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2303_-_Spr_2010_-_Week_5_-_Maxwell's_Equations_&_Light

2303_-_Spr_2010_-_Week_5_-_Maxwell's_Equations_&_Lig...

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Satellite image of the straits of Bosporus using visible and infrared. 11
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Week 5-1: Maxwell’s Homework Review Review Speed of Light Waves Next: Gauss’ Law Ampere's Law Gauss’ Law for magnetism Faraday's Law Maxwell’s displacement current Reading: Chapter 34 22
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Speed of Light To measure the speed of light, we must measure distance and time for light travel. Section 35.1 1667: Galileo hilltop experiment: 3 km Response time ~ 0.2 s too slow 3 3
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Speed of Light 1675: Roemer studies timing of eclipse of moons of Jupiter with Earth at point A. Then at point C, 6 months later, eclipse is 16.6 minutes late. Estimated c ≈ 2.3∙108 m/s View of Jupiter and the 4 Galilean moons through a small telescope 4 4
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Speed of Light 1849: Fizeau Find time for returning beam to pass through next cog Found c ~ 3.1 × 108 m/s 5 5
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Speed of Light 1860: Foucault - vary mirror rotation speed - no signal unless mirror rotates 1/8 turn in Δ T c = 2.98∙108 m/s 6 6
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Speed of Light To measure the speed of light, we need to measure distance and time. We can measure distance to 4 parts in 109 We can measure time to 1 part in 1013 Time measurements are convenient, distance measurements are difficult Therefore, we now define the speed of light c = 299,792,458 m/s, Use lasers and time measurements with the definition of c to measure distances 7 7
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Extras
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Moving Pulse y = f(x - x0) same shape moved a distance x0 to the right: x y x = x 0 0 Given a function y = f(x) : x y 0 Let x0 = vt Then y = f(x - vt) describes the same shape moving to the right with speed v. x y x = v t 0 v UIUC 99
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Week 5-2: Maxwell’s Equations Gauss’ Law Ampere's Law Gauss’ Law for magnetism Faraday's Law Maxwell’s displacement current Reading: Chapter 34.1, 34.2, 34 appendix 10 10 circuit
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Gauss's Law: The net electric flux through any closed surface is proportional to the charge enclosed by that surface. See chapter 23 Enclosed Q A d E = 0 ε space ty of free permittivi Nm 2 2 12 - 0 C 8.85x10 = ε 0 2 2 0 0 4 4 : sphere a For ε π π ε ε R Q E Q R E A d E = = = 11 11
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Ampere's Law: Calculation of B (Esp. in cases of high symmetry) See chapter 29 I d B 0 μ = space ty of free permeabili A 2 7 - 0 N 10 x 4 π μ = r I B so I rB d B π μ μ π 2 2 wire, infinite an For 0 0 = = = 12 12
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The net flux of a B field through any closed surface is zero. Isolated magnetic poles do not exist See chapter 29 0 = S d B Gauss's Law for magnetism: 13 13
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Faraday's Flux Changing magnetic flux induces E field. E.g. electric motor, generator See chapter 30 dt d d E B Φ - = d S B B = Φ S d B B 14 14
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EM Equations so far: J. C. Maxwell realized ~ 1860 that the equations of Electricity & Magnetism were inconsistent and lacked symmetry In the case of no currents or charges: Perhaps a changing flux in E should create B ? 0
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