| The theoretical analysis of electromagnetic field in the layered media is widely used in the area of marine electromagnetic detection,geographic detection,analysis for layered earth media's resistivity,eddy current testing,magnetic shilding design,microstrip line design,etc.Among these areas,the plane layered medium and cylinder layered medium are typical models.Complex electromagnetic field problems are usually simplified into these simple models.Most of the simplied layered media models have analytic solutions.These solutions have a wide scope of application,and they have a strong practical and theoretical value.In the existing literature,there are a lot of researches about the the wave problems and eddy current problems for layered media,but the static field problems,having important value in engineering area,attract few attentions.On the basis of the theory of the electromagnetic field,the purpose of this dissertation is to study analytic solutions for the static electromagnetic field distribution in the layered media and uses them into analyzing the magnetic field in the current comparator's magnetic shielding.The main contributions of this thesis can be summarized into the following aspects.(1)Analytical solutions for point source or line source's electromagnetic field for plane layered medium and cylinder layered medium are deduced.The plane layered media and cylinder layered media's boundary value problem models are established.According to Maxwell equations and layered media's boundary conditions,the boundary value problems written by scalar potential or magnetic vector potential are obtained.Solving these boundary value problems,the analytical expressions for electrostatic field,constant electric field and static magnetic field are deduced.Setting electrostatic field in plane layered media and static magnetic field in cylinder layered media as examples,the analytic expression and calculating programs are verified by the FEM's results.(2)An image method for layered media is obtained.With the help of the direct concept of the incidence coefficient,reflection coefficient and refraction coefficient,the unified expression for the position and amount of the image sources are deduced.Using these expressions,the analytic expressions in series form can be obtained directly.This image method has a clear physical meaning and it does not need to solve the recursive equation set to get the undetermined coefficient.In some cases,this image method has a higher efficieny to the traditional analytic method.Using the plane layered media's electrostatic field distribution and the cylinder layered media's static magnetic field distribution as examples,the boundary value problems' analytic solutions,the image method solutions and the FEM solutions are compared as examples.The three solutions have a good agreement to each other,so the image method is proved to be true.(3)Using the analytic solution for magnetic field in the cylinder media produced by line current source,the magnetic field of the current comparator's magnetic shielding is obtained.Respectively using the analytic expressions and commercial finite element software to study the primary current's eccentricity,external current's interference and magnetic shielding's surface air gap's influence to the accuracy of the current comparator.Different magnetic shielding structures are analyzed.According to the analyzed results,an optimization method for the magnetic shielding design is proposed.It provides a theoretical guidance for engineering application.(4)An experimental equipment is built to measure the current comparator's shielding effectiveness.The experiment equipment includes a sectional coil winding on the comparator's magnetic core.By measureing the coil's voltage,the magnetic field in the detection core can be calculated and then the shielding effectiveness of the magnetic shielding can be obtained.The experimental results have a good agreement with the theoretical ones.This proves the rightness of the theoretical solutions. |
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