PHYS 671: Homework Idue date: Tuesday, September 17th, 2013 at class meeting.Total number of points: 150. You need 100 points for full score (50points are extra credit).You are welcome to work together. If you partially use work from others (e.g.something you might have found in a book or a journal paper), you should properlycredit the author by citing the material used. Be sure to properly write prob-lem/question numbers you are answering.1. Consider a point charge q moving at constant, relativistic velocity v along theˆz-axis. [30 pts](a) Write down the particle’s electric field in all the direction perpendicularto its velocity−→v . How does your answer vary with γ? [5 pts](b) Calculate the electric flux ΦEfrom the particle using Gauss’s law. Howdoes your answer vary with γ? [10 pts] [hint: you will need the integralRπ0sin(z)dz[1−β2sin2(z)]3/2= 2γ2](c) Compare answer (a) and (b) and try to explain the ”apparent discrep-ancy” in the γ-dependence. [15 pts]2. Jackson’s 3rd edition, problem 11.4 [(a): 15 pts, (b): 15 pts].3. Jackson’s 3rd edition, problem 11.5 [20 pts].4. Jackson’s 3rd edition, problem 11.18 [40 pts].5. A 4-wavevector, kα≡ (ω/c,−→k ), can be associated to an electromagnetic wavein free space. Here−→k is the usual 3-wavevector, ω the frequency of the elec-tromagnetic wave and the the velocity of light in vacuum. [30 pts](a) What is magnitude kαkαof the 4-wavevector in term of phase velocity?[10 pts](b) How would you write the phase of a wave in term of the 4-wavevector?What can you conclude from this expression? [10 pts]1(c) Apply the Lorentz transformation to the 4-wavevector to derive the Dopplershift for a light wave, that is, the frequency observed in the laboratory fora source moving in the x-direction with velocity v = βc for an arbitrary−→k . Express the observed frequency in term of the frequency in the restframe ω0, and the angle θ in the laboratory frame. [10
View Full Document
Unlocking...