Analytical solutions for capacitance of a semi-cylindrical capacitive sensor

We report the calculation of the capacitance for a Semi-Cylindrical Capacitive Sensor (SCS). In this study, we use conformal mapping to solve the SCS problem in the curve space. The SCS problem can be solved as parallel plates capacitors in the curved space. Based on our calculation, the capacitance of the SCS depends on both the area of the SCS plates and the dielectric materials. The capacitance of the SCS increase related to increasing the wide of SCS plates, in which the SCS can hold more charge. Otherwise, the capacitance of the SCS decrease related to decreasing the wide of SCS plates. The capacitance of the SCS increases along with inserting dielectric materials. The dielectric materials reduce the net electric field, in which to restore this conditions more charges are needed.