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Electricity and Magnetism

Explore the concepts of wave phenomena, polarization, and interference in electricity and magnetism. Learn about the Poynting Vector, polarization of light, superposition of waves, standing waves, and scattering of light.

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Electricity and Magnetism

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  1. Electricity and Magnetism • Announcements • Today • More on wave phenomena • Polarization • Superposition • Standing waves • Interference (proof that light is a wave) • Scattering of light (why is the sky blue) web.mit.edu/8.02x/www

  2. Announcements • Pset #12 (last one) due today • Experiment MW due today • Kits (Red Boxes) have to be returned! (if you want a grade) • see e-mail on what we would like to get back • bring stuff to lab web.mit.edu/8.02x/www

  3. Poynting Vector • Not a typo: John Henry Poynting (1852-1914) • Wave: Direction + Magnitude • Summarize using vector: Poynting Vector S = 1/m0 E x B Magnitude: S = 1/m0 EB Power/Unit Area Direction: S B, S E web.mit.edu/8.02x/www

  4. Polarization web.mit.edu/8.02x/www

  5. Polarization web.mit.edu/8.02x/www

  6. Polarization • Polarization: • Oscillation of fields has well defined direction • Polarization only possible for transverse waves • In general, light (sun, lightbulb) is unpolarized • Superposition of waves with many different orientations • Can be polarized using e.g. polarizer foils web.mit.edu/8.02x/www

  7. Superposition of waves • We saw many examples of superposition principle • Not only true for static fields, but also for time-dependent fields -> Superposition of waves web.mit.edu/8.02x/www

  8. Superposition of waves web.mit.edu/8.02x/www

  9. Superposition of waves • Example: Standing waves Reflecting Surface Incoming wave E(z,t) = E0 sin(kz+wt) Conductor z web.mit.edu/8.02x/www

  10. Superposition of waves • Example: Standing waves Reflecting Surface Incoming wave E(z,t) = E0 sin(kz+wt) Conductor z E(z,t) = E0 sin(kz-wt) Reflected wave web.mit.edu/8.02x/www

  11. Superposition of waves Superposition of Incoming wave andReflected wave Etotal = E0 sin(kz+wt) +E0 sin(kz+wt) = 2 E0 sin(kz) cos(wt) Standing wave E t = 0 0 < t < T z l/2 Node l web.mit.edu/8.02x/www

  12. Standing Wave E E = 0 E = 0 3/2l web.mit.edu/8.02x/www

  13. Standing Wave L = M l/2; M = 1,2,3... E Microwave oven: l ~ 10cm E = 0 E = 0 l/2 l 3/2l web.mit.edu/8.02x/www

  14. Superposition of waves • Interference web.mit.edu/8.02x/www

  15. Double Slit Experiment y Max. if “constructive interference” kr1-wt = kr2-wt + M 2p a d r1 r2 Etot= E0sin(kr1-wt) + E0sin(kr2-wt) R web.mit.edu/8.02x/www

  16. Double Slit Experiment y Max. if “constructive interference” kr1-wt = kr2-wt + M 2p a d r1 r2 Etot= E0sin(kr1-wt) + E0sin(kr2-wt) R yMax = M l/d R yMin = (M+1/2) l/d R web.mit.edu/8.02x/www

  17. Interference with Matter Interference can also happen for “matter waves” Bose-Einstein condensate of atoms (Ketterle et al, Nobel Price ’01) web.mit.edu/8.02x/www

  18. Scattering of Light web.mit.edu/8.02x/www

  19. Scattering of Light Why is the sky blue during day... web.mit.edu/8.02x/www

  20. Scattering of Light Why is the sky blue during day... ... and red at sunset? Santorini, Greece web.mit.edu/8.02x/www

  21. Scattering of Light Red Light (l ~ 700 nm) Blue Light (l ~ 400 nm) web.mit.edu/8.02x/www

  22. Scattering of Light Molecules, dust (size << l) Red Light (l ~ 700 nm) Blue Light (l ~ 400 nm) web.mit.edu/8.02x/www

  23. Scattering of Light Molecules, dust (size << l) Red Light (l ~ 700 nm) Blue Light (l ~ 400 nm) Lord Rayleigh: Scattering probability ~ 1/l4 web.mit.edu/8.02x/www

  24. Scattering of Light Molecules, dust (size << l) Red Light (l ~ 700 nm) Blue Light (l ~ 400 nm) Lord Rayleigh: Scattering probability ~ 1/l4 scattering (blue)/scattering(red):-> 7004/4004 ~ 10 web.mit.edu/8.02x/www

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