A New Theory and Technique on Measurement Electric Field of Electric Quadrupole

This paper studied the problems on measurement a static, axial symmetric and passive electric field. In the circumstances of the electric field that is limited and differentiable on a symmetric axis, it provides a kind of alternating iteration method by making use of Maxwell equations. Out-of-axis electric field can be transformed into series by means of the method. The series include the field on the symmetric axis and its different order derivatives. Applying the method is very easy, quick and exact to perform numerical calculation. Using the method studied the electric field emitted by an electric quadrupole. Approximate reasoning was performed. When choosing only the first fourteen terms, on the curved surface that r and z is in a ratio of one to three, the relative errors of approximate results and their exact values of z and r components of the electric field are 0.000000003% and 0.000000004% respectively.