The Displacement CurrentGauss’s Law for MagnetismMaxwell’s EquationsPlane Electromagnetic WavesOne-Dimensional Wave EquationStanding Electromagnetic WavesPoynting VectorExample 13.1: Solar ConstantExample 13.2: Intensity of a Standing WaveEnergy TransportMomentum and Radiation PressureProduction of Electromagnetic WavesAnimation 13.1: Electric Dipole Radiation 1Animation 13.2: Electric Dipole Radiation 2Animation 13.3: Radiation From a Quarter-Wave AntennaPlane WavesSinusoidal Electromagnetic WaveSummaryAppendix: Reflection of Electromagnetic Waves at Conducting Problem-Solving Strategy: Traveling Electromagnetic WavesSolved ProblemsPlane Electromagnetic WaveOne-Dimensional Wave EquationPoynting Vector of a Charging CapacitorPoynting Vector of a ConductorConceptual QuestionsAdditional ProblemsSolar SailingReflections of True LoveCoaxial Cable and Power FlowSuperposition of Electromagnetic WavesSinusoidal Electromagnetic WaveRadiation Pressure of Electromagnetic WaveEnergy of Electromagnetic WavesWave EquationElectromagnetic Plane WaveSinusoidal Electromagnetic WaveChapter 13 Maxwell’s Equations and Electromagnetic Waves 13.1 The Displacement Current..................................................................................... 2 13.2 Gauss’s Law for Magnetism.................................................................................. 4 13.3 Maxwell’s Equations ............................................................................................. 4 13.4 Plane Electromagnetic Waves ............................................................................... 6 13.4.1 One-Dimensional Wave Equation .................................................................. 9 13.5 Standing Electromagnetic Waves........................................................................ 12 13.6 Poynting Vector................................................................................................... 14 Example 13.1: Solar Constant.................................................................................. 16 Example 13.2: Intensity of a Standing Wave........................................................... 18 13.6.1 Energy Transport .......................................................................................... 18 13.7 Momentum and Radiation Pressure..................................................................... 21 13.8 Production of Electromagnetic Waves ................................................................ 22 Animation 13.1: Electric Dipole Radiation 1......................................................... 24 Animation 13.2: Electric Dipole Radiation 2......................................................... 24 Animation 13.3: Radiation From a Quarter-Wave Antenna .................................. 25 13.8.1 Plane Waves.................................................................................................. 25 13.8.2 Sinusoidal Electromagnetic Wave................................................................ 30 13.9 Summary.............................................................................................................. 32 13.10 Appendix: Reflection of Electromagnetic Waves at Conducting Surfaces....... 34 13.11 Problem-Solving Strategy: Traveling Electromagnetic Waves......................... 38 13.12 Solved Problems ................................................................................................ 40 13.12.1 Plane Electromagnetic Wave...................................................................... 40 13.12.2 One-Dimensional Wave Equation .............................................................. 41 13.12.3 Poynting Vector of a Charging Capacitor................................................... 42 13.12.4 Poynting Vector of a Conductor ................................................................. 44 13.13 Conceptual Questions ........................................................................................ 45 13.14 Additional Problems .......................................................................................... 46 13.14.1 Solar Sailing................................................................................................ 46 013.14.2 Reflections of True Love ............................................................................ 46 13.14.3 Coaxial Cable and Power Flow................................................................... 46 13.14.4 Superposition of Electromagnetic Waves................................................... 47 13.14.5 Sinusoidal Electromagnetic Wave.............................................................. 47 13.14.6 Radiation Pressure of Electromagnetic Wave............................................. 48 13.14.7 Energy of Electromagnetic Waves.............................................................. 48 13.14.8 Wave Equation............................................................................................ 49 13.14.9 Electromagnetic Plane Wave...................................................................... 49 13.14.10 Sinusoidal Electromagnetic Wave............................................................ 49 1Maxwell’s Equations and Electromagnetic Waves 13.1 The Displacement Current In Chapter 9, we learned that if a current-carrying wire possesses certain symmetry, the magnetic field can be obtained by using Ampere’s law: 0encdIµ⋅=∫Bs (13.1.1) The equation states that the line integral of a magnetic field around an arbitrary closed loop is equal to 0encIµ, where encI is the conduction current passing through the surface bound by the closed path. In addition, we also learned in Chapter 10 that, as a consequence of the Faraday’s law of induction, a changing magnetic field can produce an electric field, according to Sdddtd⋅=− ⋅∫∫∫Es BA (13.1.2) One might then wonder whether or not the converse could be true, namely, a changing electric field produces a magnetic field. If so, then the right-hand side of Eq. (13.1.1) will have to be modified to reflect such “symmetry” between Eand B. To see how magnetic fields can be created by a time-varying electric field, consider a capacitor which is being charged. During the charging process, the electric field strength increases with time as more charge is accumulated on the plates. The conduction current that carries the
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