1. Infinitesimal Dipole

2. Outline Maxwell’s equations – Wave equations for A and for  Power: Poynting Vector Dipole antenna

3. Maxwell Equations Ampere: Faraday: Gauss:

4. Constitution Relation

5. Vector Magnetic PotentialA Applying in Faraday’s Law:  is the Electric Scalar Potential

6. Ampere’s Law:

7. Lorentz’ condition Assuming The wave equation

8. Gauss’ Law

9. Wave equation For sinusoidal fields (harmonics): where

10. Outline Maxwell’s equations – Wave equations for A and for  Power: Poynting Vector Dipole antenna

11. Poynting Vector

12. Average Poynting Vector S In free space:

13. Outline Maxwell’s equations – Wave equations for A and for  Power: Poynting Vector Infinitesimal Dipole antenna

14. Find A from Dipole with current J Line charge w/uniform charge density,  L x z  r r 0 JzJz AzAz Assume the simplest solution A z (r):

15. To find…. Assume the simplest solution A z (r):

16. Homogenous Equation (J=0) Which has general solution of:

17. Apply B.C. If radiated wave travels outwards from the source: To find C2, let’s examine what happens near the source. (in that case k tends to 0) So the wave equation reduces to

18. Now we integrate the volume around the dipole: And using the Divergence Theorem

19. Comparing both, we get:

20. Now from A we can find E & H Using the Victoria IDENTITY: And Substitute:

21. The magnetic filed intensity from the dipole is:

22. Now the E field:

23. The electric field from infinitesimal dipole:

24. General @Far field r> 2D 2 / Note that the ratio of E/H is the intrinsic impedance of the medium.

25. Power :Hertzian Dipole

26. Radiation Resistance