1. Maxwell's equations
wave equation

2. Maxwell’s equations

3. Time harmonic excitation
Maxwell's equations
Time harmonic excitation

4. boundary conditions for time varying fields
tangential electric fields are continuous
normal components of
displacement flux density
differ by a
surface charge density

5. boundary conditions for time varying fields
tangential magnetic field intensities
differ by
a surface current density
normal components of
magnetic flux density
are continuous

6. Plane waves in a vacuum

7. Plane waves in a vacuum

8. Plane waves in a vacuum

9. Plane waves in a vacuum

10. units

11. Look at the dimensions

12. Look at the numbers

13. c is the speed of light
vector wave equation

14. Galileo
Galileo attempts to measure the speed of light by a lantern relay between distant hilltops. He gets a very large answer.

15. Einstein

16. There was a young lady named Bright,
Whose speed was far faster than light;
She set out one day,
In a relative way,
And returned home the previous night.

17. Patent 6,025,810 was issued to David Strom for a "hyper-light-speed antenna." The concept is deceptively simple: "The present invention takes a transmission of energy, and instead of sending it through normal time and space, it pokes a small hole into another dimension, thus sending the energy through a place which allows transmission of energy to exceed the speed of light." It's also good for your begonias. According to the patent, this portal "allows energy from another dimension to accelerate plant growth."

18. one dimensional wave equation
vacuum
infinite parallel planes
polarization x y z Ey

19. one dimensional wave equationx y z Ey

20. MOST GENERAL SOLUTION!!
Ey = a F(z - ct) + b G(z + ct)
= a Fb G
where F & G are arbitrary functions that depend on the excitation

23. Q. E. D.
Ey = a F(z - ct) + b G(z + ct)
= a Fb G
is a solution of the wave equation!!!

24. Ey = aF(z - ct) + bG(z + ct) = aFbG
t = T z Ey
t = 2T

26. The solution consists of 2 waves F(z – ct) & G(z + ct)

27. Let c = 2 q = z - ct = 0 y = z + ct = 0 t zq zy 0 0 0 1 2 -2 2 4 -4
Ey = aF(z - ct) + bG(z + ct) = aFbG
-10 10 z
Let c = 2
q = z - ct = 0 y = z + ct = 0
t zq zy
5 t

28. Ey = aF(z - ct) + bG(z + ct) = aF() + bG()
-10 10 z
Let c = 2
q = z - ct = 0 y = z + ct = 0
t zq zy
5 t

29. Helmholtz

30. I was feeling a bit depressed the other day,
so I called the Help Hotline.
I was put through to a call-center in Ames.
I explained that I was feeling suicidal.
They were very excited at this news and wanted
to know if I could play football.