EM 1 Electromagnetic Waves Last semester we studied Classical Mechanics The fundamental laws axioms of Classical Mechanics are called Newton s Laws This semester we are studying a subject called Classical Electromagnetism There are four fundamental laws of electromagnetism called Maxwell s Equations after the Scottish physicist James Clerk Maxwell 1 Gauss s Law v v E da q enclosed e0 E fields are caused by charges v v v v d E d l B da 2 Faraday s Law E fields are also caused by changing B fields dt S L v v v v d B d l m I me E da 3 Ampere Maxwell Law 0 enclosed 0 0 dt A L A B fields are caused both by currents and by changing E fields v v B da 0 There are no magnetic monopoles 4 Gauss s Law for B fields Except for the last term in equation 3 all four of these laws had been discovered experimentally before Maxwell started his research in the 1850 s So why do we call them Maxwell s Equations Maxwell realized that Ampere s Law v v B d l L A I I m0 Ienclosed was incomplete He noticed that there are situations in which Ampere s Law fails to give the E increasing correct answer For instance if a capacitor is being charged up by a steady current then there must be a B field around the capacitor caused by the nearby currents But according to the original form of Ampere s law if we consider an imaginary loop circling the capacitor diagram below the current through this loop is zero So Ampere s Law predicts that the B field is along that loop is zero since Ithru 0 Maxwell noticed that although Last update 1 14 2019 Dubson Phys1120 Notes University of Colorado EM 2 there is no current through the loop there is imaginary loop L a changing E field flux through the loop He saw that he could fix the problem by I modifying Ampere s Law with the addition I of a new term The changing electic flux in the capacitor leads to a quantity that has the dimensions of current e0 Ithru 0 B 0 v v d E da dt A v v e E da has the dimensions of charge So 0 Notice that from Gauss s Law the quantity A e0 v v d E da has the dimensions of current Maxwell called this new quantity the dt A displacement current By replacing the current I in Ampere s Law I e0 v v d E da he was dt A able to resolve the problem This new form of Ampere s Law now called the Ampere Maxwell Law appealed to Maxwell s sense of aesthetics There was now a pleasing symmetry in the equations changing B fields create E fields Faraday s Law changing E fields create B fields Ampere Maxwell Law Maxwell realized that because of this symmetry the equations predicted a peculiar kind of selfsustaining interaction between E and B fields Maxwell thought Suppose you have a charge q and you shake it back and forth The q creates an E field but when you shake the charge you are changing the E field in the space around it This changing E field creates a B field But now you just created a B field where there was none before so you have a changing B field This changing B field will create an E field and that newly created E field will create a B field which will create an E which will create a B which will the process will go on forever Last update 1 14 2019 Dubson Phys1120 Notes University of Colorado EM 3 Maxwell showed that the equations predicted the existence of an electromagnetic wave which travels outward from the shaking charge E B E B E E B E B E Maxwell computed the speed of this strange new electromagnetic wave and found that the speed was given by a simple formula speed v c 1 3 0 108 m s eo mo This number is the same as the speed of light Maxwell had shown that light was an electromagnetic wave Before Maxwell scientists had no clear idea what light is This was a great synthesis a bringing together of previously separate fields of physics electricity magnetism and optics Before Maxwell no one knew what light was It was known that light was some kind of wave we will see the evidence for this later but no one knew what kind of wave it was Maxwell figured it out Light is an electromagnetic wave which is created by accelerating electric charge Wave speed is v distance 1 wavelength time time for 1 l to go by For light waves speed v c this is written Last update 1 14 2019 l T v l l f T c l f Dubson Phys1120 Notes University of Colorado EM 4 EM waves are transverse waves the E and B field vectors are both perpendicular to the direction of the wave Drawing an EM wave in space is quite difficult the E and B fields are everywhere and intimately mixed The figure here shows the E field along a particular line at a moment in time All EM radiation is caused by shaking accelerating electric charge The more rapidly the charge is shaken the higher the frequency of the shake the shorter the wavelength of the light since l c Now we can understand why all things glow give off light when they get hot f E up and down wavelength speed c B in and out When something is very hot its atoms are jiggling furiously Atoms are made of charges electrons and protons and the jiggling charges emit EM radiation Different wavelength ranges are given names Wavelength 0 01 nm Name Use occurrence Gamma rays Radioactivity X ray medical Ultraviolet UV Sunburns black lights 400nm 700 nm Visible Human seeing 700nm 1mm Infrared IR Heat rays microwave Communications microwave ovens radio Radio TV 0 01 nm nm nm 400 nm cm m km Electromagnetic radiation light can have any wavelength But our eyes are sensitive only to a narrow range of wavelengths between 400 nm and 700 nm Different wavelengths in this range of visible light correspond to different colors Wavelength 700 nm light appears red to us 400 Last update 1 14 2019 Dubson Phys1120 Notes University of Colorado EM 5 nm light appears violet and the wavelengths in between correspond to all the colors of the rainbow ROYGBIV All wavelengths outside this narrow band are invisible to human eyes Some important facts about EM waves EM waves are transverse The E and B field are perpendicular to each other are each E perpendicular to the direction of propagation like so c Radio receiving antennas must be oriented correctly in order to B function the wire antenna must be parallel to the E field in order for the electrons in the wire to be accelerated along the wire The E and B fields are in phase E …
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