Computation of 3D electrostatic fields excited by thin conductors

Abstract

Solution of 3D electric fields in a systém of thin charged conductors of general shapes by classical differential methods (FDM, FEM etc.) is extremely difficult duc to ingorance of boundary conditions and existence of geometrically incommernsurable subdomains within the investigated area. Application of integral methods is also complicated because the kernel functions occurring in the first-kind Fredholm equations are integrable only in 2D and not in 1D. Conductors with 2D cross-section correspond, in fact, with the physical reality, but their introduction leads to very large fully populated matrices whose processing on common PCs is still practically impossible. The paper offers an alternative algorithm consisting in substitution of each thin conductor by a set of point charges placed on a helicoidal curve surrounding it. The theoretical analysis is supplemented with a illustrative example and discussion of the results (convergence, accuracy).