1. II. Electromagnetic Waves A.Displacement Current 1.Recall Ampere’s Law: 2.As we’ve learned it, AL is incomplete. We need to add an additional current, called the displacement current, I D. ID arises from time-varying electric fields (not present in a steady current along an infinite wire): (II.A.1,2)

2. II. Electromagnetic Waves A.Displacement Current 3.General form of Ampere’s Law includes terms due to “conduction current” and “displacement current”: (II.A.3)

3. II. Electromagnetic Waves B.MAXWELL’S EQUATIONS 1.Unified description of E, B: (II.B.1-4) (Gauss’s Law) (Gauss’s Law for B) (Faraday’s Law for B) (Ampere’s Law for B)

4. II. Electromagnetic Waves B.MAXWELL’S EQUATIONS 2.Plane Wave a)As we shall see, the solution to Maxwell’s Equations is a wave of Electric and Magnetic Fields. b)Plane Wave Definition: Wave in which the transverse components are uniform on a plane perpendicular to the direction of propagation. V

5. II. Electromagnetic Waves B.MAXWELL’S EQUATIONS 2.Plane Wave a)As we shall see, the solution to Maxwell’s Equations is a wave of Electric and Magnetic Fields. b)Plane Wave Definition: Wave in which the transverse components are uniform on a plane perpendicular to the direction of propagation. E B

6. II. Electromagnetic Waves B.MAXWELL’S EQUATIONS 2.Plane Wave a)As we shall see, the solution to Maxwell’s Equations is a wave of Electric and Magnetic Fields. b)Plane Wave Definition: Wave in which the transverse components are uniform on a plane perpendicular to the direction of propagation. E B E B

7. II. Electromagnetic Waves B.MAXWELL’S EQUATIONS 2.Plane Wave a)As we shall see, the solution to Maxwell’s Equations is a wave of Electric and Magnetic Fields. b)Plane Wave Definition: Wave in which the transverse components are uniform on a plane perpendicular to the direction of propagation. E B E B E B

8. II. Electromagnetic Waves B.MAXWELL’S EQUATIONS 3.Electromagnetic Wave Properties a) Transverse wave b) Ratio between E,B: E/B = c.(II.B.5) c) Constant speed d) No medium required: E and B reinforce each other. E B E B E B E B

9. II. Electromagnetic Waves B.MAXWELL’S EQUATIONS 4.Derivation of Solution: Plane Wave a)Consider a plane wave with B z, E y propagating in the x-direction with speed v. After time t, the two wave fronts are separated by a distance  x. b) Apply Faraday’s Law to a rectangle in the xy-plane: E B E B x x  x y z B, A a x y

10. II. EM Waves B.Maxwell’s Equations 4.Derivation of Solution: Plane Wave b) Apply Faraday’s Law to a rectangle in the xy-plane: Assume  x is small enough that B z ~ uniform over surface. E B E B x x  x y z B, A a x y xx

11. II. EM Waves B.Maxwell’s Equations 4.Derivation of Solution: Plane Wave b) Apply Ampere’s Law to a rectangle in the zx-plane: Assume  x is small enough that E y ~ uniform over surface. E B E B x x  x y z E, A a x z xx

12. II. EM Waves B.Maxwell’s Equations 4.Derivation of Solution: Plane Wave b) Apply Ampere’s Law to a rectangle in the zx-plane: Assume  x is small enough that E y ~ uniform over surface. E B E B x x  x y z E, A a xx x z

13. II. EM Waves B.Maxwell’s Equations 4.Derivation of Solution: Plane Wave c)Now take partial time and space derivatives of both equations: E B E B x x  x y z z This is the wave equation with v = (     ) -1/2 = c!(II.B.7) (II.B.6)

14. II. EM Waves B.Maxwell’s Equations 5.Sinusoidal Waves a)A more accurate representation of EM Waves b)Plane waves can be a good approximation c)For wave propagating in the +x-direction: d)E,B in phase, follow RHR: c, E, B (II.B.8)

15. C.The Production of Electromagnetic Waves 3.Antennae a)Accelerating charges radiate energy as EM waves b)Oscillating voltage => accelerates charge => EM radiation ++++++ t = 0: Charge placed on metal rods connected to an AC generator. ------ E VV II. EM Waves

16. F.The Production of Electromagnetic Waves 3.Antennae a)Accelerating charges radiate energy as EM waves b)Oscillating voltage => accelerates charge => EM radiation ++++ t = 0 to T/4: Rods neutralize, and E decreases to 0. Note: Initial E propagates away from array at speed c. ---- E II. EM Waves

17. C.The Production of Electromagnetic Waves 3.Antennae a)Accelerating charges radiate energy as EM waves b)Oscillating voltage => accelerates charge => EM radiation + t = 0 to T/4: Rods neutralize, and E decreases to 0. Note: Initial E propagates away from array at speed c. - E II. EM Waves

18. C.The Production of Electromagnetic Waves 3.Antennae a)Accelerating charges radiate energy as EM waves b)Oscillating voltage => accelerates charge => EM radiation t = 0 to T/4: Rods neutralize, and E decreases to 0. Note: Initial E propagates away from array at speed c. E = 0 at t = T/4. II. EM Waves

19. C.The Production of Electromagnetic Waves 3.Antennae a)Accelerating charges radiate energy as EM waves b)Oscillating voltage => accelerates charge => EM radiation - t = T/4 to T/2: E reverses direction and grows. + II. EM Waves

20. C.The Production of Electromagnetic Waves 3.Antennae a)Accelerating charges radiate energy as EM waves b)Oscillating voltage => accelerates charge => EM radiation ---- t = T/4 to T/2: E reverses direction and grows. ++++ II. EM Waves

21. ++++++ C.The Production of Electromagnetic Waves 3.Antennae a)Accelerating charges radiate energy as EM waves b)Oscillating voltage => accelerates charge => EM radiation ------ t = T/4 to T/2: E reverses direction and grows. II. EM Waves

22. C.The Production of Electromagnetic Waves 3.Antennae a)Accelerating charges radiate energy as EM waves b)Oscillating voltage => accelerates charge => EM radiation ------ ++++++ II. EM Waves

23. C.The Production of Electromagnetic Waves 3.Antennae c)Oscillating E => Oscillating B wave ------ ++++++ v = c. B End result: A transverse wave of E propagating at speed v = (  0  0 ) -1/2 = c. II. EM Waves

24. C.The Production of Electromagnetic Waves 3.Antennae c)Oscillating E => Oscillating B wave Top View - B II. EM Waves

25. C.The Production of Electromagnetic Waves 3.Antennae c)Oscillating E => Oscillating B wave Top View - II. EM Waves

26. C.The Production of Electromagnetic Waves 3.Antennae c)Oscillating E => Oscillating B wave Top View - II. EM Waves

27. C.The Production of Electromagnetic Waves 3.Antennae c)Oscillating E => Oscillating B wave Top View II. EM Waves

28. C.The Production of Electromagnetic Waves 3.Antennae c)Oscillating E => Oscillating B wave Top View + II. EM Waves

29. C.The Production of Electromagnetic Waves 3.Antennae c)Oscillating E => Oscillating B wave Top View II. EM Waves

30. C.The Production of Electromagnetic Waves 3.Antennae c)Oscillating E => Oscillating B wave Top View - c * E and B perpendicular to each other. * E and B perpendicular to v. * E and B in phase. II. EM Waves

31. D.Properties of EM Waves 1.Field strengths of EM wave E/B = c.(II.D.1) 2.Poynting Vector: Energy Flow Rate Vector 3.Power and Intensity: P= S per unit area, I = S(avg) I= E max B max /(2  0 ), (II.D.2) = E 2 max /(2  0 c) = B 2 max (c/2  0 ).

32. D.Properties of EM Waves 4.Radiation Pressure p = I/c (complete absorption)(II.D.3) p = 2I/c(complete reflection)(II.D.4) 5.EM waves in matter n = c/v = “index of refraction”(II.D.5)      II. EM Waves

33. E.The Electromagnetic Spectrum 1.Units a)Angstrom (Å) = 10 -10 m b)Nanometer (nm) = 10 -9 m c)Micron (  m) = 10 -6 m 2.Radio, Microwave, Infrared, Visible, Ultraviolet, X-rays, Gamma rays 3.VISIBLE: “ROYGBIV” = Red, Orange, Yellow, Green, Blue, Indigo, and Violet (large wavelength to small) II. EM Waves

34. E.The Electromagnetic Spectrum 1.Units a)Angstrom (Å) = 10 -10 m b)Nanometer (nm) = 10 -9 m c)Micron (  m) = 10 -6 m 2.Radio, Microwave, Infrared, Visible, Ultraviolet, X-rays, Gamma rays 3.VISIBLE: “ROYGBIV” = Red, Orange, Yellow, Green, Blue, Indigo, and Violet (large wavelength to small) II. EM Waves

35. A.Working Definitions 1.Diffraction occurs when light source is not a perfect point source and wave encounters a sharp edge. 2.Diffraction is essentially an example of interference between a large (continuous) distribution of sources. 3.Limits resolution of instruments—but also can be used to separate multi-chormatic light. III. Diffraction

36. 4.Spreading of wave from its initial line of travel No diffraction III. Diffraction

37. 4.Spreading of wave from its initial line of travel Diffraction III. Diffraction

38. 5.Diffraction occurs when light passes through a narrow opening, around obstacles and at sharp edges. a)Application: Calculating stellar diameters by lunar occultation Unresolved point of light III. Diffraction

39. 5.Diffraction occurs when light passes through a narrow opening, around obstacles and at sharp edges. a)Application: Calculating stellar diameters by lunar occultation Unresolved point of light III. Diffraction

40. 5.Diffraction occurs when light passes through a narrow opening, around obstacles and at sharp edges. a)Application: Calculating stellar diameters by lunar occultation Unresolved point of light III. Diffraction

41. 5.Diffraction occurs when light passes through a narrow opening, around obstacles and at sharp edges. a)Application: Calculating stellar diameters by lunar occultation III. Diffraction Resolved diffraction pattern: spacing of fringes => width of star