The error evaluation of the electric field strength in the charge simulation method

In the calculation of the electric field with the charge simulation method, it is difficult to judge the magnitude of the field strength in the area, especially the accuracy of the field strength. It is found that with a common rod-plane electrode arrangement the accuracy of the curvature radius of the calculation is consistent with the error of the field strength. This situation is due to the use of the derivative in the calculation, and the field strength itself is the gradient of the potential. Therefore, a criterion for the field strength is obtained, which can be used in an unbounded area with an electrode with a definitive curvature radius. The authors give formulas for the potential and its derivative for a finite charged line and a semi-infinite charged line (including mirror charges)