Simple Nature - Light and Matter

wave terminology, we say that the wave is transverse, not longitudinal.)The wave pattern in figure i is impossible, because it divergesfrom the middle. For virtually any choice of Gaussian surface, themagnetic and electric fluxes would be nonzero, contradicting theequations Φ B = 0 and Φ E = 0. 12Reflection example 23The wave in figure j hits a silvered mirror. The metal is a goodconductor, so it has constant voltage throughout, and the electricfield equals zero inside it: the wave doesn’t penetrate and is 100%reflected. If the electric field is to be zero at the surface as well,the reflected wave must have its electric field inverted (p. 362), sothat the incident and reflected fields cancel there.But the magnetic field of the reflected wave is not inverted. This isbecause the reflected wave has to have the correct right-handedrelationship between the fields and the direction of propagation.PolarizationTwo electromagnetic waves traveling in the same direction throughspace can differ by having their electric and magnetic fields in differentdirections, a property of the wave called its polarization.j / Example 23. The incidentand reflected waves are drawnoffset from each other for clarity,but are actually on top ofeach other so that their fieldssuperpose.The speed of lightWhat is the velocity of the waves described by Maxwell’s equations?Maxwell convinced himself that light was an electromagneticwave partly because his equations predicted waves moving at the velocityof light, c. The only velocity that appears in the equations isc, so this is fairly plausible, although a real calculation is required inorder to prove that the velocity of the waves isn’t something like 2cor c/π — or zero, which is also c multiplied by a constant! The followingdiscussion, leading up to a proof that electromagnetic wavestravel at c, is meant to be understandable even if you’re reading thisbook out of order, and haven’t yet learned much about waves. Asalways with proofs in this book, the reason to read it isn’t to convinceyourself that it’s true, but rather to build your intuition. Thestyle will be visual. In all the following figures, the wave patternsare moving across the page (let’s say to the right), and it usuallydoesn’t matter whether you imagine them as representing the wave’smagnetic field or its electric field, because Maxwell’s equations ina vacuum have the same form for both fields. Whichever field weimagine the figures as representing, the other field is coming in andout of the page.The velocity of the waves is not zero. If the wave pattern was12 Even if the fields can’t be parallel to the direction of propagation, one mightwonder whether they could form some angle other than 90 degrees with it. No.One proof is given on page 703. A alternative argument, which is simpler butmore esoteric, is that if there was such a pattern, then there would be some otherframe of reference in which it would look like figure i.Section 11.6 Maxwell’s Equations 699