We point out that recent observations of the time variations in thunderstorms electric fields, both aloft and at the ground, can be interpreted in terms of a total Maxwell current density that varies slowly with time in the intervals between lightning discharges. We utilize this quasi-state behavior to estimate and map the Maxwell current densities under a small Florida thunderstorm using data provided by a large field mill network. An area integral of these current densities gives a total Maxwell current just above the ground of about 0.5 A, a value which is a reasonable lower limit for the total Maxwell current produced by the cloud, and an upper limit for the rate of charge tranport to ground between lightning flashes. Using the quasi-static behavior of the Maxwell current density, we derive an expression for the field-dependent current density under a thunderstorm during the field recovery following a lighning discharge, and we infer values of air conductivity under the small storm which range from 2 to 6¿10-13 mho/m. Finally, we present data that indicate that the area-average Maxwell current is not usually affected by lightning, but instead varies slowly throughout the evolution of the storm. Therefore, we suggest that cloud electrification processes probably do not depend on the cloud electric field, which exhibits large and rapid time variations, as much as they do on more slowly varying quantities, such as the meterological structure of the storm and/or the storm dynamics.