329sp09hw10 - ECE 329 Homework 10 Due: Thu, April 9, 2009,...

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Unformatted text preview: ECE 329 Homework 10 Due: Thu, April 9, 2009, 5PM 1. In a region of space electrostatic potential is known to be ( x, y, z ) =- 4( y 2 + 4) z . a) What is the corresponding electrostatic field E ? b) What is the volumetric charge density in the region if = 2 o ? Hint: you can use the Poissons equation in this problem. c) Repeat (b) if = o (1 + e- z 2 ) . Hint: you cannot use the Poissons equation in this problem. 2. 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 = 1 V relative to the cathode. If the potential distribution in the region < x < d is given by = ( x/d ) 4 / 3 , find the following: a) Field E at x = d/ 2 , b) Volumetric free-charge density at x = d/ 4 , c) The surface charge density s on the anode. Hint: you make use of relations E =- d dx x , o E = , and n ( D 1- D 2 ) = s , treating the interior of vacuum diode as free-space containing a free charge carrier density of...
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This note was uploaded on 11/16/2009 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.

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329sp09hw10 - ECE 329 Homework 10 Due: Thu, April 9, 2009,...

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