|MadSci Network: Physics|
Radiation means you have certain far field behavior. Generally, electric and magnetic field are in phase but perpendicular to each other, and attenuate inverse proportionally to the distance. Therefore to determine whether there is radiation, you only need to calculate the far field. There is a derivation of the far field of an accelerated particle in the following book: Julian Schwinger etc., Classical Electrodynamics, Ch32.1, Ch32.3, Perseus Books, 1998 The main steps of the derivation are as follows: 1) write down the time-domain far field representation of the scalar and vector potential for general charge and current distribution 2) derive electric and magnetic far field from scalar and vector potential. It is found their strength is proportional to an integral, the integrand of which is the time-derivative of the delayed current distribution 3) Now consider the special case of a particle. The current distribution is a Dirac delta function for the particle. It is found the above integral becomes proportional to its acceleration.
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