Fundamentals of interaction of a single-component spherical electric field strength sensor with an open system of electrodes with a non-uniform field of a point charge

The work focuses on the construction of a single-component spherical electric field strength sensor with an open system of sensitive electrodes, capable of operating in fields of varying non-uniformity with the required error. Spherical shells in the form of hollow spherical segments and their interaction with the electric field of a point source are considered as sensitive electrodes of the sensor. The main theoretical provisions are formed that facilitate the determination of the output signal of the sensor in the form of opencircuit voltage U_xx. The relationship between the output signal of the sensor and its error from the spatial measurement range and from the design dimensions of the sensitive electrodes of the sensor is established. Based on the established relationships, a mathematical model of the sensor is compiled and mathematical modeling is carried out. The result of mathematical modeling are the numerical values of U_xx and the error d from the heterogeneity of the electric field depending on the spatial range a and the angular dimensions of the sensitive electrodes θ₀ of the sensor. The graphs of these dependencies constructed using the numerical values revealed that the permissible angular dimensions of the sensitive electrodes of the sensor should lie in the range of 40° ≤ θ₀ ≤ 50°. This range provides the sensor with an error in modulus not exceeding δ ≤ 5 %. However, the optimal angular size of the sensitive electrodes of the sensor should be considered to be θ₀ ≤ 45°.

A sensor with such an angular size of the sensitive electrodes will have a minimum error in a wide spatial range of measurements and will provide the possibility of creating two- and three-component sensors without overlapping the electrodes. The results of the work can form the basis for evaluation calculations of sensors with an open electrode system.

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