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Please Fill the online Course evaluation. So far we have inputs from only 41 students http://www.purdue.edu/eval/ This is the official survey requested by university 1 Official Exam • Saturday, May 10, 1:00-3:00 pm • room: EE129 Final Exam Makeup Exam (include crew team member): • Saturday, May 03, 2:00-4:00 pm • room: physics building, Room238. • send me request with valid reasons and proofs by April 28. After that, no requests will be approved. Exam for ADA students: • Saturday, May 03, 1:00-4:00 pm • room: physics building, Room238. AOB • multiple choice problem. • Prepare your own scratch paper, pens, pencils, erasers, etc. • Use only pencil for the answer sheet • Bring your own calculators • No cell phones, no text messaging which is considered cheating. • No crib sheet of any kind is allowed. Equation sheet will be provided. 2 Last Time Maxwell Equations – complete! Wave solutions 3 Today Accelerated Charges Energy and Poynting Vector Momentum and Poynting Vector Re-Radiation (scattering) Polarized Light Why the sky is blue 4 Accelerated Charges Electromagnetic pulse can propagate in space How can we initiate such a pulse? 1. Transverse pulse propagates at speed of light 2. Since E(t) there must be B 3. Direction of v is given by: E B 5 Magnitude of the Transverse Electric Field We got the direction. Magnitude can be derived from Gauss’s law* Field ~ -qa Eradiative 1 qa 40 c 2 r 1. The direction of the transverse field is opposite to qa 2. The electric field falls off at a rate 1/r * This was first shown by Edward Purcell, BSEE Purdue, 6 Nobeal Laureate! iClicker Question A proton is briefly accelerated as shown below. What is the direction of the radiative electric field that will be detected at location A? B A A + D C 7 Sinusoidal Electromagnetic Radiation Acceleration: d2y a 2 ymax 2 sin t dt 1 qa Eradiative 40 c 2 r f 2 T 1/ f 1 qymax 2 Eradiative sin t ĵ 2 40 c r Sinusoidal E/M field 8 Sinusoidal E/M Radiation: Wavelength Instead of period can use wavelength: cT c f f 2 T 1/ f Example of sinusoidal E/M radiation: atoms radio stations E/M noise from AC wires Freeze picture in time: 9 Energy of E/M Radiation A particle will experience electric force during a short time d/c: Felec qE d p p 0 Felec t qE c What will happen to the ball? It will oscillate Energy was transferred from E/M field to the ball 2 p 2 qEd 1 K K 0 2m c 2m Amount of energy in the pulse is ~ E2 10 Energy Flux There is E/M energy stored in the pulse: Energy 0 E 2 (J/m 3 ) Volume Pulse moves in space: there is energy flux Units: J/(m2s) = W/m2 During t: Energy 0 E 2 A ct Energy flux c 0 E 2 A t flux 1 0 EB used: E=cB, 00=1/c2 11 Energy Flux: The Poynting Vector flux 1 0 EB The direction of the E/M radiation was given by E B Energy flux, the “Poynting vector”: 1 S EB 0 John Henry Poynting (1852-1914) (in W/m 2 ) • S is the rate of energy flux in E/M radiation • It points in the direction of the E/M radiation Note energy flux = [Energy/(time * Area)] Energy flux = Intensity = [Power/Area] Same Thing! 12 Example In the vicinity of the Earth, the energy intensity of radiation emitted by the sun is ~1400 W/m2. What is the approximate magnitude of the electric field in the sunlight? Solution: flux E 1 0 EB c 0 E 2 flux 725 N/C c 0 Note: this is an average (rms) value 13 Momentum of E/M Radiation • E field starts motion • Moving charge in magnetic field: Fmag qv B Fmag What if there is negative charge? Fmag q v B ‘Radiation pressure’: What is its magnitude? Average speed: v/2 v vE Fmag q B q 2 2 c Fmag vE v q /( qE ) 1 Felec 2c 2c Fmag 14 Momentum Flux Net momentum: in transverse direction: 0 in longitudinal direction: >0 Relativistic energy: E pc mc 2 2 2 2 Quantum view: light consists of photons with zero mass: E 2 pc 2 Classical (Maxwell): it is also valid, i.e. momentum = energy/speed 1 S EB 0 Momentum flux: S 1 E B (in N/m 2 ) c 0 c Units of Pressure 15 Exercise: Solar Sail What is the force due to sun light on a sail with the area 1 km2 near the Earth orbit (1400 W/m2)? Solution: E S 1 EB c 0 c flux 725 N/C c 0 S 1 E E2 6 2 E 4 . 65 10 N/m c 0 c c 0 c 2 Note: What if we have a reflective surface? 9.3 106 N/m 2 Total force on the sail: F 9.3 N 16 Effect of Radiation on a Neutral Atom Main effect: brief electric kick sideways Neutral atom: polarizes Electron is much lighter than nucleus: can model atom as outer electron connected to the rest of the atom by a spring: F=eE 17 Radiation and Neutral Atom: Resonance E y E0 sin t Fy eE y F0 sin t Amplitude of oscillation will depend on how close we are to the natural free-oscillation frequency of the ballspring system Resonance This is why you can tune a radio 18 Importance of Resonance E/M radiation waves with frequency ~106 Hz has big effect on mobile electrons in the metal of radio antenna: can tune radio to a single frequency E/M radiation with frequency ~ 1015 Hz has big effect on organic molecules: retina in your eye responds to visible light but not radio waves Very high frequency (X-rays) has little effect on atoms and can pass through matter (your body): X-ray imaging 19 Cardboard Why there is no light going through a cardboard? Electric fields are not blocked by matter Electrons and nucleus in cardboard reradiate light Behind the cardboard reradiated E/M field cancels original field 20 Effect of E/M Radiation on Matter 1. Radiative pressure – too small to be observed in most cases 2. E/M fields can affect charged particles: nucleus and electrons http://www.youtube.com/watch?v=dL9_Tldmrhs 21 Electromagnetic Spectrum 22 Color Vision Three types of receptors (cones) in retina which incorporate three different organic molecules which are in resonance with red, green and blue light frequencies (RGBvision): Response spectra for three types of receptors Max response wavelengths: S – 440 nm (6.81.1014 Hz) M – 540 nm (5.56.1014 Hz) L – 560 nm (5.36.1014 Hz) Refers 23 to length of cone Polarizer: polarization by absorption An electric field component parallel to the transmission axis is passed by a polarizer; a component perpendicular to it is absorbed. transmission axis dichroism (tourmaline, polaroid,…) So if linearly polarized beam with E is incident on a polarizer as shown, E y E cos I I 0 cos 2 Zero if =/2, I0 if =0 If unpolarized beam is incident instead, The intensity will reduce by a factor of two. I I 0 cos 2 I0 / 2 The light will become polarized along the transmission axis 24 iClicker Questions • A beam of un-polarized lights with intensity I is sent through two polarizers with transmission axis perpendicular to each other. What’s the outgoing light intensity? a) b) c) d) ½I 2I 0 1.5 I 25 Example: two polarizers This set of two linear polarizers produces LP (linearly polarized) light. What is the final intensity? – P1 transmits 1/2 of the unpolarized light: I1 = 1/2 I0 – P2 projects out the E-field component parallel to x’ axis: E2 E1 cos I E2 1 I 2 I1 cos I 0 cos 2 2 2 26 = 0 if = /2 (i.e., crossed) 7B-22 Polarizer Effects 27 Polarized Light Polaroid sunglasses and camera filters: reflected light is highly polarized: can block it Considered: using polarized car lights and polarizers-windshields 28 Polarized E/M Radiation AC voltage (~300 MHz) What will happen if distance is increased twice? E/M radiation can be polarized along one axis… no light …and it can be unpolarized: 29 UHF Transmitter and Dipole Receiver (6D-17) 30 iClicker question In which of these situations will the bulb light? A) B) C) D) E) A B C None B and C 31 Why the Sky is Blue Why there is light coming from the sky? Why is it polarized? Why is it blue? x x0 sin t d2x E ~ a 2 y0 2 sin t dt Energy flux: ~ E 2 ~ 4 Ratio of blue/red frequency is ~2 scattering intensity ratio is 16 Why is sun red at sunset? Is its light polarized? Why are distant mountains blue? 32 Why is the sunset red? The shorter wavelengths of blue light are scattered by gas molecules in the atmosphere more than longer wavelengths such as red light. When the sun is low on the horizon, the light must pass through more atmosphere than when the sun is directly above. By the time the sun’s light reaches our eyes, the shorter wavelengths such as blue and yellow have been removed by scattering, leaving only orange and red light coming straight from the sun. Today Accelerated Charges Energy and Poynting Vector Momentum and Poynting Vector Re-Radiation (scattering) Polarized Light Why the sky is blue 34 Please Fill the online Course evaluation. So far we have inputs from only 41 students http://www.purdue.edu/eval/ This is the official survey requested by university 35 Official Exam • Saturday, May 10, 1:00-3:00 pm • room: EE129 Final Exam Makeup Exam (include crew team member): • Saturday, May 03, 2:00-4:00 pm • room: physics building, Room238. • send me request with valid reasons and proofs by April 28. After that, no requests will be approved. Exam for ADA students: • Saturday, May 03, 1:00-4:00 pm • room: physics building, Room238. AOB • multiple choice problem. • Prepare your own scratch paper, pens, pencils, erasers, etc. • Use only pencil for the answer sheet • Bring your own calculators • No cell phones, no text messaging which is considered cheating. • No crib sheet of any kind is allowed. Equation sheet will be provided. 36