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Transcript
Electromagnetic Waves Physics 202, Lecture 23 E EM wave equations: Today’s Topics z Electromagnetic Waves (EM Waves) Properties of EM Wave (review) Energy Carried by EM Wave, Poynting Vector Momentum Carried by EM Wave Review for Exam 3 Next lecture: Light and Optics, Ch 35. Professor Pan will give the lectures for the rest of the semester. Energy Carried By EM Waves right hand rule again! Power per unit area [J/s•m2 = W/m2] S= 1/µ0 EB =uc B Plane wave solutions: E= Emaxsin(kx-ωt+φ) B= Bmaxsin(kx-ωt+φ) Properties: No medium is necessary. same φ, E and B are normal to each other set to be 0 E and B are in phase Direction of wave is normal to both E and B (EM waves are transverse waves) Speed of EM wave: E/B = Emax/Bmax=c Transverse wave: two polarizations possible y S z x Recall: energy densities uE= ½ ε0E2, uB= ½ B2/µ0 For a EM wave, at any time/location, uE = ½ ε0E2 = ½ B2/µ0 =uB (using E/B=c) In an electromagnetic wave, the energies carried by electric field and magnetic field are always the same. Total instantaneous energy per unit volume: u = uE + uB = � 0 E 2 = Intensity: take average over time. 2 Emax Bmax E2 cBmax = = max = 2µ0 2µ0 c 2µ0 B2 µ0 Total average energy per unit volume: 2 uavg = �0 (E )avg I = savg x Energy Carried By EM Waves Poynting vector: describes the rate of transfer of energy (power) by EM wave. Instantaneous rate at which energy is passing through unit area. S= 1/µ0 ExB c B E y E B 1 B2 2 = �0 Emax = max z 2 2µ0 y S x Power transmitted per unit of area (flux) is equal to uc in the direction of wave I = savg = uavg c 1 S Momentum Carried By EM Waves EM waves: momentum = energy/c A ΔX=cΔt Change of momentum in 100% absorption Example: Solar Radiation (sun light) The average intensity of the EM radiation from the Sun on Earth is S ~ 103 W/m2 What is the average radiation pressure for 100% absorption? Change of momentum in 100% reflection Radiation Pressure (P): 100% absorption 100% reflection Δp = p P= S/c Δp = 2p P= 2S/c What is the force exerted by EM radiation by the Sun on a surface of 1 m2 (with 100% absorption)? Mariner 10: “Sail on sunlight” Spherical Waves and Plane Waves Spherical EM waves: Radiation from a point source. By laws of energy conservation, intensity (flux) of spherical EM waves goes as ~1/r2. About Exam-3 When and where Monday April 18 5:30-7:00 pm Location: Same as last time. • Ingraham B10: Sections 301, 302, 303, 304, 305, 307, 309, 322, 323 • Van Vleck B102: Sections 308, 310, 324, 325, 326, 327, 329, 330 spherical wave Plane waves: Beams are in parallel. Intensity (flux) of plane EM waves remains as a constant. plane wave Format Closed book, 20-25 multiple-choices questions , same style as midterm 1. 1+1 8x11 formula sheet allowed, must be self prepared, no photo copying/download-printing of solutions, lecture slides, etc. Bring a calculator (but no computer). Only basic calculation functionality can be used. Bring a 2B pencil for Scantron. Write down and bubble your ID and section # Special requests: All requests for specially arranged tests must be made by noon today and are held in our 202 labs. (for approved testers only) 2 Exam-3: Chapters Covered Ch 31: Faraday’s Law (all sections) Ch 32: Inductance (all sections) Ch 33: Alternating-Current Circuits (33.1 – 33.7, RC time constant) Ch 34: Electromagnetic Waves (all sections) Basics of waves from ch 16 may be useful Material from HW11 (due 4/20) will be on the exam. Suggested preparations: Homework problems Homework problems again “Quick quiz” for conceptual understanding Additional problems at the end of chapters Pay special attention to signs and directions! Reviews: This lecture There will be additional office hours on Friday, Sat/Sun in the lab rooms. Ch34 representative questions (not meant to be complete) HW 11. Rate of change of electric flux given capacitor or some other electric field configuration, the resulting displacement current. How are magnitude of B and E field related in EM waves? Given λ, what is f? or vice versa Given E (or B) = A sin(kx-wt), what is the amplitude of B (or E), λ, f, etc. What would be the length of a λ/4 antenna if I want to transmit ##MHz radio waves? What is the maximum radiation pressure exerted by (some light source like sun, laser pointer, light bulb of given intensity) on reflective surface or absorbing surface? Ch. 34: EM waves Maxwell’s equations + Lorentz force law Plane EM waves Wave equations Speed of light E/B = c c = λf Energy carried by EM waves Poynting vector, intensity Momentum and radiation pressure Production of EM waves by an antenna (λ/4) EM wave spectrum Visible, radio, IR, x-ray, etc. Ch 31: Faradays’ Law Faraday’s law of induction Lenz’s law Induced current and induced emf in a conductors are in such a direction as to set up a magnetic field that opposes the change that produces them. Motional emf Generators and motors Eddy currents 3 Ch31 representative questions HW 7 & 8 Given changing magnetic field spanning some area, what is the emf induced? Current in N coils with resistance R? Direction? Given constant magnetic field but changing area, what is the induced emf? Current? Direction? Given constant magnetic field and coil but coil is rotating (e.g. generator), what is emf, current, direction? Sliding bar circuit in magnetic field: What is the force required to keep the bar moving at a constant velocity? (motional emf) Ch32 representative questions HW 9 Given inductance and current that is changing, what is the induced emf at certain time? Given R and L plus a battery, what is the current at certain time after the switch is closed? When does the current reach xx% of the final value? In a RL circuit, what is the potential across R? L? compare the two. What is the inductance of a coil(s)? Air-core solenoid? How much energy is stored in the magnetic field of a solenoid given its dimensions, number of turns and current? What is the mutual inductance of two solenoids given number of turns, flux, and current? Induced emf? Frequency of LC circuit, RLC circuit Critical resistance of RLC circuit, behavior when R > Rcritical, R < Rcritical, R = Rcritical, Ch. 32 Inductance Self-Induction and Inductance: ε0 = -L*dI/dt RL Circuits I = Imax(1-e-t/τ), I = = Imax(e-t/τ), τ = L/R Energy in a magnetic field U = ½ LI2, uB = B2/(2µ0) Mutual inductance M12 = N2Φ12/I1 = M21 = N1Φ21/I2=M ε2 = -M12dI1/dt , ε1 = -M21dI2/dt , Oscillations in an LC Circuit: ω = 1/sqrt(LC) RLC Circuit General behavior, resonant frequency Ch 33: AC Circuits Resistors, inductors, & capacitors in AC circuit Capacitive reactance (XC), inductive reactance (XL) Impedance Z = sqrt(R2+(XL-XC)2) Phase angle between current and voltage: • φ=tan-1((XL-XC)/R) Irms, Vrms RLC Series circuit Power in an AC Circuit Resonances in a series RLC circuit 4 Ch33 representative questions Rms current and voltage Given R, L, C, what is the power delivered in an AC circuit? Resonant frequency? Given R, L, & C, what are the inductive and capacitive reactance? Impedance? Phase? What is the maximum current in a L or C circuit for a given Vrms and f? In RLC circuit, what is the voltage across R, L, C for a given Vrms and f? 5