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Electrospinning utilizes an electrical force to generate a fine, charged jet from the surface of a viscous liquid. This jet moves straight towards a grounded collector for a certain distance, then bends into spiral coils; finally, the jet solidifies and collects as nonwoven cloth. The onset and development of the electrical bending instability were investigated. Under certain conditions, high applied voltage prohibited the onset of bending and a straight jet reached the collector. Submicron fibers were produced by collecting a straight jet on a moving collector. The diameter, velocity and the longitudinal stress along the jet axis were measured using custom-built equipment. The relaxation of longitudinal stress along the jet was experimentally verified. Buckling instabilities of electrospinning jets were observed and compared with the behavior of uncharged jets. A novel pendulum-like motion of a straight electrified jet was observed and the resulting hierarchical structures made from buckled fibers were presented. A theoretical model was proposed and simulated results showed reasonable agreement with the experimental observations.