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March 25, 2005 Physics for Scientists&Engineers 2 1Physics for Scientists &Physics for Scientists &EngineersEngineers 22Spring Semester 2005Lecture 34March 25, 2005 Physics for Scientists&Engineers 2 2ReviewReview! The speed of an electromagnetic wave can be expressed in terms oftwo fundamental constants related to electric fields and magneticfields, the magnetic permeability and the electric permittivity of thevacuum! The speed of light is constant in any reference frame• Relativity! For an electromagnetic wave, the wavelength and frequency of the waveare related to the speed of lightc =1µ0!0c =!fMarch 25, 2005 Physics for Scientists&Engineers 2 3Review (2)Review (2)The Electromagnetic SpectrumMarch 25, 2005 Physics for Scientists&Engineers 2 4Traveling Electromagnetic WavesTraveling Electromagnetic Waves! Sub-atomic processes can produce electromagnetic waves such asgamma rays, X-rays, and light! Electromagnetic waves can also be produced by an oscillator connectedto an antenna! The connection between the circuitand the circuit on the right isaccomplished using a transformer! A dipole antenna is used toapproximate an electric dipole! The voltage and current in theantenna vary sinusoidally with timeand cause charge in the antenna tooscillate with frequency ! of the circuit! The electromagnetic waves created by moving charges travel from theantenna with speed c and frequency f = !/(2")March 25, 2005 Physics for Scientists&Engineers 2 5Traveling Electromagnetic Waves (2)Traveling Electromagnetic Waves (2)! We can think of these travelingelectromagnetic waves as wavefronts spreading out sphericallyfrom the antenna! However, at a large distance fromthe antenna, the wave fronts willappear to be almost flat, or planar! So we can think of theelectromagnetic wave in terms of our assumed form E(!r ,t) = Emaxsin kx !"t( )B(!r ,t) = Bmaxsin kx !"t( )March 25, 2005 Physics for Scientists&Engineers 2 6Traveling Electromagnetic Waves (3)Traveling Electromagnetic Waves (3)! If we now place in the path of these electromagnetic waves, a secondRLC circuit tuned to the same frequency !0 as the emitting circuit,voltage and current will be induced in this second circuit! These induced oscillations are the basic idea of radio transmission andreception! If the second circuit has! smaller voltages and currents will be induced, providing selective tuningfor different frequencies! This principle of transmission of electromagnetic waves was discoveredby German physicist Heinrich Hertz (1857-1894) in 1888, and then usedby Italian physicist Guglielmo Marconi (1874-1937) to transmit wirelesssignals!0,2= 1 / LC "!0March 25, 2005 Physics for Scientists&Engineers 2 7EnergyEnergy TransportTransport! When we walk out into the sunlight, we feel warmth! If we stay out too long in the bright sunshine, we will get sunburn! These phenomena are related to electromagnetic waves emitted fromthe Sun! These electromagnetic waves carry energy generated in the nuclearreactions of the Sun to our skin! The rate of energy transported by an electromagnetic wave is usuallydefined as! This quantity is called the Poynting vector after British physicist JohnPoynting (1852-1914) who first discussed its properties !S =1µ0!E !!BMarch 25, 2005 Physics for Scientists&Engineers 2 8EnergyEnergy Transport (2)Transport (2)! The magnitude of the Poynting vector is related to the instantaneousrate at which energy transported by an electromagnetic wave over agiven area• more simply, the instantaneous power per unit area! The units of the Poynting vector are W/m2! For an electromagnetic wave, in which B is perpendicular to E, we canwrite S =!S =powerarea!"#$%&instantaneousS =1µ0EBMarch 25, 2005 Physics for Scientists&Engineers 2 9EnergyEnergy Transport (3)Transport (3)! We know that the magnitude of the electric field and the magneticfield are directly related via E/B = c! We can express the instantaneous power per unit area of anelectromagnetic wave in terms of the magnitude the electric field orthe magnetic field! However, usually it is easier to measure an electric field than amagnetic field so we express the instantaneous power per unit area as! We can now substitute a sinusoidal form for the electric field andobtain an expression for the transmitted power per unit areaS =1cµ0E2E = Emaxsin kx !"t( )March 25, 2005 Physics for Scientists&Engineers 2 10Energy Transport (4)Energy Transport (4)! The usual method of describing the power per unit area in anelectromagnetic wave is the intensity I of the wave given by! The units of intensity are the same as the units of the Poynting vector,W/m2! The average of sin2(kx-!t) over time is 1/2! So we can express the intensity asI = Save=powerarea!"#$%&ave=1cµ0Emax2sin2kx '(t( ))*+,aveI =1cµ0Erms2 Erms= Emax/ 2( )March 25, 2005 Physics for Scientists&Engineers 2 11Energy Transport (5)Energy Transport (5)! Because the magnitude of the electric and magnetic fields of theelectromagnetic wave are related by E = cB, and c is such a largenumber, one might conclude that the energy transported by theelectric field is much larger than the energy transmitted by themagnetic field! Actually the energy transported by the electric field is the same as theenergy transported by the magnetic field! We can understand this fact by remembering that the energy densityof an electric field is given by! And the energy density of a magnetic field is given byuE=12!0E2uB=12µ0B2March 25, 2005 Physics for Scientists&Engineers 2 12Energy Transport (6)Energy Transport (6)! If we substitute! We get! We obtain the result that the energy density of electricfield is the same as the energy density of the magneticfield everywhere in the electromagnetic waveE = cBc =1µ0!0uE=12!0cB( )2=12!0Bµ0!0"#$%&'2=12µ0B2= uBMarch 25, 2005 Physics for Scientists&Engineers 2 13Radiation PressureRadiation Pressure! When you walk out into the sunlight, you feel warmth, butyou do not feel any force from the sunlight! Sunlight is exerting a pressure on you, but that pressure issmall enough that you do not notice it! Because these electromagnetic waves are radiated fromthe Sun and travel to you on the Earth, we call theseelectromagnetic waves radiation! This type of radiation is not the same as radioactiveradiation resulting from the decay of unstable nuclei! Let’s calculate the magnitude of the pressure exerted bythese radiated electromagnetic wavesMarch 25, 2005 Physics for Scientists&Engineers 2 14Radiation Pressure (2)Radiation


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