Alternating iteration method on approximate reasoning of electric field

This paper studied the problem of approximate reasoning on a static, active and axial symmetric electric field. Making use of Maxwell's equation set and infinitesimal calculus provides a kind of alternating iteration method when the field on the symmetric axis is limited and differentiate as well as the charge distribution is. Out-of-axis electric field can be transformed into series form by means of the alternating iteration method. This series contains one-dimensional integration of axial symmetric charge distribution and its different order derivatives, and also the electric field on the symmetric axis and its different order derivatives. Approximate reasoning is performed to the electric field generated by the sixth power of charge distribution in sphere symmetry. When choosing only the first seven terms, on the curved surface that r and z are in a ratio of about two to three, the results given by the numerical calculation indicate that the relative error of z component is 0.00000000099%, and that of r component is 0.00000000281%.