PHYS 671 Homework I due date Tuesday September 17th 2013 at class meeting Total number of points 150 You need 100 points for full score 50 points 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 properly credit the author by citing the material used Be sure to properly write problem question numbers you are answering 1 Consider a point charge q moving at constant relativistic velocity v along the z axis 30 pts a Write down the particle s electric field in all the direction perpendicular to its velocity v How does your answer vary with 5 pts b Calculate the electric flux E from the particle using Gauss s law How does your answer vary with 10 pts hint you will need the integral R sin z dz 2 2 0 1 2 sin2 z 3 2 c Compare answer a and b and try to explain the apparent discrepancy in the 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 k c k can be associated to an electromagnetic wave in free space Here k is the usual 3 wavevector the frequency of the electromagnetic wave and the the velocity of light in vacuum 30 pts a What is magnitude k k of 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 Doppler shift for a light wave that is the frequency observed in the laboratory for a source moving in the x direction with velocity v c for an arbitrary k Express the observed frequency in term of the frequency in the rest frame 0 and the angle in the laboratory frame 10 pts 2
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