[理学]175608502_高等电动力学4.ppt

Chapter 4Time-Varying Boundary-Value Problems Uniqueness Theorem Orthogonal Curvilinear Coordinate Systems Solution of Vector Helmholtz Equations Method of Direct Solution Method of Longitudinal Components Method of Scalar Wave Functions Method of Hertz Vectors Boundary Conditions of Helmholtz Equations Separation of Variables Electromagnetic Waves in Cylindrical Systems Solutions in Rectangular Coordinates Solutions in Circular Cylindrical Coordinates Solutions in Spherical Coordinates Vector Eigenfunctions and Normal Modesion Separation of Variables 11 orthogonal coordinate systems Separation of Variables 11 orthogonal coordinate systems Separation of Variables 11 orthogonal coordinate systems Electromagnetic Waves in Cylindrical Systems Scalar Helmholtz equation in cylindrical system Let Substitute into Helmholtz equation and devided by U Solution of the equation of z Electromagnetic Waves in Cylindrical Systems Solution of the equation of z Electromagnetic Waves in Cylindrical Systems Electromagnetic Waves in Cylindrical Systems Electromagnetic Waves in Cylindrical Systems Electromagnetic Waves in Cylindrical Systems Solution of Helmholtz Equations in Ractangular Coordinates becomes In general cylindrical coordinates, scalar Helmholtz equation For rectangular coordinates, set as It can be separate into two equations: becomes or Substituting to the equation and subtracting yields Let Solution of Helmholtz Equations in Ractangular Coordinates Equations for x and y Equation for z Equations become Solutions become Solution of Helmholtz Equations in Ractangular Coordinates Solution of Helmholtz Equations in Ractangular Coordinates Ractangular Harmonics Solution of Helmholtz Equations in Ractangular Coordinates Field components For traveling waves along +z Solution of Helmholtz Equations in Ractangular Coordinates For rectangular coordinates, set as Field components Solution of Helmholtz Equations in Ractangular Coordinates For rectangular coordi