Ch 7 Radiation of Electromagnetic Waves 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
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 waves The problem is usually solved in terms of potentials 特征:与1/r正比的电磁场! 2. It is a boundary value problem Source charge and current excites EMF, EMF in turn affects source distribution -- boundary value problem For convenience our discussions are limited to a simple case Distribution of source is known
1. What is EM radiation EM field is excited by time-dependent charge and currents. It may propagate in form of waves. The problem is usually solved in terms of potentials. 2．It is a boundary value problem Source (charge and current) excites EMF, EMF in turn affects source distribution --- boundary value problem! For convenience, our discussions are limited to a simple case – Distribution of source is known. 特征：与1/r 正比的电磁场！
87. 1 vector potential and scalar potential potentials are slightly different from the static cases 1.a) vector potentia sinceB=0, we can introduce vector potential A as the static field,B=VxA
§7.1 vector potential and scalar potential potentials are slightly different from the static cases since ，we can introduce vector potential as the static field, B = 0 A B A = 1.a）vector potential
= 1.b) scalar potential Since×E=-≠0, scalar potential can not be defined as before aA OA V×E V×A=-V× V×(E+) t Define scalar func⑨ 0A 0A e+ at
Since ，scalar potential can not be defined as before 0 = − t B E 1.b）scalar potential B A = t A A t E = − = − ( ) = 0 + t A E = − + t A E Define scalar func t A E = − −
2). Gauge invariance Potentials are not uniquely determined they differ by a gauge transformation. A>A'=A+Vy q→>9=q at Gauge: Given a set of (A, 9) (A, give identical electric and magnetic fields
2)．Gauge invariance t A A A → = − → = + (A, ) Potentials are not uniquely determined, they differ by a gauge transformation. Gauge: Given a set of give identical electric and magnetic fields ' ' ( , ) A