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329sp08hw9 - ECE 329 Homework 9 Due Tue 5PM 1 Consider a...

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ECE 329 Homework 9 Due: Tue, March 25, 2008, 5PM 1. Consider a simplified model of a vacuum diode consisting of a cathode in the x = 0 plane and an anode in the x = d plane, where the anode is held to a constant potential V 0 = 1 V relative to the cathode. If the potential distribution in the region 0 < x < d is given by V = V 0 ( x/d ) 4 / 3 , find the following: (a) E at x = d/ 2 , (b) volumetric free-charge density ρ at x = d/ 4 , and (c) the surface charge ρ s on the anode. Hint: you make use of the relations E = - dV dx ˆ x , · o E = ρ , and ˆ n · ( D 1 - D 2 ) = ρ s , treating the interior of the vacuum diode as free-space containing a free charge carrier density of ρ . 2. Consider two infinite, plane parallel, perfectly conducting plates at
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