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In the present study, the deformation of a droplet is numerically modeled by considering the dynamic model for electric charge migration at the drop interface under the effect of a uniform electric field. The drop and its ambient are both considered behaving as leaky dielectric fluids. Solving the charge conservation equation at the interface, which is the most important part of this study, the effect of conduction and convection of charges on different deformation modes will be explored. In this work, the interface is followed by the level set method and the ghost fluid method (GFM) is used to model the jumps at the interface. Physical properties are also chosen in a way that solving the charge conservation equation becomes prominent. The small drop deformation is investigated qualitatively by changing various effective parameters. In cases, different patterns of charges and flows are observed indicating the importance of electric charges at the interface. It is also shown that the transient behavior of deformation parameter can be either a monotonic or a nonmonotonic approach toward the steady-state. Moreover, large drop deformations are studied in different ranges of capillary numbers. It will be shown that for the selected range of physical parameters, considering the dynamic model of electric charges strongly affects the oblate deformation. Nevertheless, for the prolate deformation, the results are approximately similar to those obtained from the static model.