电磁场与电磁波课件76238207.ppt

2005-1-25 第一章 电磁场的数学物理基础 第一课 第一课 第一课 1.1 Vector Algebra 1.2 Orthogonal Coordinate System 1、Rectangular Coordinate System 2、 Cylindrical Coordinate 4、The relationship among coordinates’ unit vectors 1.3 Gradient of the Scalar Field 1.4 Vector Field’s Flux Divergence 1.5 Vector Field’s Circulation and Curl 1.6 Curl-free Field and Divergence-free Field 1.7 Laplacian Operator Green’s Theorem 1.8 Helmholtz’s Theorem The vector field’s circulation and vortex source For example the velocity field It is unnecessary that vector field are all excited by flux source. There exists another kind of vector source that are totally in difference. The line of the vector field that having been excited by the source will be of closed, the flux on any of a closed surface will be zero, but, the integral of it along a closed line will be a specific value not for zero instead For instance, the integral of a magnetic field on a closed line will be proportional to the current on the surface that is enclosed by the line, showing” The equation reveals the relationship between the circulation of a magnetic field and the current source If the circulation of a vector field on any closed line is zero for constant, it can be said that the vector’s field is such of curl-free field, and it is also known by the name of conservative field. If the circulation of a vector field on any closed line is not zero , saying the vector’s field the curl-have field, the source for excitation is called the vortex source. Current is the vortex source of magnetic field. The Concept of Circulation The circulation of a vector field on a closed line C is defined by the line integral of the given vector towards the closed line C, that is, Given a small surface ?S on point M , its boundary line is denoted as C，the normal of the surface n and the circulating direction of the line follow the right hand law, When?S?0，the limitation is called the Circulation surface density of