This is an open book test. Notes, texts, study aids are allowed. You have 120 minutes. If time runs short, try for at least partial credit on each problem by indicating the correct method. Each part of each question is worth 5 points (100 total).
a) A coaxial cable carries a signal in TEM mode. What does that mean?
b) The cable is insulated with material of dielectric constant K = 4. How fast does a signal travel along the cable?
c) Inner and outer conductor diameters are 0.1 cm and 1 cm respectively. What is the cable impedance?
d) The cable carries a signal of frequency 1 MHz and average power 1 kW. What is the maximum current carried on the inner conductor?
e) List a few of the changes you would expect if the conductors and insulators were not perfect.
a) The electrons each have kinetic energy of T = 1 MeV in the laboratory reference frame. What is their velocity in the lab frame?
b) Find the magnitude of the electric field E of one electron at the position of the other in the lab frame.
c) Find the magnetic field B produced by one electron at the other in the lab frame.
d) Find the Lorentz force of one electron at the other in the lab frame.
e) By what factor is the force different in the proper frame of the pair?
a) If the frequency of the wave is nu = 10^4 Hertz, is the material to be considered a "good" conductor?
b) What is the wavelength of the wave in this material?
c) The intensity as the wave passes the origin is Sav = 1 kW/m^2. How far will the wave travel before the intensity is reduced by a factor 100?
d) Write down an expression for the electric field E of this wave. Assume the wave vector points in the +z direction and the polarization lies in the x-z plane.
e) Give a corresponding expression for the magnetic field B of the wave.
a) The radius of the ring of magnets containing these electrons (in a tunnel under the Alps) is about R = 5 kilometers. What is the average magnetic field B seen by the electrons?
b) Find the transverse electric field E' arising from B as seen by the electron in an inertial frame S' tangent to the orbit, at the instant when the electron finds itself at rest in S'
c) What is the acceleration of the electron in S' at that instant?
d) Estimate the energy lost to radiation by one electron making one complete circuit of this ring.
e) When the improvements now underway succeed in doubling the electron energy, by what factor will the radiation loss per turn increase? Hint: don't forget the change in B, as R is fixed by the tunnel. (Most of the cost of the upgrade goes into supplying power to make up for this additional radiation loss.)