Unformatted text preview:

Lecture 33: FRI 03 APR Ch.33.1–3,5: E&M WavesMaxwell, Waves and LightElectromagnetic WavesPowerPoint PresentationSlide 5Slide 6Maxwell’s RainbowSlide 8Slide 9The Poynting Vector: Points in Direction of Power FlowEM Wave Intensity, Energy DensitySolar EnergyEM Spherical WavesExampleLecture 33: FRI 03 APRLecture 33: FRI 03 APR Ch.33.1–3,5: E&M Waves Ch.33.1–3,5: E&M WavesJames Clerk Maxwell (1831-1879) Physics 2102Jonathan DowlingQuickTime™ and a decompressorare needed to see this picture.A solution to the Maxwell equations in empty space is a “traveling wave”…c =1μ0ε0=3×108m/sc =1μ0ε0=3×108m/sThe “electric” waves travelat the speed of light!Light itself is a wave of electricity and magnetism!Maxwell, Waves and LightMaxwell, Waves and Lightd2Edx2=−μ0ε0d2Edt2⇒ E =E0sink(x−ct)d2Edx2=−μ0ε0d2Edt2⇒ E =E0sink(x−ct)electric and magnetic “forces” can travel! ∫∫•=•SCdAEdtddsB00εμ∫∫•=•SCdAEdtddsB00εμ∫∫•−=•SCdABdtddsE∫∫•−=•SCdABdtddsEA solution to Maxwell’s equations in free space:)sin( txkEEmω−=)sin( txkBBmω−=n.propagatio of speed ,ck=ωc =EmBm=1μ0ε0=299,462,954 ms(=(187,163 miles/secVisible light, infrared, ultraviolet,radio waves, X rays, Gammarays are all electromagnetic waves.Electromagnetic WavesElectromagnetic WavesQuickTime™ and a decompressorare needed to see this picture.Radio waves are reflected by the layer of the Earth’s atmosphere called the ionosphere. This allows for transmission between two points which are far from each other on the globe, despite the curvature of the earth. Marconi’s experiment discovered the ionosphere! Experts thought he was crazy and this would never work.Fig. 33-1The wavelength/frequency range in which electromagnetic (EM) waves (light) are visible is only a tiny fraction of the entire electromagnetic spectrum.Maxwell’s RainbowFig. 33-2(33-2)An LC oscillator causes currents to flow sinusoidally, which in turn produces oscillating electric and magnetic fields, which then propagate through space as EM waves.Fig. 33-3Oscillation Frequency:1LCω =Next slideThe Traveling Electromagnetic (EM) Wave, Qualitatively(33-3)Fig. 33-5Mathematical Description of Traveling EM WavesElectric Field:( )sinmE E kx tω= −Magnetic Field:( )sinmB B kx tω= −Wave Speed:0 01cμ ε=Wavenumber:2kπλ=Angular frequency:2πωτ=Vacuum Permittivity:0εVacuum Permeability:0μAll EM waves travel a c in vacuumAmplitude Ratio:mmEcB=Magnitude Ratio:( )( )E tcB t=EM Wave Simulation(33-5)Electromagnetic waves are able to transport energy from transmitterto receiver (example: from the Sun to our skin).The power transported by the wave and itsdirection is quantified by the Poynting vector.John Henry Poynting (1852-1914) 211|| EcEBS00==μμThe Poynting Vector: The Poynting Vector: Points in Direction of Power FlowPoints in Direction of Power FlowEBSUnits: Watt/m2For a wave, sinceE is perpendicular to B: BESrrr×=0μ1In a wave, the fields change with time. Therefore the Poynting vector changes too!! The direction is constant, but the magnitude changes from 0 to a maximum value.____________222___)(sin11tkxEcEcSImωμμ−===00The average of sin2 overone cycle is ½:221mEcI0=μ221mEcI0=μ21rmsEcI0=μ21rmsEcI0=μBoth fields have the same energy density. 2 22 201 1 1 1( )2 2 2 2E BB Bu E cB uε ε εε μ μ0 00 0 0= = = = =or, EM Wave Intensity, Energy EM Wave Intensity, Energy DensityDensityA better measure of the amount of energy in an EM wave is obtained by averaging the Poynting vector over one wave cycle. The resulting quantity is called intensity. Units are also Watts/m2.The total EM energy density is then0220/ με BEu ==0220/ με BEu ==Solar EnergySolar EnergyThe light from the sun has an intensity of about 1kW/m2. What would be the total power incident on a roof of dimensions 8mCxC20mC?IC=C1kW/m2 is power per unit area.P=IA=(103 W/m2) x 8m x 20m=0.16 MegaWatt!!The solar panel shown (BP-275) has dimensions 47in x 29in. The incident power is then 880 W. The actual solar panel delivers 75W (4.45A at 17V): less than 10% efficiency….The solar panel shown (BP-275) has dimensions 47in x 29in. The incident power is then 880 W. The actual solar panel delivers 75W (4.45A at 17V): less than 10% efficiency….QuickTime™ and a decompressorare needed to see this picture.The electric meter on a solar home runs backwards — Entergy Pays YOU!The electric meter on a solar home runs backwards — Entergy Pays YOU!The intensity of a wave is power per unit area. If one has a source that emits isotropically (equally in all directions) the power emitted by the source pierces a larger and larger sphere as the wave travels outwards: 1/r2 Law! 24 rPIsπ=24 rPIsπ=So the power per unit area decreases as the inverse of distance squared.So the power per unit area decreases as the inverse of distance squared.EM Spherical WavesEM Spherical WavesExampleExampleA radio station transmits a 10 kW signal at a frequency of 100 MHz. At a distance of 1km from the antenna, find the amplitude of the electric and magnetic field strengths, and the energy incident normally on a square plate of side 10cm in 5 minutes. 222/8.0)1(4104mmWkmkWrPIs===ππmVIcEEcImm/775.02212==⇒=00μμnTcEBmm58.2/ ==mJSAtUAtUAPS


View Full Document

LSU PHYS 2102 - Electromagnetic Waves

Documents in this Course
Load more
Download Electromagnetic Waves
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Electromagnetic Waves and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Electromagnetic Waves 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?