Physics 212 Lecture 23

1. Physics 212 Lecture 23

2. Music • Who is the Artist? • Soul Rebels Brass Band • John Boutte • New Orleans Nightcrawlers • Paul Sanchez & Shammar Allen • Alex McMurray and Matt Perrine Why? Threadhead Records Beats Shazam !! Fan-funded and volunteer run record company Wonderful music from New Orleans Hint: Thursday’s artists also did a great set at Lagniappe stage last Jazzfest

3. “i wish every lecture was this straightforward” “I thought the prelecture was confusing. It will present an equation and then declare that the rms variable should be used instead. I don’t completely understand the difference and what root mean square is used for. Thanks!” We’ll mention this again – plschk back to Lec. 21 Your Comments “Not too bad, but clarify all the stuff on energy. Energy density and total energy are confusing.” “The first part of the pre-lecture was awesome. Then the energy was just so much material in so little time. Please go over energy but slower and with more examples please” We’ll do another example of power in e.m. waves “Is pointing vector really spelled ‘poynting’; vector???” “Why did the electromagnetic field give away all its energy? Because there was no poynt in keeping it. Why is the electromagnetic wave insecure about his looks? Because he’s a ‘plain’ wave. I hope you enjoyed this LIGHT humor...” “you don’t read lecture thoughts after midnight right? ;(” 05

4. Plane Waves from Last Time Argument of sin/cos gives direction of propagation E and B are perpendicular and in phase Oscillate in time and space Direction of propagation given by E X B E0 = cB0

5. Understanding the speed and direction of the wave Ex t = 0 z Ex t = p/2w z Ex = Eosin(kz-wt) What has happened to the waveform in this time interval? It has MOVED TO THE RIGHT by l/4

6. Checkpoint 1a “since the electomagnetic wave is in the x direction it will be Ex” “e is in the y direction and since k and t are different signs, the wave it moving in the positive direction” “B field propagates in the positive z direction and lies in the yz-plane.”

7. Checkpoint 1a No – moving in the minus z direction No – has Ey rather than Ex

8. Checkpoint 2a c=3.0 x 108 m/s Wavelength is equal to the speed of light divided by the frequency. Check: Look at size of antenna on base unit

9. Doppler Shift The Big Idea As source approaches: Wavelength decreases Frequency Increases

10. b = v/c b > 0 if source & observer are approaching b < 0 if source & observer are separating Doppler Shift for e-m Waves What’s Different from Sound or Water Waves ? Sound /Water Waves : You can calculate (no relativity needed) BUT Result is somewhat complicated: is source or observer moving wrt medium? Electromagnetic Waves : You need relativity (time dilation) to calculate BUT Result is simple: only depends on relative motion of source & observer

11. f f’ v f or f’ v The Doppler Shift is the SAME for both cases ! f’/f ONLY DEPENDS ON THE RELATIVE VELOCITY Doppler Shift for e-m Waves

12. b << 1 Taylor Series: Expand around b = 0 NOTE: Evaluate: Doppler Shift for e-m Waves A Note on Approximations Remember b > 0 for approach b < 0 for separation WHY ??

13. Frequencies shifted lower Star separating from us (Expanding Universe) Red Shift (for Astronomical Objects) Wavelengths shifted higher wavelength Our Sun Star in a distant galaxy

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

15. Checkpoint 2b A) B) C) ficlicker = 900 MHz “Running away from an iClicker will decrease the frequency which may let you see something.” “You need to increase the frequency at which the waves reach you, so you should run towards the iclicker” “Whether you move or the clicker moves, no visible wave will be availableency.”

16. Checkpoint 2b A) B) C) Need to approach i>clicker (b > 0) Approximation Exercise: ficlicker = 900 MHz Need to shift frequency UP How fast would you need to run to see the i>clicker radiation?

17. Waves Carry Energy

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

19. Waves Carry Energy

20. Comment on Poynting Vector Just another way to keep track of all this - Its magnitude is equal to I – Its direction is the direction of propagation of the wave

21. Power in EM Waves: Example A cell phone tower has a transmitter with a power of 100 W. What is the magnitude of the peak electric field a distance 1500 m (~ 1 mile) from the tower? Assume the transmitter is a point source. What is the intensity of the wave 1500 m from the tower?A) 1.5 nW/m2B) 3.5 mW/m2 C) 6 mW/m2

22. 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 “increasing E will increase amplitude, therefore engergy” “By increasing the frequency, we will increase the energy.” “Increasing the frequency or the field would increase the energy carried” “both dont effect because energy isntdependant”

23. 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 • But then again, what are we keeping constant here? • WHAT ABOUT PHOTONS? • The energy of one photon is Ephoton= hf = hw/2p • Uwave = NphotonsEphoton = 1/2 e0E02

24. 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

25. Calculation 1 y x z Which of the following graphs represents the z-dependence of Bx at t = 0? X X (A) (B) (C) (D) E and B are “in phase” (or 180o out of phase) Wave moves in +z direction y E x B z An electromagnetic wave is described by: where is the unit vector in the +y direction.

26. Calculation 2 y x z What is the form of B for this wave? (C) (A) (D) (B) Wave moves in –z direction y +z points out of screen -z points into screen E x B An electromagnetic wave is described by:

27. Calculation 3 Which of the following plots represents Bx(z) at time t = p/2w ? (A) (B) (C) (D) y at wt = p/2: +z points out of screen -z points into screen E x B An electromagnetic wave is described by: Wave moves in negative z-direction

28. 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 !” • As professor approaches stoplight, the frequency of its emitted light will be shifted UP • The speed of light does not change • Therefore, the wavelength (c/f) would be shifted to a smaller value • If he goes fast enough, he could observe a green light !

29. Follow-Up How fast would the professor have to go to see the light as green? (lgreen = 500 nm, lred = 600 nm) (A) 540 m/s (B) 5.4 X104 m/s (C) 5.4 X 107 m/s (D) 5.4 X 108 m/s Relativistic Doppler effect: Note approximation for small b is not bad: Change the charge to SPEEDING! 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 !” c = 3 X 108 m/s  v = 5.4 X 107 m/s