PHYS 012 1st Edition Lecture 19 Outline of Last Lecture I. Electromagnetic Wavesa. Ex) Linearly-polarized electromagnetic wave travelling in the +x directioni. Waves will actually oscillate; the diagram above is frozen in time.ii. E = Emaxcos(kx – ωt) ; E = Emaxcos(kx + ωt) if wave was travelling in –x directioniii. B = Bmaxcos(kx – ωt) ; B = Bmaxcos(kx + ωt) if wave was travelling in –x directioniv. ω = angular frequency = 2πf = 2π/T ; f = frequency = 1/T ; T = periodv. k = 2π/λ ; λ = wavelength1. measured in m-1b. Find wave propagation using right hand rulec. E is always perpendicular to B.d. E and B are in phase (reaching maximum values at the same time).e. E = cB; c = speed of light or any electromagnetic wave travelling through a vacuum = 1/√(μ0ξ)f. In a vacuum, the wave speed is c; c = λfg. Ex) Alternating current voltage supply connected to two conductive barsi. Current will continuously switch directions, causing E and B to switch directions.ii. In an LC circuit…1. to receive signals from alternating electric field:These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.2. to receive signals from alternating magnetic field:3. ω = 1/√(LC)II. Energy in electromagnetic Wavesa. Poynting vector: S = EB/μ0i. measure of intensityii. intensity = power/area = Savg. = EmaxBmax/2μ0 = cB2max/2μ0 = cE2max/2μ01. Emax = cBmaxIII. Energy Density of Electromagnetic Wavea. B and E contribute the same amount to total energy (uB = uE).i. uB = B2/2μ0 = E2/2c2μ0 = ξ0E2/2ii. uE = ξ0E2/2b. Total energy density = utotal = uB + uE = ξ0E2i. This is an instantaneous value that depends on where you are along the wave.1. uavg.total = ξ0E2max/2 = B2max/2μ0Outline of Current Lecture IV. Intensitya. Savg. = Pavg./Areab. E = cBc. Savg. = EmaxBmax)/2μ0V. Electromagnetic Spectruma. c = λfb. increasing f = decreasing λ = higher energyc. visible light falls between λ = 400nm and λ = 700nmVI. Polarizationa. electric field can point in any directioni. polarized light contains an electric field only oriented in one directionb. the intensity of initially unpolarized light is reduced by a factor of ½ when it passes through a polarizerc. Malus’ Law: I = I0cos2θi. for when already polarized light passes through a second filterii. θ = angle between direction of electric field and transmission
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