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Physics 212 Lecture 23

Physics 212 Lecture 23. Main Point 1.

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Physics 212 Lecture 23

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  1. Physics 212 Lecture 23

  2. Main Point 1 First, we established that the electric and magnetic field oscillations in a plane electromagnetic wave are in phase with each other and that the direction of propagation of these waves can be obtained from the cross product of E and B. We determined that the frequency (and wavelength) of electromagnetic waves vary by almost 20 orders of magnitude from radio waves to photons at the Tevatron at Fermilab.

  3. Main Point 2 Second, we introduced the Doppler shift, the frequency shift due to the relative motion of the source of these waves and the observer.

  4. Main Point 3 Finally, we determined that the energy density in the electric and magnetic fields in an electromagnetic wave are equal. We defined the intensity of the wave as the averate power transmitted per unit area. We formalized the energy transport by introducing the Poynting vector, defined as the cross product of the electric and magnetic fields, normalized by m0. The direction of this vector is the direction of propagation of the wave while its magnitude is equal to the instantaneous power in the wave per unit area.

  5. Plane Waves

  6. Checkpoint 1a

  7. Checkpoint 1b Which of the following actions will increase the energy carried by an electromagnetic wave?A. Increase E keeping w constant B. Increase w keeping E constantC. Both of the above will increase the energy D. Neither of the above will increase the energy

  8. Checkpoint 2a c=3.0 x 108 m/s

  9. Checkpoint 2b A) B) C) ficlicker = 900 MHz

  10. Doppler Shift +v if they are approaching -v if they are separating f f’ v f or f’ v

  11. If f = 24,000,000,000 Hz (k-band radar gun) c = 300,000,000 m/s Police radars get twice the effect since the EM waves make a round trip:

  12. Waves Carry Energy

  13. Intensity Intensity = energy delivered per unit time, per unit area (U = energy) Area = A Length = cdt Sunlight on Earth: I ~ 1000J/s/m2 ~ 1 kW/m2

  14. Light has Momentum! For E-M waves: pressure Radiation pressure If it has energy and its moving, then it also has momentum: Analogy from mechanics:

  15. Connections seen in equations: E = hf p = h/l Planck’s constant h = 6.63e-34 J-s PHOTONS We believe the energy in an e-m wave is carried by photons Question: What are Photons? Answer: Photons are Photons. Photons possess both wave and particle properties Particle: Energy and Momentum localized Wave: They have definite frequency & wavelength (fl = c) Question: How can something be both a particle and a wave? Answer: It can’t (when we observe it) What we see depends on how we choose to measure it ! The mystery of quantum mechanics: More on this in PHYS 214

  16. Calculation 1 y x z Which of the following graphs represents the z-dependence of Bx at t = 0? (A) (B) (C) (D) An electromagnetic wave is described by: where is the unit vector in the +y direction.

  17. Calculation 2 y x z What is the form of B for this wave? (C) (A) (D) (B) An electromagnetic wave is described by:

  18. Calculation 3 Which of the following plots represents Bx(z) at time t = p/2w ? (A) (B) (C) (D) An electromagnetic wave is described by:

  19. Calculation 4 Is it possible that the professor’s argument is correct? (lgreen = 500 nm, lred = 600 nm) (A) YES (B) NO A certain unnamed physics professor was arrested for running a stoplight. He said the light was green. A pedestian said it was red. The professor then said: “We are both being truthful; you just need to account for the Doppler effect !”

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