1. EM Spectrum Physics 102 Professor Lee Carkner Lecture 25

2. Final Exam  Covers:  Chapters 21-22 (2/3)  Chapters 13-20 (1/3)  Structured like previous tests  About 15 multiple choice, 6 problems  Practice problems online  Sample equation sheet on web page

3. PAL #24 EM Waves  Radio tuner with L = 10 nH to tune in f = 90.3 MHz  f = 1/2  (LC) ½  LC = (1/2  f) 2  C = (1/2  f) 2 (1/L)  C = (1/(2)(  )(90.3X10 6 )) 2 (1/10X10 -9 )  C = 3.11X10 -10 F  What value of L will tune in 106.5 MHz?  L = (1/2  f) 2 (1/C)  L = (1/(2)(  )(106.5X10 6 )) 2 (1/3.11X10 -10 )  L = 7.2X10 -9 H = 7.2 nH

4. Direction of B Vectors  If the antenna is vertical the E vectors go up and down and the direction of propagation is north  B vectors are at right angles to E vectors and so are horizontal, east and west

5. Energy in EM Wave   Each has an energy density (J per m 3 ):  u E = ½  0 E 2  u B = ½(1/  0 )B 2   u = u E + u B   We want to know how much energy we get per unit time over a certain area  Called the intensity, I

6. Intensity of Flashlight

7. Intensity  The value of u depends on where the EM wave is in its cycle   The energy density of each field is the same   The intensity depends on how much energy the wave delivers, which depends on the energy density and the speed:  I = uc = (½  0 E rms 2 + ½  0 E rms 2 )c I = c  0 E rms 2  Units: joules per second per square meter (W/m 2 )

8. Intensity of Light  We normally don’t know much about the E field of a light wave, but rather we know something about the source of the wave   As the waves travel out the power is spread out over a sphere of radius r (r is the distance away): I = P s / 4  r 2   Light (like sound) falls off with an inverse square law

9. Inverse Square Law

10. Radiation Pressure   If someone shines a flashlight on you, the light is trying to push you away   EM pressure is due to the fact that light has momentum which can be transmitted to an object through absorption or reflection

11. Momentum Transfer  The change in momentum due to light is given by:   Where  p is the momentum change and  U is the energy change   For reflection the momentum change is twice as much:  p = 2  U/c

12. Light Pressure  From Newton’s second law  The amount of energy delivered in time  t is:   where I is the intensity and A is the area  Since pressure (p r ) is force per unit area the pressure becomes: p r = I/c (total absorption) p r = 2I /c (total reflection)

13. Light Sail   A light sail is a very large, very thin, very reflective piece of fabric to which a spacecraft is attached   Can also use a laser  Light sail powered craft need no engines or fuel  Do need very large sails

14. EM Waves and Energy  The energy of an EM wave is proportional to the frequency  where h = Planck’s constant = 6.63 X 10 -34 J s   Radio waves and X-rays produce different effects   The Earth’s atmosphere  Our eyes

15. Atmospheric Transmission Gamma + X-ray blocked Infrared blocked O 2, N 2 Absorption H 2 O, CO 2 Absorption

16. Sensitivity of Your Eye

17. Light from the Sun   The sun (like all stars) is actually producing EM waves with a variety of wavelengths via many different processes  Your eyes can only see the visible portion   Like the radiation produced by any hot object  The sun produces more yellow and red light than blue, so the sun looks orange

18. Solar Emission Spectrum

19. Radio Waves from the Sun

20. Solar Spectrum  Sun emits most strongly at visible wavelengths   Produces stronger IR at cooler regions   Produces high energy radiation in outer layers   Also produces low energy radiation in magnetic loops 

21. Next Time  Final exam:  Section 1: Thursday 9am  Section 2: Tuesday noon

22. If you have a LC oscillator receiving electromagnetic waves with a fixed L and a variable C, how would you change C to double the frequency? A)Quarter C B)Half C C)Double C D)Quadruple C E)You cannot get exactly double f by changing C

23. The E and B fields of an electromagnetic wave are oriented A)parallel to the direction of travel and to each other B)perpendicular to the direction of travel and to each other C)parallel to the direction of travel and perpendicular to each other D)perpendicular to the direction of travel and parallel to each other E)Always 180 degrees from each other and the direction of travel

24. If the frequency of the wave emitted by a radio transmitter is doubled, what happens to the wavelength and the speed? A)wavelength is halved, speed is halved B)wavelength is halved, speed is same C)wavelength is same, speed is same D)wavelength is same, speed is doubled E)wavelength is doubled, speed is halved