In this study we derive an analytical expression to describe the electrostatic field in a dust cloud with grain trajectories defined by fluid dynamics and grain charging via contact electrification. In order to solve for the electric field, we merge the fluid dynamic--driven grain motion directly into the basic electrostatic formalism to end up with an electric field dependent on meteorological variables within the dust cloud. We find that the E field is driven by two processes: the currents associated with the charging grains and the increasing velocity difference of varying-sized grains at early times. The resulting processes give rise to an exponentially growing electric field, which for Mars applications, quickly approaches breakdown values. Variations in the growth of the electric field are found with varying grains sizes and varying ambient atmospheric conductivity.