The Study About The Boundary Value Problem Of Electrostatic Field

It is mainly discussed on the plane electrostatic field of different boundary conditions in this thesis. In an usual electromagnetic teaching material, the solution of the most basic planar field is the Principle of superposition, which is applied widely, but for some complex problems associated with boundary value, only the formal solution available. In this paper, we use some specific methods for solving a number of problems with more complicated boundary shape in planar field, and make a solution and visualization about electrostatic field in a charged conductor or a multiply connected domain formed by dielectric medium with a more complicated geometrical shape.Separation of variables is one basic method of boundary value problems. First ofall, we should analyze the specific electrostatic field boundary value problem correctly, list the boundary conditions, obtain the series solution with undetermined constantsincluded, and then work out the undetermined constants in the series solutionaccording to boundary conditions.Image method is an indirect method to solve boundary value problems. The basic principle is to use an imaginary charge (just like a charge) placed outside the targetfield to replace the effect on the field distribution caused by inductive charge (or polarization charge) of conductor surface (or dielectric interface) equivalently, thereby convert the problems of solving practical boundary value into solution of unboundedspace. The theoretical foundation of Image method is the uniqueness theorem.Adopting analytic function transform W = f ( z), the field area with complicated boundary shape in z plane can transform into field area with simple boundary shape in another complex plane . Thus the boundary value problem defined in new complexplane get results easily. The boundary that the new field area is imposed the boundarycondition of formerly field area and get the new potential function afterward. Then,using analytic function transform, the independent variable belonged to new potential functionφ(u , v)can transform back to former independen t variable. This potential functionφ[u ( x , y ) , v ( x ,y)] is the solution of the former potential field. Green function method is to express the response of any source forcing as theoverlap of the response of source forcing of each point in space. It'll make theproblem-solving simplified by solving the response of unit incentive to answer the responseof any source forcing. Several varied forms of Green function are also discussed in this thesis, including limited form, series expansion form and integral one and deduce some forms of equivalent relations on the basis of comparisonFinite difference method is a numerical method which is based on the principle of difference. It converts the problem of continuous domain of electromagnetic field intothe question of discrete system, take advantage of the numerical solution of the discrete points in the net-like, discrete model to approach the true answer of continuous field. In the numerical method of boundary value problem, it's quite simple. Under the available circumstances of computer storage capacity, it's probably to approach the real question more accurate and obtain numerical solution with enough precision for discrete models under a more sophisticated network.various methods of problem-solving skills combined with examples is introduced detaily in this paper, then conclude and analyze their strengths and weaknesses, whichcan help us to master the problem-solving skills of electrostatic field boundary value.