Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

Sample Final Exam, Physics 4303

Instructions:  This is an open book and open notes exam.  You may use devices on which you have made notes, but you are not allowed to consult any online resources. You may use a calculator.  Do each problem on the sheets of paper provided.  Do each problem on a separate piece of paper, since each problem will be graded separately.  Make sure your name and ID number are on every sheet.  If you use more than one sheet for a problem, staple together all the sheets.

1. (50 pts.) Consider an electromagnetic wave in vacuum that is incident normally with a

conductor that fills the space z > 0.  Assume the wave frequency is high enough so that the skin depth in the conductor can be neglected, so that the conductor can be characterized by a conductance Σ integrated over the skin depth.  (a) Determine the electric and magnetic fields in the conductor at z = 0 in terms of the electric field of the incident wave; (b) Calculate the   Poynting flux of the incident and reflected waves, and show that the Joule dissipation in the  conductor is equal to the difference between the incident and reflected Poynting fluxes.

2. (50 pts.) A particle with charge q oscillates so that its position is given by r, = z0  sin ωtz.  (a) Starting from equation (11.62), determine the radiation electric field, assuming that the particle’s motion is non-relativistic (i.e., ωz0/c << 1).  You can assume the observation point is far from the charge, so that you can determine the retarded time based on the origin.  Note that it is sufficient to consider points in the xz plane. (b) Calculate the differential power dP/dΩ averaged over the period of the oscillation, and sketch it as a polar plot. (c) Suppose  the particle is relativistic.  Without doing any further calculations, make a qualitative sketch of the differential power in this case.

3.  (50 pts.) The π+  meson has a mass of 140 MeV and a mean lifetime in its rest frame of

2.6x10− 8 seconds.  It decays into a muon and neutrino, π+ → μ+ + νμ, where the muon has a mass of 106 MeV and the neutrino is essentially massless. (a) A cosmic ray impacting the atmosphere creates a π+ with a total energy of 10 GeV that propagates downward.  Find the lifetime of the pion in the Earth’s rest frame and calculate the distance it travels before it decays. (b) After the decay, the neutrino momentum in the cm frame is in the downward direction.  Find the energies of the muon and neutrino in both the cm frame and the frame of the Earth.  What is the direction of the muon momentum in the Earth frame?

4.  (50 pts.) An infinitely long, straight wire carries a current I and has no charge in its rest frame K.  A charge q sits at rest in this frame at a distance s from the wire. (a) Find the electric and  magnetic field in frame K and calculate the force on the charge. (b) Now consider a Lorentz transformation to a frame K that moves at a velocity V in the direction along  the wire.  What  are the electric and magnetic fields in this frame? (c)  Determine the current I and the linear  charge density λ in frame K .  Show that the fields produced by this current and charge are consistent with the results in part (b).  What is the force on the charge in this frame?