The alternating direction iterative of axial symmetric electrostatic field without charge current distribution

Abstract

In this paper, the problems of calculating and solution about axial symmetric electric fields were studied. And accurate theory model was established which can apply in high-performance numerical calculation. The new calculating method was proposed using Maxwell's equations and calculus under the condition that electric field is static, axial symmetric, without charge current distribution, finite, differentiable, integrable. This new calculating method was called alternating iterative method, and expression form was also given. The electric field outside of axis can be expressed as each order derivative and one-dimensional integration of electric field which on the symmetric axis. By means of this method, the result is progression form, which is the best form for computer approximate calculation. It is very easy, quickly and accurately to carry out numerical calculation by using this method. This paper provided this new calculation method, not only has important theoretical significance, but also has broad prospect of application. © 2011 Springer-Verlag Berlin Heidelberg.