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Lecture 15 Notes - Recap of last lecture EM waves also...

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Recap of last lecture EM waves also satisfy the wave eqn. and the E & B fields vary sinusoidally When propagation through a medium the velocity changes from c to v = c/n where n is called the refractive index = where ε =K ε 0 and µ = K m µ 0 m KK
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Recap of last lecture The rate of the energy flow per unit area for an EM wave is described by the Poynting vector S. Intensity = time average of S dp/dV = EB/ µ 0 c 2 = S/c 2 = I/c 2 EM waves carry momentum with a momentum density momentum flow per unit area dp/Adt = S/c =I/c this is called Radiation pressure. When radiation is completely absorbed by a surface the momentum I/c is transferred to the surface, when it is completely reflected then change in momentum or momentum absorbed = 2I/c
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Problem 32.28 Arc lamps of a NASA facility produce light with an Intensity of 2500 W/m 2 at the floor of the facility To simulate sunlight near Venus. A) what is the average Radiation pressure on a totally light absorbing part of The floor and b) a totally reflecting part of the floor. c) What is the average momentum density in the light at the floor. a) P rad = I/c = 2500 W/m 2 / 3x10 8 m/s = 8.33 x10 -6 pascal = 8.23x10 -11 atm. b) P rad = 2I/c = 16.66x10 -6 pascal c) dp/dV = I/c 2 = 2.78x10 -14 kg/m 2 .s
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Standing EM waves Similar to mechanical waves EM waves of exactly same amplitude and frequency but 180 0 phase shift can form standing waves (for example EM after reflecting from a perfectly conduction surface). Adding the EM wave and its reflection just as we did for waves on a string we get E y (x,t) = -2E max sinkx sin ω t B z (x,t) = -2B max coskx cos ω t Nodal and antinodal planes for E and B are λ /4 apart (90 0 phase shifted). E field nodes at x=0, λ /2, λ …. E field antinodes at x = λ /4, 3 λ /4,….
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