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A plasma actuator has been studied using a self-consistent multibody system of quiescent air, plasma, and dielectric. Equations governing the motion of charged and neutral species have been solved with Poisson’s equation. Based on first principles analysis, a functional relationship between electrodynamic force and electrical and physical control parameters has been approximated and numerically tested for air. The magnitude of approximated force increases with the fourth power of the amplitude of rf potential. Thus, the induced fluid velocity also increases. The induced velocity shows momentum injection very close to the actuator surface. There is, however, a very small increase in the induced velocity with the forcing frequency. For the specific range of operational parameters considered, the proposed force relation may help speed up the plasma actuator design process.