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Ch 32 Maxwell’s Equations 1)Gauss’ Law for Electrostatics 2)Gauss’ Law for Magnetostatic 3)Faraday's Law 4)Maxwell-Ampere Law They predict that light is an E&M Wave propagating at speed =3x10 8 m/s (Edinburgh, Scotland) The first Unification of Physical Laws. The pursuit has never stopped….

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Can you ever just get a north pole or a south pole ???

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Gauss’s Law for Magnetism Reminder of the definition of magnetic flux As of today 4/21/05 there is no evidence of magnetic monopoles See :Phys.Rev.Lett.85:5292,2000

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Gauss’s Law for Magnetism Only magnetic dipoles exist

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The Search for magnetic monopoles Goes ON! Null result sets the lower bound on a monopole mass to be about m= GeV

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Carl Friedrich Gauss The total flux passing through a closed surface is proportional to the charge enclosed within that surface.

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KEY TO USING Gauss’s Law The shape of the surrounding surface is one that MIMICS the symmetry of the charge distribution …..

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Faraday: Changing Flux due to moving permanent magnet British Physicist

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Induced EMF produced by a changing Magnetic Flux!

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Induced electric fields We will assume here that B is increasing into the page

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Electric Field circulates about a changing magnetic field (into the page here)

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Maxwell thought is there a symmetry here? Can there be a circulating magnetic field around a changing electric field? Maxwell’s Law of Induction WAIT!!! Didn’t we already see that B circulates around a current carrying WIRE ?!!?

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Recall Ampere’s Law Andre Marie Ampere ( )

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For r>R, radius of wire the magnetic field must have cylindrical symmetry Long Straight Wire with a constant current

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Ampere-Maxwell Law and Maxwell’s Displacement current

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Displacement Current

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Maxwell’s Equations Gauss’s Law Gauss’s Law for Magnetism Ampere’s Maxwell’s Law Ampere’s Maxwell’s Law Faraday’s Law

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Information AGE, Medicine, Engineering …. Based on the physics of E&M waves T.V. telecommuncations, radio transmission, radar … Challenge of today’s engineers to try to envision what global interconnections will be in 20 years (Halliday and Resnick 04) Starting point understanding Electro-mag waves which is summarized by Maxwell’s rainbow!

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E&M Waves and Maxwell Crowning achievement was to show that light is a traveling E&M wave The basis for the study of optics! Phys. 213 and Dr. Romberger Phys. Science 440 In mid 1800s only infrared, visible and ultraviolet forms of light were only E&M waves know Heinrich Hertz later showed that what we call radio waves also..

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Maxwell’s Rainbow

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Human Eye Sensitivity

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Traveling Waves Consider a transformer: A generating LC circuit which establishes a frequencey and a secondary coil with a dipole antenna. You have a changing E and B field coupled together!!! However, changes don’t appear instantaneously, they happen a the speed of light with the disturbance traveling outward at that speed. Will see

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Looking toward the wave front the amplitudes are related by the cross product Wave is transverse/perpendicular to the direction of travel Field vary sinusoidally At speed of light!!

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Traveling E&M wave No need for a medium on wave generates the other. Prediction of Maxwell’s equation and proved by Einstein with a little bit of symmetry 1905

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Faraday’s Law of Induction Maxwell’s Law of Induction Faraday’s Law Ampere’s Maxwell’s Law Ampere’s Maxwell’s Law

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Faraday’s Law of Induction Applying Faraday’s law to the loop above

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Maxwell’s Law of Induction Applying Maxwell’s law of induction to the loop above

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The Wave Equation Source free region ie no wires and no charges Solution

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Spherical Wave Energy John Henry Poynting ( ): E&M waves transport energy! From which we define intensity

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Looking toward the wave front the amplitudes are related by the cross product Wave is transverse/perpendicular to the direction of travel Field vary sinusoidally At speed of light!!

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