Single-component spherical electric field strength sensor with an open system of electrodes in the field of a conducting plane

This work aims to study the interaction of a single-component spherical electric field strength sensor with an open system of sensing electrodes and an electric field near a conductive grounded plane. The sensing electrodes are hollow spherical segments with an angular size of Θ0, diametrically located on a virtual sphere of radius R. A brief theory of the sensor's interaction with the field near the conducting plane is developed. The theory is based on the fundamental equations necessary for constructing a mathematical model of the sensor, allowing one to determine the electric charges q1 and q2 on the sensing electrodes, the open-circuit voltage Uxx between the sensing electrodes, and the interelectrode capacitance C. A mathematical model of the sensor was developed, and mathematical modeling was performed. As a result of mathematical modeling, numerical values of the interelectrode capacitance C, differential charge Δq = q1 – q2 and open-circuit voltage Uxx were obtained. The numerical values were obtained by varying the distance d from the sensor center to the conducting plane for different angular values Θ0 of the spherical segments. For convenience, the relative parameter α = R / d characterizing the spatial measurement range was used in the calculations instead of the distance d. The spatial measurement range varied within the limits 0 < α ≤ 1 with a step of 0.1. The angular size of the spherical segments Θ0 varied from 30° to 90° with a step of 15°. Research has shown that Uxx should be selected as the sensor output signal, with the angular sizes of the spherical segments Θ0≤45°. This choice will provide the sensor with an error caused by the influence of the conductive plane that does not exceed δ(α) ≤ 4.77% over the entire spatial measurement range of 0 < α ≤ 1. When the spatial range is reduced to α = 0.5, the sensor error will not exceed δ(α) ≤ 0.36%. The results of the study confirmed the possibility of using the sensor near a conductive grounded plane.