1. Maxwell’s Equations and Electromagnetic Waves
4/9/2015
Kevin Holway

2. Maxwell's Equations Galilean field transformations Maxwell’s equations
Electromagnetic waves
Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, Licensed under Public Domain via Wikimedia Commons -

3. Maxwell's Equations Galilean field transformations Maxwell’s equations
Electromagnetic waves
Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, Licensed under Public Domain via Wikimedia Commons -

4. An electric and a magnetic field. No fields.
Sharon runs past Bill while holding a positive charge q. In Bill’s reference frame, the charge creates
Only an electric field.
Only a magnetic field.
An electric and a magnetic field.
No fields. 4 4

5. An electric and a magnetic field. No fields.
Sharon runs past Bill while holding a positive charge q. In Sharon’s reference frame, the charge creates
Only an electric field.
Only a magnetic field.
An electric and a magnetic field.
No fields. 5 5

6. Galilean transformations and Galilean invariance
Position, Velocity, Acceleration
By N2L, will agree on force

7. Then Bill measures a force on Sharon’s charge that is: Zero Non-zero
x x x x x
Sharon runs past Bill while holding a positive charge q through a uniform, constant magnetic field that Bill created.
Then Bill measures a force on Sharon’s charge that is:
Zero
Non-zero 7 7

8. Then Sharon measures a force on her charge that is: Zero Non-zero
x x x x x
Sharon runs past Bill while holding a positive charge q through a uniform, constant magnetic field that Bill created.
Then Sharon measures a force on her charge that is:
Zero
Non-zero 8 8

10. Experimenters on earth have created the magnetic field shown
Experimenters on earth have created the magnetic field shown. A rocket flies through the field, from right to left. Which are the field (or fields) in the rocket’s reference frame? 10 10

11. 11 11

12. Not quite relativity…

13. Maxwell's Equations Galilean field transformations Maxwell’s equations
Electromagnetic waves
Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, Licensed under Public Domain via Wikimedia Commons -

14. The equations so far
and displacement current

15. The electric field is decreasing. Which is the induced magnetic field?
E. There’s no induced field in this case. 15 15

16. Example: induced magnetic field
in a discharging capacitor

17. Maxwell's equations
Along with Lorentz force law, this is the fundamental content
of classical electromagnetic theory

18. Maxwell's equations in vacuum

19. Maxwell's equations in vacuum (differential form)

20. Maxwell's Equations Galilean field transformations Maxwell’s equations
Electromagnetic waves
Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, Licensed under Public Domain via Wikimedia Commons -

21. "We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena."
Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, Licensed under Public Domain via Wikimedia Commons -

22. Prediction by Maxwell: Propagating Wave With Speed of Light c
Sinusoidal plane wave
<get better animation>

23. Demo: sources and linearly polarized light (dipole antenna)

25. How is light created? Accelerating charges
Img at right: "Black body" by Darth Kule - Own work. Licensed under Public Domain via Wikimedia Commons -

26. How is light created? Quantum mechanical processes

27. Cerenkov Radiation: Particle Motion Faster Than Light in a Medium
How is light created? Cerenkov radiation

28. Demo: Spectra (gas discharge tubes and diffraction gratings)

30. Wavelength determines color but color does not determine wavelength!
Color is a complex perception of the world
constructed by your brain.

32. Why are living creatures tuned to the visual spectrum?
Sun emits the most energy in visual range of spectrum (Stefan-Boltzmann law).
Water vapor in atmosphere blocks most light except the visual range.

33. Maxwell's Equations Galilean field transformations Maxwell’s equations
Electromagnetic waves
Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, Licensed under Public Domain via Wikimedia Commons -

34. "Mantis shrimp from front" by Jenny - originally posted to Flickr as mantis shrimp. Licensed under CC BY 2.0 via Wikimedia Commons -