Conformal Mapping Applied To The Study Of Plane Electrostatic Field

In electromagnetic field theory, conformal mapping is a special and practical method for solving the boundary value problems of electrostatic field. By conformal mapping, complicated boundaries can be transformed into simpler configurations, meanwhile, both Laplace's equation and Poisson's equation will not be changed, thus the boundary value problems is simplified or transformed. Conformal mapping is particularly valuable to solve some problems with complicated boundaries.This paper deals with some problems about solving the boundary value problems of electrostatic field by using conformal mapping: (1) overview of the historical formation process of conformal mapping and the range of application; (2) quoting and analyzing the related fundamental theories includes the concept of analytic function, the concept of conformal mapping, and the invariability of Laplace's equation and Poisson's equation under the mapping; (3) analyzing the purpose and the basic idea of conformal mapping; (4) concluding the meanings of combination of conformal mapping and other methods for solving boundary value problems, and illustrating the meanings with examples separately; (5) giving the characteristic of the electrostatic field distribution and the general expression of electric field strength under the conformal mapping.Theories of conformal mapping are discussed in this paper, in order to clarify the thinking of conformal mapping, to sum up some concrete application methods of conformal mapping, and to provide references for applying conformal mapping to solving the boundary value problems of electrostatic field.