电磁场理论第八周课件电磁场论第八周课件电磁场理论第八周课件电磁场理论第八周课件.pptVIP

Review The method of separation of variables: we look for solutions that are products of functions, each of which depends on only one of the coordinates (separable solutions). The partial differential equation is changed into an ordinary differential equation; Boundary conditions are also separated; By solving the so called eigen-value problem, the eigen-value, eigen-function and the eigen-solution are obtained; Review Based on the linearity of the PDE, a solution of the series form can be got. The eigen-solutions are complete and orthogonal with each other, so the undetermined coefficients in the series can be evaluated. Tips : typical boundary conditions and the corresponding solutions should be memorized. (periodic, independent of one coordinate, homogeneous boundary condition, bounded and unbounded areas) Review Boundary value problems: Dirichlet problem, Neumann problem, Robbin problem. (Dirichlet, Neumann and Robin boundary conditions ) The theorem of uniqueness: if the solution to the above mentioned boundary value problems exists, then it is unique. The importance of the theorem. The method of images: planar surface between dielectric and conductor. Review The method of images Cylindrical surface between a conductor and a dielectric : position of the image, line charge density of the image; Spherical surface between a conductor and a dielectric: position and charge of the image; Planar surface between two dielectrics: electric medium, magnetic medium. Review The method of separation of variables for the cylindrical coordinate system. Focus should be on the two dimensional planar static field. Boundary conditions represented by the potential functions: 电磁场理论第八周讲稿 §4.3 直角坐标系内的分离变量法 §4.4 圆柱坐标系内的分离变量法 §4.5 球坐标系内的分离变量法 *§4.6 δ函数 §4.3 直角坐标系内的分离变量法 1、调和函数及场的叠加原理 2、直角坐标系内的分离变量法 例题 1、调和函数及场的叠加原理 静态场的基本向题都可以归结为求势的泊松方程或拉普拉斯方程满足一定边界条件的解。 待求势函数必须既要满足拉普拉斯方程，同时也要满足给定场域的边界条件。 泊松方程与拉普拉斯方程解的关系跟非齐次常微分方程与齐次常微分方程的解类似，即泊松方程的解是拉普