矢量分析及场论基础.ppt

矢量分析及场论基础 第一页，共三十七页，2022年，8月28日 Vector analysis Introduction Vector analysis is the language used in the study of electromagnetic fields. Without the use of vectors, the field equations will be unwieldy to write and onerous to remember. A single equation in vector form is sufficient to represent up to three scalar equations. We begin our discussion by defining scalar and vector quantities. 第二页，共三十七页，2022年，8月28日 §0-1 标量(Scalar)和矢量(Vector) Most of the quantities encountered in electromagnetic fields can easily be divided into two classes, scalars and vectors. 标量：A physical quantity can be completely described by its magnitude is called a scalar. For example, mass(质量)、time、temperature、work(功)、electric charge(电荷) Each of these quantities is completely describable by a single number. In fact, all real numbers are scalars. 第三页，共三十七页，2022年，8月28日 矢量： A physical quantity having a magnitude as well as a direction is called a vector. For example, force、velocity(速度)、torque(力矩)、acceleration(加速度)、electric field、magnetic field. The magnitude of a vector is depicted by a line segment, and the direction is indicated by means of an arrow. 第四页，共三十七页，2022年，8月28日 Vector operations 矢量运算 Vector addition 加法 Vector subtraction 减法 Multiplication of a vector by a scalar 矢量乘以标量 Product of two vectors两矢量的乘积 Dot product 点积 Cross product 叉积 第五页，共三十七页，2022年，8月28日 §0-2 The orthogonal coordinate systems 正交坐标系 Up to this point we have kept our discussion quite general and used graphical representations when manipulating vectors. From a mathematical point of view it is very convenient to work with vectors when they are resolved into components along three mutually orthogonal directions. 第六页，共三十七页，2022年，8月28日 We will mainly use three orthogonal coordinate systems: We shall now digress to discuss each of these coordinate systems and then resume our discussion of vectors. 坐标系是相对于参考原点确定空间任一点位置的唯一方法， 它可以由三个互相垂直的曲面的交点来确定。 于是，在该点上这些曲面的法线便可规定为坐标轴。 在分析电磁场问题时，往往