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Electromagnetic Waves

Electromagnetic Waves. Chapter 35. Electromagnetic (EM) Waves. Can travel through space Radio, Microwaves, IR, Light, UV, X-rays, Gamma Rays All on the electromagnetic spectrum. James Clerk Maxwell. Maxwell’s Equations Guass’s Law – The greater the charge, the greater the electric field

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Electromagnetic Waves

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  1. Electromagnetic Waves Chapter 35

  2. Electromagnetic (EM) Waves • Can travel through space • Radio, Microwaves, IR, Light, UV, X-rays, Gamma Rays • All on the electromagnetic spectrum

  3. James Clerk Maxwell Maxwell’s Equations • Guass’s Law – The greater the charge, the greater the electric field • Guass’s Law for magnetism - Magnetic flux is zero through a closed surface • Faraday’s Law – An electric field is produced by a changing magnetic field • Ampere-Maxwell Law - A magnetic field is produced by a changing electric field (moving charge)

  4. Guass’s Law Guass’s Law for magnetism Faraday’s Law Ampere-Maxwell Law

  5. An electric field is produced by: • Charged particle (moving or stationary) • Changing magnetic field A magnetic field is produced by: • A curent (moving charge) • Changing electric field

  6. Lorentz Force Results • An electric field exerts a force on any charged particle • A magnetic field exerts a force on a moving charged particle

  7. Producing Electromagnetic Waves DC case • Current flows to either antenna (like a capacitor) • Electric field produced • Magnetic field produced (right hand rule)

  8. AC case • Changing direction of current • Field line close up to form a loop • Magnitude of E and B decrease with 1/r • Energy is proportional to E2 or B2

  9. EM Wave • Sinusoidal • E and B are perpendicular to one another • E and B are in phase • Accelerating electric charges produce electromagnetic waves

  10. Speed of EM Waves v = 1 √eomo eo = 8.85 X 10-12 C2/Nm2 (permittivity) mo = 4p X 10-7 Ns2/C2 (permeability) Calculate the speed of light using these constants

  11. Wave Properties • First man-made EM waves detected by Hertz (8 years of Maxwell’s death) l = wavelength (meters) f = frequency (cycles/s or Hertz) f l = c (in a vacuum)

  12. Electromagnetic Spectrum

  13. Visible light • 4 X 10-7 m to 7X 10-7 m (400 to 700 nm) • Electrons • Radio – running electrons up and down an antenna • Electrons moving within atoms and molecules • X-rays - Electrons are rapidly decellerated by striking metal • Gamma Rays – Nuclear decay

  14. Waves: Ex 1 Calculate the wavelength of a 60 Hz EM wave f l = c • = c/f • = (3.0 X 108 m/s)/60 s-1 = 5 X 106 m What range of the spectrum is this?

  15. Waves: Ex 2 Calculate the wavelength of a 93.3 MHz FM radio station f l = c • = c/f • = (3.0 X 108 m/s)/(93.3 X 106 s-1) = 3.22 m

  16. Waves: Ex 3 Calculate the frequency of 500 nm blue light. f l = c f= c/ l f = (3.0 X 108 m/s)/500 X 10-9 m = 6 X 1014 Hz

  17. Waves: Ex 4 When you speak to a telephone to someone 4000 km away, how long does it take the sound to travel? v = d/t t = d/v T = (4000 X 103 m)/(3 X 108 m/s) = 1.3 X10-2 s Speed is less because of wires

  18. Measuring the Speed of Light • Galileo – Tried to measure from mountaintop to mountaintop. • Roemer – Measured time needed for light to travel from Io (Jupiter’s moon) • Michealson’s Experiment

  19. Measured time needed for light to travel and be observed • Only certain rotational speeds allowed observer to see the light • Tried it on mountains in southern California (35 km)

  20. c = 2.99792458 X 108 m/s c = 3.0 X 108 m/s • Slightly slower in air • Same for all EM waves

  21. Energy and EM Waves • All EM waves carry energy • Exactly half by electric field and half by magnetic field E = cB (relates E and B) S = ½ eocE2o = ½ cB2o mo (ave rate of energy transported per unit area, per unit time)

  22. Radio Transmitter • Carrier Frequency – Frequency that one “tunes in” • AM - 530 to 1600 kHz • FM – 88 to 108 MHz • Broadcast TV - 54 to 88 mHz, 174 to 216 MHz

  23. AM Radio • Amplitude Modulated • Program signal mixes with carrier signal • Frequency of wave does not change, only amlitude

  24. FM Radio • Frequency Modulated • Frequency of total signal varies (slightly) • 101.3 and 101.5 but never 101.4

  25. Receiving a Signal • Straight Antenna – Electric field of EM wave produces a current in the electrons in the antenna • Loop Antenna – Magnetic field of EM wave induces a current • Tune in a station – uses the resonant frequency of an LC circuit (variable capacitors/inductors)

  26. Radio: Ex 1 An FM station is 103.1 mHz. Calculate the wavelength: f l = c • = c/f • = (3.0 X 108 m/s)/(103.1 X 106 s-1) = 2.91 m

  27. What is the value of the capacitance for this tuning circuit if L = 0.40 mH? fo = 1 2p √LC C = 1/(4p2fo2L) C = 1/ (4)(3.14)2(1.0x108

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