Chapter 34Electromagnetic Waves and lightElectromagnetic waves in our lifeMicrowave oven, EM wave is used to deliver energy.Radio/TV, cell phones, EM wave is used to carry information.Telephone and internet: electrical signal in copper wires is NOT EM wave, but fiber optics is the backbone of the network.The wireless connection for your laptop, the bluetoothheadset for your iPod, …Without EM wave, there would be no life on Earth. – why?Plane EM waves, the simplest formA review: a wave is a disturbance that propagates through space and time, usually with transference of energy PLAYACTIVE FIGUREAn EM wave is the oscillation between electric and magnetic fields.The electric field oscillates in the x-y plane, along the y direction; the magnetic field oscillates in the x-z plane and along the zdirection. The EM wave propagates along the x axis, with the speed of light c, in vacuum.EBWave propagationA sinusoidal EM wave moves in the x direction with the speed of light c, in vacuum.PLAYACTIVE FIGUREThe electric field direction (here the y axis direction) is called the polarization direction. When this polarization direction does not change with time, it is said that the EM wave is linearly polarized. Another common polarization is the circular polarization, when the electric field direction moves in a circleThe magnitudes E and B of the fields depend upon x (the location in the wave) and t (time) only:()maxE E cos kx tω= −()maxB B cos kx tω= −Here k is the wave number.Rays, wave front and plane waveA ray is a line along which the wave travels.In a homogeneous medium for EM waves (vacuum being one), rays follow straight lines.The surface that connects points of equal phase in a group of rays (waves) is called the wave front. When this wave front is a geometric plane, this collection of waves is called a plane wave.Maxwell’s equations of EM wavesGauss’s Law of electric field:0E AEqdΦε= ⋅ =∫Gauss’s Law of magnetic field:B A 0BdΦ= ⋅ =∫Here the emf is actually distributed over the conducting ring. From the definition of potential,we know that the emf here equals: E sV d∆= ⋅E semf d= ⋅∫Faraday’s Law of induction:BdemfdtΦ= −So Faraday’s Law of induction now reads:E sBdddtΦ⋅ = −∫Maxwell’s modification to Ampere’s LawAmpere’s Law of magnetic field:0B sd Iµ⋅ =∫Here the current flows in a wire.Now let’s examine the case when there is a capacitor in the current path:Ampere’s Law applies to the wire part. The current flows into the upper plate of the capacitor, flows out from the lower plate, creating charge accumulation in the capacitor and build up the electric field. Constructing a Gaussian surface which has two parts: S1and S2.Maxwell’s modification to Ampere’s Law2 20E SEqESΦε= ⋅ = =Gauss’ Law says that:So one has:0 0 01 1Edd d q dqIdt dt dtΦε ε ε = = ≡ Here Idis called the displacement current. With it, the Ampere’s Law is now completed as:( )0 0 0 0B sEddd I I IdtΦµ µ ε µ⋅ = + = +∫It is often called Ampere-Maxwell LawMaxwell’s equations of EM wavesGauss’s Law of electric field:Gauss’s Law of magnetic field:Faraday’s Law of induction:Ampere-Maxwell Law:0E Aqdε⋅ =∫B A 0d⋅ =∫E sBdddtΦ⋅ = −∫0 0 0B sEdd IdtΦµ ε µ⋅ = +∫These four equations are called Maxwell’s Equations. These are the integral forms. The differential forms are:0Eqε∇ ⋅ =B 0∇ ⋅ =BEt∂∇× = −∂0 0 0EB Jtµ ε µ∂∇× = +∂ With Lorenz force Law, we complete the laws of classical electromagnetism.F E v Bq q= + × James Clerk Maxwell1831 – 1879Scottish physicistProvided a mathematical theory that showed a close relationship between all electric and magnetic phenomenaHis equations predict the existence of electromagnetic waves that propagate through spaceHis equations unified the electric and magnetic fields, and provide foundations to many modern scientific studies and applications.Energy in EM wavesFrom Maxwell’s equations, one can prove:The speed of light is 0 01cε µ=The electric field to magnetic field ratio is EcB=The energy flow in an EM wave is described by the Poynting vector01S E Bµ= × 2 20 0 02 2 2max max max maxavE B E cBI Scµ µ µ= = = =The wave energy intensity isThe energy density is220012 2B EBu u Eεµ= = =Producing EM waves through an antennaUse a half-wave antenna as an exampleTwo conducting rods are connected to a source of alternating voltageThe length of each rod is one-quarter of the wavelength of the radiation to be emittedThe oscillator forces the charges to accelerate between the two rodsThe antenna can be approximated by an oscillating electric dipoleThe magnetic field lines form concentric circles around the antenna and are perpendicular to the electric field lines at all pointsThe electric and magnetic fields are 90oout of phase at all timesThis dipole energy dies out quickly as you move away from the antennaThe EM wave SpectrumRadio wavesMicrowavesInfraredUltraviolet, UVVisible lightGamma and X raysNotes on the EM wave SpectrumRadio WavesWavelengths of more than 104m to about 0.1 m Used in radio and television communication systemsMicrowavesWavelengths from about 0.3 m to 10-4mWell suited for radar systemsMicrowave ovens are an applicationInfrared wavesWavelengths of about 10-3m to 7 x 10-7mIncorrectly called “heat waves”Produced by hot objects and moleculesReadily absorbed by most materialsVisible lightPart of the spectrum detected by the human eyeMost sensitive at about 5.5 x 10-7m (yellow-green)Ultraviolet, X-rays and Gamma raysMore About Visible LightDifferent frequencies (or wavelengths in vacuum) correspond to different colorsThe range of wavelength in vacuum is from red (λ~ 7 x 10-7m) to violet (λ ~4 x 10-7m)More notes on the EM wave SpectrumUltraviolet lightCovers about 4 x 10-7m to 6 x 10-10mSun is an important source of uv lightMost uv light from the sun is absorbed in the stratosphere by ozoneX-raysWavelengths of about 10-8m to 10-12mMost common source is acceleration of high-energy electrons striking a metal targetUsed as a diagnostic tool in medicineGamma raysWavelengths of about 10-10m to 10-14mEmitted by
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