The alternating direction iterative of static electric field for axial symmetric charge distribution

Abstract

In this paper, the problems of calculating and solution about axial symmetric electric fields were studied. An accurate theoretic model was established that it can be applied in high-performance numerical calculation. The new calculating method was proposed using Maxwell's equations and calculus under the conditions of static, axial symmetric, contains charge, finite, differentiable and integrabel. This new calculating method was called alternating iterative method and its expression form was also given here. 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 and also electric charge. By means of this method, the result is progression form, which is the best form for computer approximate calculation. It's very easy, quick and accurate to carry out numerical calculation by using this method. The calculation method provided in this paper has important theoretical significance and broad prospect of application. © 2011 Springer-Verlag Berlin Heidelberg.