, Egypt Tel.: +20 0121617504 (e-mail: alfaisal772001@yahoo.com) Here we study the gravitational stability of a fluid cylinder under transverse time-dependent electric field for axisymmetric perturbations. We obtained second order differential equation of Mathieu, cf. Mclachlan (1964), Morse & Feshbach (1953) and Woodson & Melcher (1968). The details and characteristics of the in-stability domains have been obtained with using the normal mode analysis. II. FORMULATION OF THE PROBLEM Consider a self-gravitating fluid cylinder surrounded by self-gravitating medium of negligible motion. The cylinder of (radius o R ) dielectric constant i ε while the surrounding medium is being with dielectric constant e ε . We assume that the quase-static approximation, (see Baker 1983, Mohamed 1986 and Radwan 1991), is valid and initially there is no surface charges at the interfaces so that the surface charge density will be assumed to be zero during the perturbation. The fluid cylinder is pervaded by the longitudinal time-dependent electric field ( ) (0, 0, ) cos 1 i o o E E t ω = The surrounding medium is penetrated by the varying transverse time-dependent electric field () (0, ,0) cos 2 e o o o R E E t r β ω = where o E is the amplitude of the electric field inside the fluid jet, t is the time and ω is the electric field frequency. The components of , ie o E are considered along the cylindrical polar coordinates ( ) , 0, r z with the z-axis coinciding with the axis of the cylinder. The fluid is acted by the pressure gradient, self-gravitating and electrodynamic forces while Axisymmetric Electrogravitational Stability of Fluid Cylinder Ambient With Transverse Varying Oscillating Field Ahmed E. Radwan, Alfaisal A. Hasan IAENG International Journal of Applied Mathematics, 38:3, IJAM_38_3_02 _______________________________________________________________________________ (Advance online publication: 21 August 2008)