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UVM PHYS 012 - Electromagnetic Waves
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PSY 012 1st Edition Lecture 18Outline of Last Lecture I. Self inductance constant, La. Measured in Henrys (H)i. 1 H = 1 (Vs)/Ab. Depends on configurationc. For solenoid: L = (N2Aμ0)/li. εind = -L(ΔI/Δt)ii. N (ΔΦ/Δt) = -L(ΔI/Δt) ; L = (NΦ)/Iiii. Φ = Aμ0(N/l)III. Energya. Depends on currentb. For solenoid, energy = (AlB2)/2μ0III. Energy density, μBa. μB = B2/2μ0i. True for energy density of any magnetic field in free space.IV. RL circuits: circuits with a resistor and an inductora. Back εmf is generated when I is increasing. No εmf is generated when I is constant.i. I = (ε/R)(1-e-t/τ)1. τ = time constant = L/Rii. When t = 0, I = 0.iii. As t approaches infinity, I approaches ε/R.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.b. Forward εmf is generated when I is decreasing.i. I = I0e-t/τii. When t = 0, I = I0.iii. As t approaches infinity, I approaches 0.V. Transformersa. Magnetic field will constantly be switching directions, causing a constantly changing flux which generates a continuous εmf.i. Diagram above shows only one direction the magnetic field can be going.ii. The change in flux will be the same in both the primary and secondary circuits.iii. Ip/Is = Vs/Vp = Ns/NpVI. LC Circuits: circuits containing an inductor and a capacitora. Capacitor is initially fully-charged, causing I to increase.b. Imax is reached when charge on capacitor is zero.i. Energy transformed from electric field to magnetic field.c. Current causes charge to build up on opposite capacitor plate, causing the polarity of the capacitor to reverse.d. This reversed polarity on the capacitor creates a current flowing in the opposite direction and increasing its magnitude to Imax.e. The current will continue switching directions around the circuit like this with an angular frequency (ω0) equal to 1/√(LC), assuming no resistance.f. Still charges create an electric field, moving charges create a magnetic field, and accelerating charges create radiation.Outline of Current Lecture II. 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:2. to receive signals from alternating magnetic field:3. ω = 1/√(LC)III. Energy in electromagnetic Wavesa. Poynting vector: S = EB/μ0i. measure of intensityii. intensity = power/area = Savg. = EmaxBmax/2μ0 = cB2max/2μ0 =cE2max/2μ01. Emax = cBmaxIV. 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 =


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UVM PHYS 012 - Electromagnetic Waves

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