EM Waves Around

EM Waves aroundElectromagnetic WavesChapter 23Energy from the Sun – EM wavesLight – EM wavesGalaxy M104 (see http://hubblesite.org/)1

Galaxies/NGC 4038-4039History - Maxwell’s TheoryIn 1865, James Clerk Maxwell developed a theoryabout electricity and magnetism.His starting points were:1. Electric field lines originate on charges andterminate on – charges.2. Magnetic field lines form closed loops.3. A time varying magnetic field induces an electricfield4. A magnetic field is created by a current.Charges and Fields, SummaryStationary charges produce only electric fieldsCharges in uniform motion (constant velocity) produceelectric and magnetic fieldsCharges that are accelerated produce electric andmagnetic fields and electromagnetic wavesElectromagnetic Waves, SummaryA changing magnetic field produces an electric fieldA changing electric field produces a magnetic fieldThese fields are in phaseAt any point, both fields reach their maximum valueat the same timeMaxwell’s theory is a mathematical formulation thatrelates electric and magnetic phenomena.His theory, among other things, predicted that electricand magnetic fields can travel through space as wavesand he was able to predict the speed of travel.travelThe uniting of electricity and magnetism resulted in theTheory of Electromagnetism.Maxwell’s PredictionsA time dependent electric field produces a magneticfield and visa versa.Accelerating charges will radiate electromagneticwaves.Electromagnetic waves travel at the speed of light c:c 2.99792458 108 m / sThe electric and magnetic fields in the wave arefluctuating in both space and time.2

Producing EM WavesEM Waves and HertzIn 1887, Heinrich Hertz generated and detectedelectromagnetic waves in his lab.The waves radiated from a transmitter circuit andwere detected in a receiver circuit.Hertz used the fact that electrical circuits haveresonant frequencies just like mechanical systems do.A traveling electromagnetic wave produced byan ac generator attached to an antenna.Electromagnetic waves will be produced when a chargeundergoes acceleration.accelerationIf an ac voltage is applied to an antenna, the chargeswill be accelerated up and down and radiate EM waves.The radiated waves are made up of electric andmagnetic fields.A traveling electromagnetic wave produced byan ac generator attached to an antenna.At t 0 the electric fieldat point P is downward.After one quarter of a cycle,at t 1/4 T, the electric fieldat P vanishes.A short time later the electricfield at P is still downward, butnow with a reduced magnitude.Note that the field created att 0 has moved to point Q.The decreasing electric field atpoint P creates a magnetic fieldat point Q pointing into theviewgraphThe charge on the antenna hasreversed polarity now, and theelectric field at P points upward.When the oscillator has completed halfa cycle, t 1/2 T, the field at point P isupward and of maximum magnitude.At t 3/4 T the field at P vanishesagain. The fields produced atearlier times continue to moveaway from the antenna.Field directions in an electromagnetic waveComputer SimulationAt a time when the electric fieldproduced by the antenna pointsdownward, the magnetic fieldpoints into the page. In general,the electric and magnetic fields inan electromagnetic wave arealways at right angles to eachother.An electromagnetic wave propagating in thepositive x direction. Note that E and B areperpendicular to each other and in phase. Thedirection of propagation is given by the thumbof the right hand, after pointing the fingers inthe direction of E and curling them toward B(palm towards index.html3

Receiving radio wavesProperties of EM WavesBasic elements of a tuning circuitused to receive radio waves. First, anincoming wave sets up an alternatingcurrent in the antenna. Next, theresonance frequency of the LC circuitis adjusted to match the frequency ofthe radio wave, resulting in arelatively large current in the circuit.This current is then fed into anamplifier to further increase thesignal.The radiated EM waves have certain properties: EM waves all travel at the speed of light c.c2 1/(e0μ0) the E and B fields are perpendicular to each other the E and B fields are in phase (both reach a maximum andminimum at the same time)for EM waves in vacuum E cB The E and B fields are perpendicular to the direction oftravel (transverse waves)LightPlane WavesLight is an electromagnetic waveEM waves in free space are plane waves. That meansthat the E and B fields are confined to a plane anduniform within the plane at all time.As we said, EM waves travel at the speed of light.Light speed can be derived from two otherquantities we have already used:c Electromagnetic radiation is greatest whencharges accelerate at right angles to theline of sight. Zero radiation is observedwhen the charges accelerate along the lineof sight. These observations apply toelectromagnetic waves of all frequencies.1μ 0ε 0 3 10 8 m/sc fλ 3 108 m/sλfwavelengthfrequencyAs light waves travel through space they:transport energytransport momentumLight from Sun – about 8 minutesLight from stars – years!EM waves can be generated in different frequency bands:radio, microwave, infrared, visible, ultraviolet, x-rays, gamma raysNotes on The EM SpectrumRadio WavesUsed in radio and television communication systemsNote that the visible portion of the spectrum is relatively narrow.The boundaries between various bands of the spectrum are not sharp,but instead are somewhat arbitrary. (1 nm 10-9mMicrowavesWavelengths from about 1 mm to 30 cmWell suited for radar systemsMicrowave ovens are an application4

Notes on the EM Spectrum, 2Infrared wavesNotes on the EM Spectrum, 3Ultraviolet lightIncorrectly called “heat waves”Covers about 400 nm to 0.6 nmProduced by hot objects and moleculesSun is an important source of uv lightReadily absorbed by most materialsMost uv light from the sun is absorbed in thestratosphere by ozoneVisible lightPart of the spectrum detected by the human eyeMost sensitive at about 560 nm (yellow-green)X-raysMost common source is acceleration of high-energyelectrons striking a metal targetUsed as a diagnostic tool in medicineProblemNotes on the EM Spectrum, finalFind the frequency of blue light with a wavelength of 470 nm.Gamma raysEmitted by radioactive nucleiHighly penetrating and cause serious damage whenabsorbed by living tissueLooking at objects in different portions of thespectrum can produce different informationc λff cλ 3 108 6.4 1014 Hz470 10 9ProblemAs you drive by an AM radio station, you notice a sign sayingthat its antenna is 142 m high. If this height represents onequarter-wavelength of its signal, what is the frequency of thestation?λtherefore λ 4 142 568 m4c 3 108 528 kHzf λ568142 m Doppler Effect and EM WavesA Doppler Effect occurs for em waves, but differs from thatof sound wavesFor sound waves, motion relative to a medium is mostimportantFor light waves, the medium plays no role since the lightwaves do not require a medium for propagationDoppler Equation for EM WavesThe Doppler effect for em waves u f 0 f s 1 c The speed of sound depends on its frame of referencefo is the observed frequencyThe speed of em waves is the same in all coordinatesystems that are at rest or moving with a constant velocitywith respect to each otherfs is the frequency emitted by the sourceu is the relative speed between the source and theobserverThe equation is valid only when u is much smaller than c5

Doppler Equation, contEnergy and Momentum in EM WavesThe EM waves carry energyThe positive sign is used when the object and sourceare moving toward each otherThe energy density u (energy per unit volume) in a regionof empty space where electric and magnetic fields arepresent isThe negative sign is used when the object and sourceare moving away from each other11 21 2u ε0E 2 B ε0E 2 Bμ022 μ0Astronomers refer to a red shift when objects aremoving away from the earth since the wavelengthsare shifted toward the red end of the spectrumThe average power per unit area in an EM wave is alsocalled intensity of the wave (I power/area: units W/m2)examples:Nexrad (The Doppler weather radar)I NAVSTAR Navigation system1 ε0 212Emax ε 0cEmax2 μ02?Radiation PressureQuestionThe EM waves carry energy and momentum pIf a light beam carries momentum, should a person holdinga flashlight feel a recoil analogous to the recoil of a riflewhen it is fired?For an electromagnetic wave absorbed by an area A theaverage momentum transferred to the surface isΔp IAΔtcThis momentum transfer is responsiblefor the phenomenon of radiation pressure.When an EM wave is completely absorbed by a surfaceperpendicular to the direction of propagation of thewave, the rate of change of momentum equals the forceon the surface (units Pa 1N/m2. pressure force/area).pressure IcFor a totally reflectivesurfacepressure 2IcQuestion?Why is the radiation pressure on a perfectly reflectingsurface twice as great as on a perfectly absorbingsurface?The reflection of light6

Reflection and RefractionWhen a light ray travels from one medium to another,part of the incident light is reflected and part of the lightis transmitted at the boundary between the two media.The transmitted part is said to be refracted in thesecond medium.incident rayreflected rayTypes of ReflectionIf the surface from which thelight is reflected is smooth,then the light undergoesspecular reflection (parallelrays will all be reflected in thesame directions).If, on the other hand, thesurface is rough, then the lightwill undergo diffuse reflection(parallel rays will be reflectedin a variety of directions)refracted rayThe Law of ReflectionFor specular reflection the incident angle θi equals thereflected angle θr:θi θ rThe Refraction of LightThe angles aremeasured relative tothe normal as shown.Snell’s LawThe Refraction of LightThe speed of light is different in different materials. Wedefine the index of refraction, n, of a material to be the ratioof the speed of light in vacuum to the speed of light in thematerial:cn In general, when light enters a new material its direction willchange. The angle of refraction θ2 is related to the angle ofincidence θ1 by Snell’s Law:where v is the velocity of light in the medium.Normal linevWhen light travels from one medium to another its velocityand wavelength change, but its frequency remainsconstant.Snell’s Law can also be written asFor a vacuum, n 1The angles θ1 and θ2 aremeasured relative to the linenormal to the surface betweenthe two materials.For other media, n 1n is a unitless ratiosin θ1 sin θ 2 v1v2n1 sin θ1 n2 sin θ 2θ1AirGlassθ27

Application – Day and Night Settings on AutoMirrorsExample: Which way will the rays bend?n 1.4n 2n 1.6n 1.2 With the daytime setting, the bright beam of reflectedlight is directed into the driver’s eyes With the nighttime setting, the dim beam of reflectedlight is directed into the driver’s eyes, while the brightbeam goes elsewhereWhich of these rays can be the refracted ray?n1 sin θ1 n2 sin θ 2problemProblemA Common MirageYou have a semicircular disk of glass with an index ofrefraction of n 1.52. Find the incident angle θ for whichthe beam of light in the figure will hit the indicated pointon the screen.problemn1 sin θ1 n2 sin θ 2Total Internal Reflection1 sin θ1 1.52 sin θ 2Thereforeθ 2 14tan θ 2 osin θ1 1.52 sin14oTherefore520When light travels from a medium with n1 n2, there is anangle, called the critical angle θc, at which all the light isreflected and none is transmitted. This process is known astotal internal reflection.θ1 21.6oThe incident ray is both reflected andrefracted.Total Internal Reflection8