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329fall09hw5 - E z = ±-3 8 ± ± 2 ˆ z ≤ z ≤ d-3 8 ±...

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ECE 329 Homework 5 Due: September 29, 2009, 5 PM 1. Copper is a highly conducting material with a conductivity of σ = 5 . 8 × 10 7 S/m and a free-electron density of N e = 8 . 45 × 10 28 m - 3 . a) Given that the charge of an electron is q = - e = - 1 . 6 × 10 - 19 C, calculate the DC electron mobility for copper. b) Determine the resistance R of a copper wire of radius r = 1 . 5 mm and length l = 400 m. c) What would be the magnitude of electric field E within the wire of part (b) if the wire were conducting a current of 3 A? You may assume uniform current distribution across the cross section of the wire. d) How long would it take an electron to drift from one end of the wire to the other? 2. The region between two infinite, plane parallel, perfectly conducting plates at z = 0 and z = 1 m is filled with two slabs of perfect dielectric materials having constant electric permittivities 1 for 0 < z < d (region 1) and 2 for d < z < 1 (region 2). The bottom plate is held at a constant potential
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Unformatted text preview: E ( z ) = ±-3 8 ± ± 2 ˆ z ≤ z ≤ d-3 8 ± ± 1 ˆ z d ≤ z ≤ 1 (1) a) Write the expression for the electrostatic potential V ( z ) for < z < 1 m in terms of ± 1 , ± 2 , and d . b) Does V ( z ) determined in part (a) satisfy Laplace’s Equation in the region < z < 1 m? Explain your answer. c) If the two parallel plates were each confined to have a finite area A (where √ A ± d , so that fringing fields may be neglected), what would be the capacitance C of the structure in terms of ± 1 , ± 2 , and d ? Hint: You may derive C in one of two ways: (1) as the ratio Q/V of the total charge accumulated on the top plate to the total voltage drop between the plates, or (2) the combination of the capacitance of each dielectric slab in series C = ( C-1 1 + C-1 2 )-1 . 1...
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