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p.1067

p.1067. Ch 34 Electromagnetic Waves 34.1 Displacement Current and the General Form of Ampere’s Law I d =  0 d  E /dt B · ds =  0 (I + I d ). . P34.1 (p.971). Ch 34 Electromagnetic Waves 34.2 Maxwell’s Equations. Ch 34 Electromagnetic Waves 34.3 Plane Electromagnetic Waves.

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p.1067

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  1. p.1067

  2. Ch 34 Electromagnetic Waves34.1 Displacement Current and the General Form of Ampere’s LawId= 0dE/dtB·ds = 0(I + Id) 

  3. P34.1 (p.971)

  4. Ch 34 Electromagnetic Waves 34.2 Maxwell’s Equations

  5. Ch 34 Electromagnetic Waves 34.3 Plane Electromagnetic Waves

  6. Properties of EM Waves • Transverse • E and B  propagation direction with E  B at all times • Propagation direction: E x B • Sinusoidal • Ey = Emaxcos(kx – t) • Bz = Bmaxcos(kx – t) • Emax/Bmax = E/B = c • c = (1/00)1/2      

  7. P34.8 (p.971) P34.9 (p.971)

  8. CT1: A planar electromagnetic wave is propagating through space. Its electric field vector is given by E = Emaxcos(kz – t) i. Its magnetic field vector is • B = Bmaxcos(kz – t) j • B = Bmaxcos(ky – t) k • B = Bmaxcos(ky – t) i • B = Bmaxcos(kz – t) k     

  9. Ch 34 Electromagnetic Waves 34.4 Energy Carried by Electromagnetic Waves A. Poynting’s Vector S = E x B / 0 Intensity = Power / Area = S Propagation direction is the direction of S B. Average Intensity Iav = EmaxBmax/20 P34.16 (p.972)    

  10. CT2: At a fixed point, P, the electric and magnetic field vectors in an electromagnetic wave oscillate at angular frequency . At what angular frequency does the Poynting vector oscillate at that point? • 2 •  • /2 • 4

  11. Ch 34 Electromagnetic Waves 34.5 Momentum and Radiation Pressure p = U/c (absorbed wave – normal incidence) p = 2U/c (reflected wave – normal incidence) Pressure = S/c (absorbed wave – normal incidence) Pressure = 2S/c (reflected wave – normal incidence) P34.33 (p.973)

  12. Ch 34 Electromagnetic Waves 34.7 The Spectrum of Electromagnetic Waves Maxwell’s Rainbow: c = f

  13. CT3: A long wavelength EM wave has a • higher frequency than a short wavelength EM wave • the same frequency as a short wavelength EM wave • lower frequency than a short wavelength EM wave

  14. Polling Question: Which material would you like to review most? • Exam 1 • Exam 2 • New Material

  15. Polling Question: Which chapters from the Exam 1 material would you like to review most? • 13 • 23 • 24 • 25

  16. Polling Question: Which chapters from Exam 2 material would you like to review most? • 26 • 27 • 28 • 29 • 30

  17. Polling Question: Which chapters from the new material would you like to review most? • 31 • 32 • 33 • 34

  18. Polling Question: Which type of material would you like to review most? • problems • concept questions • general principles

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