圆周运动和直线运动时的辐射方向Radiationfieldfromarelativistic.PPTVIP

§7.1 vector potential and scalar potential potentials are slightly different from the static cases 2)．Gauge invariance l?规范不变性：在规范变换下物理规律满足的动力学方程保持不变的性质（在微观世界是一条物理学基本原理）。 Get one, get 2nd for free. Solution of d’alembert eq under Lorenz gauge indicates that EM interaction takes time. To study radiation, we use Lorenz gauge. §7.2　Retarded potential §7.3 Electric dipole radiation l?we limit our discussion to charge distribution of periodic motion. Furthermore, size of charge distribution is much smaller than the distance between charge and the observation point. Discussion: （1）E oscillates along longitude and B along latitude lines. Direction of propagating, E and B are orthogonal to each other (right-hand). （2）E,B are proportional to ，so they are propagating spherical waves. They are transverse （TEM波） and maybe regarded as plane wave as . （3）without （ ）, it can be shown that E is no longer perpendicular to k, electric lines are not close, but magnetic lines are still close （TM波）. 4．Energy flux, angular distribution and power of radiation Example: Short antenna §7.4 Magnetic dipole radiation and electric quadrupole radiation §7.5 Radiation from a localized charge in arbitrary motion (Bo-p124) 短天线辐射能力不强。 通常天线长度与波长同数量级，不能用简单的偶极辐射公式。 例：半波天线（长度为半波长） 必须直接用推迟势计算 天线电流要与外场联合作为边值问题求解，一般较复杂。 对于细长直天线，电流分布应是驻波，两端是波节。如 辐射电磁场 The energy flux 要得到高度定向的辐射，可利用天线阵的干涉效应。 张角 电四极辐射 磁偶极辐射 method1：use the retarded potential 粒子看作小体积电荷分布，直接积分 method2：using Lorentz transformation Lienard-Wiechert potential At rest frame where At Lab frame Derivative was performed with respective to t，x. However * * 7.1、potentials of electromagnetic field, gauge invariance 7.2、d’Alembert equation and retarded potential 7.3、electric dipole radiation 7.4、EM radiation from arbitrary motion charge Ch 7 Radiation of Electromagnetic Waves 1. What is EM radiation EM field is excited by time-dependent charge and currents. It may propagate in form of w