1. radiation

2. R E x H power out = power in spherical surface area = 4 R p power in 2 p
power in

3. E must be in the surface of the sphere.
power in R
power out = power in
spherical surface
area = R 2 p
E x H 

4. R E
Stationary charges do not
radiate. E not in sphere.
E  R-2

5. Charges in motion with a constant velocity do not radiate
Charges in motion with a constant velocity do not radiate. E not in sphere. E  R-2 R E

6. no kink kink Coulomb field A AB accelerate BC constant velocity B C
“kink” joins two Coulomb fields
kink
Radius of
sphere = ct

7. J K L Et
cDt Eo
from triangle
r = ct A B C
 vt
v = aDt
acceleration

8. r = ct Eo
 vt
v = aDt J K L Et
cDt A B C

9. accelerated charges radiate em waves
E decays as 1/R
accelerated charges radiate em waves
time-varying currents radiate
in a preferred direction

10. A
vector potential A DV I R r r’

11. transform into spherical coordinates vector potential A I R ADV I R r’
vector potential A
Current element
DI = I DL uz
transform into
spherical
coordinates

12. .01 1
100 

13. far field

14. far field

15. z Eq Hj  r
I DL y j x

16. small loop
half wave dipole

17. far field

18. current loop r q
In far field, E will be in the uj direction and H will be in the uq direction
I DL uj j a

19. I DL uj a j r q
note

20. Could a realistic antenna be described in terms of
the sum of many small
antennas?

21. educated guess list
far field
What is this?

22. educated guess list I(z) confined to length of antenna h Imax at z = 0
Integrable function

24. z r q r’ q’ z’

25. I(z’) =Io

26. x =

27. AM radio -

28. -
AM radio -