Chapter 7 - Chapter 7: Plane Electromagnetic Waves and Wave...

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Chapter 7: Plane Electromagnetic Waves and Wave Propagation
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An Historical Perspective: Faraday Time-varying magnetic field generates electric field. Maxwell Time-varying electric field generates magnetic field. 1791 1831 1873 1887 1879 1905 Einstein's special theory of relativity Hertz discovered radio waves; Maxwell's theory accepted Faraday born Faraday's law; Maxwell born Maxwell died; Einstein born Maxwell equations
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A Note about Oscillatory Behavior: { energy exchange energy storing example mechanisms mecha energy energy Common feature of oscillatory behavior: type 1 type 2 energy storing mechanisms Oscillations require energy exchange mechanism(s) 2 2 2 2 22 11 , medium nism(s) mass-spring system restoring force mass & spring LC oscillator , , & wire EM wave not required E B Ed B d E B dt dt QI LC mv kx ε μ
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Organization of Lecture Notes on Ch. 7: In Jackson, plane waves in dielectric media are treated in Secs. 7.1 and 7.2. Various special cases (plasma medium and high-frequency limit) are treated in Sec. 7.5. Plane waves in conductors are treated in Sec. 5.18 [e.g. Eqs. (5.163)-(5.169)] and Sec. 8.1 [e.g. Eqs. (8.9), (8.10), (8.12), (8.14), and (8.15)] by methods different from those in Secs. 7.1 and 7.2. Here, we will cover these sections in Jackson with a unified treatment of plane waves in both dielectrics and conductors, and at all frequencies. Equations in Jackson will be examined in greater detail, but in somewhat different order. So, in the lecture notes, the three sections on these materials will be numbered Secs. I, II, and III rather than following Jackson’s section numbers. However, Secs. 7.3, 7.4, 7.8, and 7.9 of Jackson will be followed closely in subsequent lecture notes (and numbered as in Jackson) . We begin with a derivation of the generalized dielectric constant ε / 0 , which is applicable to both dielectric and conducting media.
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restoring force () Fx x : electron collision frequency : damping force (rate of change of electron momentum due to collisions) m γ x ± x : displacement of the electron from its equilibrium position x = 0. N N 2 0 0 ( 0 ) ( 0 ) As in Sec. 4.6, we neglect higher-order terms. m x F xF F ' x ω = ++ " Dipole Moment of a Single Electron: The equation of motion for an atomic or molecular electron with mass m and charge – e in the presence of an external electric field E ( x , t ) can be written: I. Derivation of the Generalized Dielectric Constant ε / 0 [Sec. 7.5 (part A)] N 2 0 0 restoring force due to electron displacement ( , ) (7.49) The "binding frquency" is the natural oscillation f γω =− ²³´ ±± ± me t m m xE x x x 22 00 requency of the electron if it is set to oscillate about 0 under the restoring force . Since 1/ , the restoring force is independent of . ωω = −∝ mm m x
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I. Derivation of the Generalized Dielectric Constant ε / 0 ( continued ) 2 0 2 0 Rewrite (7.49), ( , ) , as ( ) ( , ) Let* ( , ) = ( )e and expand ( ) about the equilibrium position 0, we obtain ( ) (0) it me t m m t t ω γω =− ++ = == + xE x x x xx x E x Ex x E ±± ± ± of the order of (0) () ( 0 ) ( 0 ) , where is the scale length of ( ). For example, if ( ) is a wave field, then . By neglect x wavelength λ ⋅∇ + E E " ²³´³µ ing ( ) (0), we have
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This note was uploaded on 05/14/2010 for the course EAD 234 taught by Professor Ncl during the Spring '10 term at École Normale Supérieure.

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Chapter 7 - Chapter 7: Plane Electromagnetic Waves and Wave...

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