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Maxwell’s Equations and Electromagnetic Waves 4/9/2015 Kevin Holway Maxwell's Equations Galilean field transformations Maxwell’s equations Electromagnetic waves Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890. Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:James_Clerk_Maxwell.png#/media/File:James_Clerk_Maxwell.png Maxwell's Equations Galilean field transformations Maxwell’s equations Electromagnetic waves Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890. Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:James_Clerk_Maxwell.png#/media/File:James_Clerk_Maxwell.png Sharon runs past Bill while holding a positive charge q. In Bill’s reference frame, the charge creates A. Only an electric field. B. Only a magnetic field. C. An electric and a magnetic field. D. No fields. Sharon runs past Bill while holding a positive charge q. In Sharon’s reference frame, the charge creates A. Only an electric field. B. Only a magnetic field. C. An electric and a magnetic field. D. No fields. Galilean transformations and Galilean invariance Sharon runs past Bill while holding a positive charge q through a uniform, constant magnetic field that Bill created. Then Bill measures a force on Sharon’s charge that is: A. Zero B. Non-zero x x x x x x x x x x x x x x x Sharon runs past Bill while holding a positive charge q through a uniform, constant magnetic field that Bill created. Then Sharon measures a force on her charge that is: A. Zero B. Non-zero x x x x x x x x x x x x x x x Experimenters on earth have created the magnetic field shown. A rocket flies through the field, from right to left. Which are the field (or fields) in the rocket’s reference frame? Not quite relativity… Maxwell's Equations Galilean field transformations Maxwell’s equations Electromagnetic waves Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890. Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:James_Clerk_Maxwell.png#/media/File:James_Clerk_Maxwell.png The equations so far and displacement current The electric field is decreasing. Which is the induced magnetic field? E. There’s no induced field in this case. Example: induced magnetic field in a discharging capacitor Maxwell's equations Along with Lorentz force law, this is the fundamental content of classical electromagnetic theory Maxwell's equations in vacuum Maxwell's equations in vacuum (differential form) Maxwell's Equations Galilean field transformations Maxwell’s equations Electromagnetic waves Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890. Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:James_Clerk_Maxwell.png#/media/File:James_Clerk_Maxwell.png "We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena." Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890. Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:James_Clerk_Maxwell.png#/media/File:James_Clerk_Maxwell.png Prediction by Maxwell: Propagating Wave With Speed of Light c Sinusoidal plane wave <get better animation> Demo: sources and linearly polarized light (dipole antenna) http://www2.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html How is light created? Accelerating charges Img at right: "Black body" by Darth Kule - Own work. Licensed under Public Domain via Wikimedia Commons http://commons.wikimedia.org/wiki/File:Black_body.svg#/media/File:Black_body.svg How is light created? Quantum mechanical processes How is light created? Cerenkov radiation Demo: Spectra (gas discharge tubes and diffraction gratings) http://www2.lbl.gov/MicroWorlds/ALSTool/EMSpec/EMSpec2.html Wavelength determines color but color does not determine wavelength! Color is a complex perception of the world constructed by your brain. Why are living creatures tuned to the visual spectrum? Sun emits the most energy in visual range of spectrum (Stefan-Boltzmann law). Water vapor in atmosphere blocks most light except the visual range. Maxwell's Equations Galilean field transformations Maxwell’s equations Electromagnetic waves Image: "James Clerk Maxwell" by George J. Stodart - Frontpiece in James Maxwell, The Scientific Papers of James Clerk Maxwell. Ed: W. D. Niven. New York: Dover, 1890. Licensed under Public Domain via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:James_Clerk_Maxwell.png#/media/File:James_Clerk_Maxwell.png "Mantis shrimp from front" by Jenny - originally posted to Flickr as mantis shrimp. Licensed under CC BY 2.0 via Wikimedia Commons http://commons.wikimedia.org/wiki/File:Mantis_shrimp_from_front.jpg#/media/File:Mantis_shrimp_from_front.jpg