04/06/2015PHY 712 Spring 2015 -- Lecture 281 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 28: Continue reading Chap. 14 – Radiation.

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04/06/2015PHY 712 Spring Lecture 281 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 28: Continue reading Chap. 14 – Radiation by moving charges 1.Motion in a line 2.Motion in a circle 3.Spectral analysis of radiation

04/06/2015PHY 712 Spring Lecture 282

04/06/2015PHY 712 Spring Lecture 283 Radiation from a moving charged particle x y z Rq(t)Rq(t) r r-R q (t) q

04/06/2015PHY 712 Spring Lecture 284 Liénard-Wiechert fields (cgs Gaussian units):

04/06/2015PHY 712 Spring Lecture 285 Electric field far from source:

04/06/2015PHY 712 Spring Lecture 286 Poynting vector:

04/06/2015PHY 712 Spring Lecture 287 Power radiated

04/06/2015PHY 712 Spring Lecture 288 Radiation from a moving charged particle x y z Rq(t)Rq(t) r r-R q (t r )=R q  v.

04/06/2015PHY 712 Spring Lecture 289 Radiation power in non-relativistic case -- continued

04/06/2015PHY 712 Spring Lecture 2810 Radiation distribution in the relativistic case This expression gives us the energy per unit field time t. We are often interested in the power per unit retarded time t r =t-R/c:

04/06/2015PHY 712 Spring Lecture 2811 Radiation distribution in the relativistic case -- continued For linear acceleration:

04/06/2015PHY 712 Spring Lecture 2812 Power from linearly accelerating particle  =0  =0.5  =0.7

04/06/2015PHY 712 Spring Lecture 2813 Power from linearly accelerating particle

04/06/2015PHY 712 Spring Lecture 2814 Power distribution for linear acceleration -- continued y z x    r 

04/06/2015PHY 712 Spring Lecture 2815 Power distribution for circular acceleration y z x    r 

04/06/2015PHY 712 Spring Lecture 2816 y z x    r  Power distribution for circular acceleration 

04/06/2015PHY 712 Spring Lecture 2817 Spectral composition of electromagnetic radiation Previously we determined the power distribution from a charged particle:

04/06/2015PHY 712 Spring Lecture 2818 Spectral composition of electromagnetic radiation -- continued Parseval’s theorem Marc-Antoine Parseval des Chênes

04/06/2015PHY 712 Spring Lecture 2819 Spectral composition of electromagnetic radiation -- continued

04/06/2015PHY 712 Spring Lecture 2820 Spectral composition of electromagnetic radiation -- continued

04/06/2015PHY 712 Spring Lecture 2821 Spectral composition of electromagnetic radiation -- continued

04/06/2015PHY 712 Spring Lecture 2822 Spectral composition of electromagnetic radiation -- continued

04/06/2015PHY 712 Spring Lecture 2823 Spectral composition of electromagnetic radiation -- continued

04/06/2015PHY 712 Spring Lecture 2824 Example – radiation from a collinear acceleration burst

04/06/2015PHY 712 Spring Lecture 2825 Example: r  vv

04/06/2015PHY 712 Spring Lecture 2826 Spectral composition of electromagnetic radiation -- continued