Extensive air shower radio electric fields can be evaluated at large impact parameter with analytical expressions. Such a theoretical tool is most valuable in the present phase where the capabilities of the radio detection of extensive air shower are under investigations. It can help shaping strategies for the analysis of radio detection data. It can also be used to perform non trivial test of much more detailed numerical approaches which are currently under development. The approximation leading to such a formulation will be presented and two applications will be discussed: the "inverse" problem of how to go from a sampling of the radio electric field on a few antennas to the main characteristics of the extensive air shower, and the question of the antenna spacing of a giant array for ultra high energy cosmic rays.