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**Unformatted text preview: **EE138: Homework Assignment #1 U HOMEWORK DUE: 10/07/2009 (in class) HOMEWORK QUIZ: 10/09/2009 (in class) Problem #1: Because of a wartime shortage of copper, the electromagnets at Oak Ridge National Lab used to separate U‐235 isotopes were wound with pure silver (atomic volume 10.3 cc/mole). If 100 meters of silver wire 3 mm in diameter required 3.6 watts when carrying 4 amps of current, calculate for silver the (a) resistivity, (b) mobility, (c) collision time, (d) mean free path, (e) Hall coefficient, and (f) the Hall field in a transverse magnetic field of 0.3 tesla. Assume silver has one free electron per atom, and a temperature of 300K. Problem #2: We shall learn later in the course that the random electron velocity in metals is not really given by Equation 1.13 in S&W, but is actually higher, and is essentially temperature‐independent . Assuming that to be the case, for the six quantities in Problem #1, would you expect them to increase, decrease, or remain the same if the silver was cooled to liquid nitrogen temperatures? Please include your reasoning in your answer. Ignore the small effects of thermal lattice contraction, and assume that the current, magnetic field, and carrier concentration are unchanged. Problem #3: (a) Adding dopants to a sample of silicon is found to reduce the Hall coefficient by a factor of 10 and increase the conductivity by a factor of 5. What effect has this dopant addition had on the mean free path? (b) In a Hall experiment with a transverse magnetic field of 20 tesla, the total electric field is at angle 20o to the current. Assuming the charge carriers to be electrons, what is their collision time? (c) If you doubled the width of a Hall sample but kept J and B the same, how would that affect the Hall field? the Hall voltage? the net charge density along the edges? Problem #4: (a) Using exponential form similar to Equation 1.30 in S&W, write an expression for the electric field of a plane wave of blue light ( = 450 nm) traveling in the negative y direction with its magnetic fields in the z‐direction. Insert numerical values for angular frequency and wave number. (b) Part of this wave enters an ideal dielectric with = or = 4 x 10‐11 F/m. Calculate the wavelength, wave number, frequency, angular frequency, and velocity of this blue light within the dielectric. (c) Part of the same wave enters a conductor with a conductivity of 104 S/cm. By how much will the electric field of this wave be attenuated in traveling through 100 nm of the conductor? Assume the material to be nonmagnetic. U U U U U U (d) Assuming that the second term in Equation 1.38 in S&W is dominant in the conductor, what will be the wavelength (distance between nodes) of this light in this material? Problem #5: (a) You look at the sun through goggles that have been coated with a thin layer of highly‐
conductive metal such as silver. Briefly explain why and in which way the color of light will be altered. (b) For use in a liquid crystal display, you want an electrode that is transparent to all visible light. You decide to use a doped semiconducting oxide with a mobility of 10‐2 m2/V‐s. What is the maximum conductivity you can expect from your oxide? Assume = o U ...

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