System and method to measure or generate an electrical field downhole

The invention relates to measuring and generating electrical fields downhole. In one embodiment a system is provided that includes an amplifier connected to a first electrode in electrical contact with the Earth via an operative capacitive coupling. An additional electrode and amplifier are disposed in the borehole opposite the first electrode and constitute a first pair of electrodes spaced in a direction orthogonal to the axis. A second electrode is part of a group of counter electrodes spaced from each other and disposed outside the borehole. The first pair of electrodes and the amplifiers are configured to be one of a source that generates an electrical field in a direction substantially orthogonal to the axis of the borehole and a sensor that measures an electric field substantially orthogonal to the axis of the borehole.