EM-1Electromagnetic WavesLast semester, we studied Classical Mechanics. The fundamental laws (axioms) of Classical Mechanics are called Newton's Laws, and we were able to write them all down and understand them in their full, complete form. 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). In this course, Faraday's Law is the only one of Maxwell's Equations which we shall actually write down in complete form. The other 3 laws are a bit too mathematically complex to write down in full detail, but we have seen simplified versions of these laws. In words, Maxwell's 4 equations are:(1) Electric fields are created by charges. (The full form of this equation is called Gauss's Law. We have seen this equation in a simplified form: due to Q2| Q || E | kr=r .)(2) Magnetic fields are created by currents. (This equation is called Ampere's Law, and we have seen this equation is the simplified form 0due to straight wireI| B |2 rm=pr .)(3) Magnetic field lines always form closed loops. (This equation has no standard name.)(4) Electric fields are created by changing magnetic fields. (Faraday's Law).Actually, 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 made a change to Ampere's Law, equation (2). Maxwell argued, on theoretical grounds, that Ampere's Law must be incomplete; it needs a modification. Maxwell's noticed thatthere are situations in which a electric current inevitably involves a changing electric field. For instance, if a capacitor is being charged up by a steady current, then there must be an increasing electric field between the plates, due tothe increasing charge brought to theplates by the steady current.Maxwell's showed that, in order toproperly describe such situations,Last update: 1/14/2019 Dubson Phys2020 Notes, University of Colorado E (increasing)I IEM-2Ampere's Law must be modified so that it reads "Magnetic fields are created by currents and by changing electric fields." 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 self-sustaining 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 (it changed from zero to non-zero). 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). Maxwell showed that the equations predicted the existence of an electromagnetic wave which travels outward from the shaking charge:Maxwell computed the speed of this strange, new electromagnetic wave and found that the speedwas given by a simple formula: 8o o1speed v = c 3.0 10 m/s= = �e m.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.Last update: 1/14/2019 Dubson Phys2020 Notes, University of Colorado EE EE EE B BBBEM-3Light is an electromagnetic wave which is created by accelerating electric charge.Last update: 1/14/2019 Dubson Phys2020 Notes, University of ColoradoEM-4Review of Waves:Wave vs. particle: When a particle moves from location A to B, mass is transported. When a wave travels from A to B, no mass is transported. A wave carries energy, momentum, and information, but not matter. Before electromagnetic waves were discovered, all the kinds of waves that were known required a medium to carry the wave. Water waves, sound waves, and waves on a string are disturbances in a medium (water, air, string). But EM waves can travel in vacuum — no mediumnecessary. This was extremely surprising to 19th century physicists. So surprising, in fact, that they could not believe it. Rather than believe the evidence of experiment, scientists clung to theirnotions about how all waves should behave. They invented (made up) a medium to carry the EM wave, and gave it the (appropriately fairy-tale-like) name of the luminiferous aether. But there isno aether. The EM wave is unlike any other kind of wave. The EM wave is its own medium. It rolls out it own red carpet as it goes.Traveling Waves can be categorized as:Traveling waves can also be categorized as:transverse: displacement of the medium is perpendicular (transverse) to the direction of the wave velocity (like a wave on water or a string or drumhead).orlongitudinal: displacement of the medium is parallel to the direction of the wave velocity (like sound wave or a slinky that has been push-pulled).Longitudinal Wave:Sinusoidal waves have a wavelength () and a frequency (f). period T = time for 1 wavelength to pass by. Last update: 1/14/2019 Dubson Phys2020 Notes, University of Colorado wave speed vsinusoidal: impulse: vor wave velocity vdisplacementEM-5frequency f = 1 / T = rate at which wavelength's pass by.Example: T = 0.1 s f = 1 / 0.1 s = 10 s-1 = 10 Hz (meaning 10 wavelengths go by each sec)Wave speed is distance 1 wavelengthvtime time for 1 to go by Tl= = =l v fTl= = lFor light waves, speed v = c, this is written c f= lEM 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. The E and B-field are
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