1. 03/20/2015PHY 712 Spring 2015 -- Lecture 221 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 22: Start reading Chap. 9 A.Electromagnetic waves due to specific sources B.Dipole radiation patterns

2. 03/20/2015PHY 712 Spring 2015 -- Lecture 222

3. 03/20/2015PHY 712 Spring 2015 -- Lecture 223

4. 03/20/2015PHY 712 Spring 2015 -- Lecture 224 Formulation of Maxwell’s equations in terms of vector and scalar potentials

5. 03/20/2015PHY 712 Spring 2015 -- Lecture 225 Formulation of Maxwell’s equations in terms of vector and scalar potentials -- continued

6. 03/20/2015PHY 712 Spring 2015 -- Lecture 226 Solution of Maxwell’s equations in the Lorentz gauge -- continued

7. 03/20/2015PHY 712 Spring 2015 -- Lecture 227 Electromagnetic waves from time harmonic sources

8. 03/20/2015PHY 712 Spring 2015 -- Lecture 228 Electromagnetic waves from time harmonic sources – continued:

9. 03/20/2015PHY 712 Spring 2015 -- Lecture 229 Electromagnetic waves from time harmonic sources – continued:

10. 03/20/2015PHY 712 Spring 2015 -- Lecture 2210 Electromagnetic waves from time harmonic sources – continued:

11. 03/20/2015PHY 712 Spring 2015 -- Lecture 2211 Electromagnetic waves from time harmonic sources – continued:

12. 03/20/2015PHY 712 Spring 2015 -- Lecture 2212 Forms of spherical Bessel and Hankel functions:

13. 03/20/2015PHY 712 Spring 2015 -- Lecture 2213 Electromagnetic waves from time harmonic sources – continued:

14. 03/20/2015PHY 712 Spring 2015 -- Lecture 2214 Electromagnetic waves from time harmonic sources – continued:

15. 03/20/2015PHY 712 Spring 2015 -- Lecture 2215 Electromagnetic waves from time harmonic sources – continued:

16. 03/20/2015PHY 712 Spring 2015 -- Lecture 2216 Electromagnetic waves from time harmonic sources – continued: Note: in this case we have assumed a restricted extent of the source such that kr’<<1.

17. 03/20/2015PHY 712 Spring 2015 -- Lecture 2217 Electromagnetic waves from time harmonic sources – continued:

18. 03/20/2015PHY 712 Spring 2015 -- Lecture 2218 Example of dipole radiation source

19. 03/20/2015PHY 712 Spring 2015 -- Lecture 2219 Example of dipole radiation source -- continued Relationship to pure dipole approximation (exact when kR  0)