1. 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 by moving charges 1.Motion in a line 2.Motion in a circle 3.Spectral analysis of radiation

2. 04/06/2015PHY 712 Spring 2015 -- Lecture 282

3. 04/06/2015PHY 712 Spring 2015 -- Lecture 283 Radiation from a moving charged particle x y z Rq(t)Rq(t) r r-R q (t) q

4. 04/06/2015PHY 712 Spring 2015 -- Lecture 284 Liénard-Wiechert fields (cgs Gaussian units):

5. 04/06/2015PHY 712 Spring 2015 -- Lecture 285 Electric field far from source:

6. 04/06/2015PHY 712 Spring 2015 -- Lecture 286 Poynting vector:

7. 04/06/2015PHY 712 Spring 2015 -- Lecture 287 Power radiated

8. 04/06/2015PHY 712 Spring 2015 -- Lecture 288 Radiation from a moving charged particle x y z Rq(t)Rq(t) r r-R q (t r )=R q  v.

9. 04/06/2015PHY 712 Spring 2015 -- Lecture 289 Radiation power in non-relativistic case -- continued

10. 04/06/2015PHY 712 Spring 2015 -- 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:

11. 04/06/2015PHY 712 Spring 2015 -- Lecture 2811 Radiation distribution in the relativistic case -- continued For linear acceleration:

12. 04/06/2015PHY 712 Spring 2015 -- Lecture 2812 Power from linearly accelerating particle  =0  =0.5  =0.7

13. 04/06/2015PHY 712 Spring 2015 -- Lecture 2813 Power from linearly accelerating particle

14. 04/06/2015PHY 712 Spring 2015 -- Lecture 2814 Power distribution for linear acceleration -- continued y z x    r 

15. 04/06/2015PHY 712 Spring 2015 -- Lecture 2815 Power distribution for circular acceleration y z x    r 

16. 04/06/2015PHY 712 Spring 2015 -- Lecture 2816 y z x    r  Power distribution for circular acceleration 

17. 04/06/2015PHY 712 Spring 2015 -- Lecture 2817 Spectral composition of electromagnetic radiation Previously we determined the power distribution from a charged particle:

18. 04/06/2015PHY 712 Spring 2015 -- Lecture 2818 Spectral composition of electromagnetic radiation -- continued Parseval’s theorem Marc-Antoine Parseval des Chênes 1755-1836 http://www-history.mcs.st-andrews.ac.uk/Biographies/Parseval.html

19. 04/06/2015PHY 712 Spring 2015 -- Lecture 2819 Spectral composition of electromagnetic radiation -- continued

20. 04/06/2015PHY 712 Spring 2015 -- Lecture 2820 Spectral composition of electromagnetic radiation -- continued

21. 04/06/2015PHY 712 Spring 2015 -- Lecture 2821 Spectral composition of electromagnetic radiation -- continued

22. 04/06/2015PHY 712 Spring 2015 -- Lecture 2822 Spectral composition of electromagnetic radiation -- continued

23. 04/06/2015PHY 712 Spring 2015 -- Lecture 2823 Spectral composition of electromagnetic radiation -- continued

24. 04/06/2015PHY 712 Spring 2015 -- Lecture 2824 Example – radiation from a collinear acceleration burst

25. 04/06/2015PHY 712 Spring 2015 -- Lecture 2825 Example: r  vv

26. 04/06/2015PHY 712 Spring 2015 -- Lecture 2826 Spectral composition of electromagnetic radiation -- continued