1. Monday Week 2 Lecture Jeff Eldred1
Monday Week 2 Lecture
Jeff Eldred
Relativistic Kinematics, Retarded Potentials, Synchrotron Radiation 1 1 1 1 1

2. Overview Relativistic Kinematics Part II: Retarded Time2
Overview
Relativistic Kinematics
Example of Neutrino Beams
Part II: Retarded Time
Retarded Time
Potential from a moving point charge
Lienard Wiechert Potentials
Power Radiated from a moving charge 2 2 2 2 2

3. 3
Relativistic Decay 3 3 3 3 3

4. Relativistic Decay Center of Mass Frame. Conservation of Momentum:
Conservation of Energy:
Solve for p, E: 4 4 4 4

5. Relativistic Decay
Solve for p, E:
Boost into Lab Frame: 5 5 5 5

6. Pion & Kaon Decays 6 6 6 6

7. 7
Retarded Time 7 7 7 7 7

8. Fields at the Speed of Light
Einsteinian causality requires that no information propagate faster than the speed of light .
The changes in E & B fields propagate at the speed of light, radiating outward from a changing source.
See Java Demo. 8 8 8 8

9. Retarded Time
A point in space is affected by the E-fields originating from a source in the past, at a time called the retarded time.
In the past, the position of the source will have changed and that will in turn impact the time that should be evaluated. 9 9 9 9

10. Retarded Time & Light Cone10 10 10 10

11. Retarded Potentials 11 11 11 11

12. 12
Moving Point Charge 12 12 12 12 12

13. Moving Point Charge
Solve by change of variables: 13 13 13 13

14. Change of Variables 14 14 14 14

15. Moving Point Charge Potentials
We have derived:
A similar derivation shows that: 15 15 15 15

16. Match what we found before?
There is a trick we can use: 16 16 16 16

17. Lienard-Wiechert Potentials
Actually this form is valid even for point sources not moving in a straight line at constant velocity. 17 17 17 17

18. Fields from a Point Charge18 18 18 18

19. 19
Power Radiated 19 19 19 19 19

20. Power Radiated Radiation in reference frame in which Beta is small:
Integrate over Poynting for radiation:
Linear acceleration:
Circular acceleration: 20 20 20 20