The instability of a self-gravitating fluid cylinder surrounded by a self-gravitating tenuous medium pervaded by transverse varying electric field is discussed under the combined effect of the capillary, self-gravitating, and electric forces. This has been done for all axisymmetric and nonaxisymmetric modes of perturbation. The problem is formulated and solved with excluding the singular solutions, and the stability criterion is derived. Several published works are obtained as limiting cases from the present general case and investigated, and moreover the results are interpreted physically. The model is stable due to the stabilizing effect of the transverse electric field in all modes of perturbation. The destabilizing effect of the capillary and self-gravitating forces is found in small domain in the axisymmetric perturbation. However, the stabilizing effects of the capillary and self-gravitating forces in large axisymmetric domains and in all nonaxisymmetric domains modify and improve the instability of the present model.