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# 10sfinal - Electromagnetic Theory II Final Examination 29...

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Electromagnetic Theory II Final Examination 29 April 2010, 12:30-2:30 pm Instructions: Answer the following 10 questions, each of which is worth 10 points. Explain your reasoning in each case. Use SI units throughout. Points will be deducted for gaps in logic as well as for errors in calculation. Extra points will be deducted if an incorrect answer is presented with incorrect units! A sheet of useful formulas is provided at the end of the exam booklet. 1

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Questions 1 and 2 . The photon is a “particle” of light with energy-momentum 4-vector q μ = ( ω/c, k ) where ω and k are the frequency and vector wave number of the electro- magnetic wave. Then q 2 = q μ q μ = 0 for light whereas p 2 = - m 2 c 2 for a massive particle like the electron. This is why we say that a photon is a massless particle. In the following we consider the process photon( q μ ) + electron( p μ ) photon( q 0 μ ) + electron( p 0 μ ) where the initial electron is at rest p = 0. The Compton effect is that ω 0 < ω due to the recoil of the struck electron. 1. Assuming that the initial photon is traveling in the positive z -direction and that the scattered photon is in the xz -plane, write out the components of the 4-vectors p μ , q μ , q 0 μ in terms of ω , ω 0 and the photon scattering angle θ . 2. Apply relativistic energy-momentum conservation to this process to determine ω 0 as a function of ω and θ . (Hint: you may find it useful to consider the Lorentz invariant ( q - q 0 ) 2 where q μ , q 0 μ are the 4-momenta of the initial and final photons.) 2
Questions 3 and 4 . For a hollow wave guide of general cross section parallel to the z -axis and with the z, t dependence of the fields assumed to be e ikz - iωt , recall that the modes are

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10sfinal - Electromagnetic Theory II Final Examination 29...

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