Some Boundary Value Problems About The Electrostatic Field Have Been Solved And Described

Some research and discussion about the method for solving electromagnetic field problems are made in this paper. It is mainly used that some methods for specific skills to solve some plane field problems with more complex boundary shapes.The electrostatic fields are solved and visualized in complex geometry of the charged conductor or dielectric formation of complex connected domain.The solutions to the electrostatic boundary value problems mainly classified into two categories, namely, analytic method and numerical method.Variable separation method, image method, Green function method, conformal transformation method, finite difference method, numerical calculation method are commonly used for solving electrostatic field boundary value problems.Various methods have their own characteristics and applicable conditions, and they complement each other, in practice the specific issues should be combined to select a suitable method, usually used in conjunction with a variety of solution. [1] The electrostatic field within the conductor angular region: flexibility of the direct method or conformal transformation by selecting the appropriate coordinate system derive electrostatic fields of a special angular domain and arbitrary angular distribution. [2]The research polarization electric field strength within the uniform dielectric ellipsoid: potential distribution In vivo the dielectric ellipsoid in uniform external electric field is obtained by the derivation of rigorous and the use of ellipsoidal coordinates. the mathematical expression of the polarization electric field strength in the ellipsoid body is obtained and the angle between the direction of the polarization field and the direction of the external electric field is calculated. [3] The electric field of columnar distribution electric charge of convex lens-shaped cross section: it is very difficult to obtain the solution with the Poisson equation or the Laplace equation for the convex shape is the more complex geometry, not a full spherical or cylindrical surface, field electric strength and electric potential of the columnar distribution charge of convex lens-shaped cross section are easy obtained by the use of conformal mapping and the equipotential lines are depicted. [4]Dielectric sphere with eccentric spherical particle: people have been concerned about electromagnetic field boundary problems of layered dielectric and inhomogeneous dielectric, the electric fields inside and outside the ball are obtained and the approximate expression of electric dipole moment and electric quadrupole moment outside the ball are given by using the separation of variables. [5] The electrostatic field near point conductor surface: the conical conductor for the study. in the steady state, the electric potential near the tip of the conductor satisfies the Laplace equation, after separation of variables, through the joint German Le functions and the introduction of boundary conditions, the potential distribution near the tip of the conductor can be obtained . The equipotential lines near the tip of the conductor which graphically show the potential distribution of cutting-edge by furthermore mathematical tool Mathematica are depicted .The methods of solving the five boundary value problems in the text have a certain physical meaning and practical content, which open up new avenues for the depth study of electromagnetic theory and provide a basis for engineering applications.