PHYS 308 Homework
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   Homework #5: Due Friday, February 27, by 5:00pm.

  1. problem 2.75. Do just the curls and divergences (show you work for each of these--no "sudden miracles" here) part. Ignore the sentence that starts out "If the curl turns out to be... ."
  2. Suppose that aluminum donates 1 of its electrons to the conduction band of electrons while a current is flowing through it.
    (a) An aluminum wire of radius r=0.120mm has a current of 2.75Amps flowing through it. Find the magnitude of the current density J.
    (b) Find the number density 'n' of these conduction electrons in units of #/m3. A very useful web page for this part is
    (c) Find the magintude of the "drift velocity" v of the electrons in this aluminum wire.
  3. One of our standard 24-gauge wires in the electronics lab is made of copper, and has a diameter of 0.5106mm.
    (a) Find the resistance of 15cm of this wire.
    (b) If a current of 1.60A is running through the wire, find the magnitude of the current density in this wire.
    (c) Find the typical speed of the electrons in this wire.
    (d) Find the average time τ between collisions for the electrons in this wire.
  4. problem 4.22. Note that the return path will have much less resistance than the copper wire cable. Hint: Think about the cross-sectional area of that return path.
  5. problem 4.25. Note Eqs. (4.22) and (4.23) which deal with multiple charge carriers.
  6. The quantity 'kT' is a powerful thing that allows you to make fairly intelligent estimates of the available thermal energy involved in many situations. Getting a feel for the amounts of these energies at various temperatures will make your life in physics easier. Calculate the following:
    (a) The temperature (in Kelvin, of course) that corresponds to 1.0eV of energy. Recall that kBoltzmann=8.6174x10-5 eV/K.
    (b) The energy in units of eV associated with room temperature of 295K.
    (c) The energy in units of eV at the surface of the sun (5,800K).
    (d) The temperature required to provide the energy ionize a hydrogen atom in its ground state with n=1 (recall En=(-)13.6eV Z2/n2 where Z=atomic number).
  7. I have an infinitesimally thin square sheet of metal whose sides are 1.5m long. I put a total of 22μC of charge on this infinitesimally thin sheet of metal. Derive the expression for the magnitude of the electric field at a distance of 12mm above the central point of this sheet--calculate that number. You must show all of your work--including drawings--to get credit for this problem.
   That's all for homework #5.