The non-linear AC transport trough a quantum wire with an impurity in the presence of finite-range electron-electron interactions is investigated. We discuss the influence of the spatial shape of the electric field onto the transport properties of the system and find that the scaling behavior of the occupation probability of the sidebands depends on the range of the voltage drop. We observe a cross-over between the Tien-Gordon like scaling of the sidebands and a regime in which the scaling reflects the ranges of both, the electron- electron interaction and the electric field.