329sp08hw9

329sp08hw9 - ECE 329 Homework 9 Due: Tue, March 25, 2008,...

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ECE 329 Homework 9 Due: Tue, March 25, 2008, 5PM 1. Consider a simplifed 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 , fnd 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 infnite, plane parallel, perFectly conducting plates at x =0
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