1. Exam is Tuesday Nov. 25th in class
Thursday, November 12, 2003
WARNING:
Exam is Tuesday Nov. 25th in class
Review Sessions:
In class: Friday 12-1 pm; 2-3 pm
Me: Monday 4-6 pm
Office Hours:
Brian F.: Friday 1-2 pm 4-344
Various: Sunday 1-5 pm TEAL
Brian P.: Monday 3-4 pm 4-344
Monday 6-8 pm 6-106
Please me questions
Class 28

2. Class 30: Outline Hour 1: Displacement Current Hour 2:
Thursday, November 12, 2003
Class 30: Outline
Hour 1:
Displacement Current
Hour 2:
Electromagnetic waves
Class 28

3. Last Time: Driven RLC Circuits

4. Resistance Reactance Impedance
AC Circuits: Summary
Element I0
Current vs. Voltage
Resistance Reactance Impedance
Resistor
In Phase
Capacitor
Leads
Inductor
Lags
Although derived from single element circuits, these relationships hold generally!

5. Driven RLC Series Circuit
Impedance

6. Resonance
C-like:
f < 0
I leads
L-like:
f > 0
I lags

7. This Time: Putting it All Together

8. Displacement Current

9. Ampere’s Law: Capacitor
Consider a charging capacitor: I
Use Ampere’s Law to calculate the magnetic field just above the top plate
1) Red Amperian Area, Ienc= I
2) Green Amperian Area, I = 0
What’s Going On?

10. This is called (for historic reasons) the Displacement Current
We don’t have current between the capacitor plates but we do have a changing E field. Can we “make” a current out of that?
This is called (for historic reasons) the Displacement Current

11. Maxwell-Ampere’s Law

12. PRS Questions: Capacitor

13. In Class Problem: Displacement Current

14. Maxwell’s Equations

15. Electromagnetism Review
E fields are created by: (1) electric charges (2) time changing B fields
B fields are created by (1) moving electric charges (NOT magnetic charges) (2) time changing E fields
E (B) fields exert forces on (moving) electric charges
Gauss’s Law
Faraday’s Law
Ampere’s Law
Maxwell’s Addition
Lorentz Force

16. Maxwell’s Equations

17. Electromagnetic Radiation

18. A Question of Time…

19. Electromagnetic Radiation: Plane Waves

20. Traveling Waves Consider f(x) = x=0 What is g(x,t) = f(x-vt)? x=0 t=0
t=t0
x=2vt0
t=2t0
f(x-vt) is traveling wave moving to the right!

21. Traveling Sine Wave Now consider f(x) = y = y0sin(kx): Amplitude (y0)
What is g(x,t) = f(x+vt)? Travels to left at velocity v
y = y0sin(k(x+vt)) = y0sin(kx+kvt)

22. Traveling Sine Wave
At x=0, just a function of time:
Amplitude (y0)

23. Traveling Sine Wave

24. Electromagnetic WavesHz
Remember:

25. Electromagnetic Radiation: Plane Waves
Watch 2 Ways:
1) Sine wave traveling to right (+x)
2) Collection of out of phase oscillators (watch one position)
Don’t confuse vectors with heights – they are magnitudes of E (gold) and B (blue)

26. PRS Question: Wave

27. Group Work: Java Problem 1

28. Properties of EM Waves Travel (through vacuum) with speed of light
At every point in the wave and any instant of time, E and B are in phase with one another, with
E and B fields perpendicular to one another, and to the direction of propagation (they are transverse):

29. Direction of Propagation

30. PRS Question: Direction of Propagation

31. Energy & the Poynting Vector

32. Energy in EM Waves Energy densities: Consider cylinder:
What is rate of energy flow per unit area?

33. Poynting Vector and Intensity
Direction of energy flow = direction of wave propagation
units: Joules per square meter per sec
Intensity I:

34. Energy Flow: Resistor
On surface of resistor is INWARD

35. PRS Questions: Poynting Vector

36. Energy Flow: Inductor
On surface of inductor with increasing current is INWARD

37. Energy Flow: Inductor
On surface of inductor with decreasing current is OUTWARD

38. In Class Problem: Poynting Vector

39. Momentum & Radiation Pressure
EM waves transport energy:
They also transport momentum:
And exert a pressure:
This is only for hitting an absorbing surface. For hitting a perfectly reflecting surface the values are doubled:

40. Standing Waves

41. Standing Waves
What happens if two waves headed in opposite directions are allowed to interfere?

42. Standing Waves: Who Cares?
Most commonly seen in resonating systems:
Musical Instruments, Microwave Ovens

43. Standing Waves: Bridge

44. Microwave Ovens: Hot Spots
Can you measure the speed of light with marshmallows?

45. Microwave Ovens: Hot Spots

46. Microwave Ovens: Hot SpotsOR

47. Microwave Ovens: Hot Spots

48. Microwave Ovens: Hot Spots

49. Group Work: Standing Waves
Play with Problem 2 in Java Example!