Transport of molecules through biological membranes is a fundamental process in biology, facilitated by selective channels and general pores. The architecture of some outer membrane pores in Gram-negative bacteria, common to other eukaryotic pores, suggests them as prototypes of electrostatically regulated nanosieve devices. In this study, we sensed the internal electrostatics of the two most abundant outer membrane channels of Escherichia coli, using norfloxacin as a dipolar probe in single molecule electrophysiology. The voltage dependence of the association rate constant of norfloxacin interacting with these nanochannels follows an exponential trend, unexpected for neutral molecules. We combined electrophysiology, channel mutagenesis, and enhanced sampling molecular dynamics simulations to explain this molecular mechanism. Voltage and temperature dependent ion current measurements allowed us to quantify the transversal electric field inside the channel as well as the distance where the applied potential drops. Finally, we proposed a general model for transport of polar molecules through these electrostatic nanosieves. Our model helps to further understand the basis for permeability in Gram-negative pathogens, contributing to fill in the innovation gap that has limited the discovery of effective antibiotics in the last 20 years.