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20095ee101_1_HW3

# 20095ee101_1_HW3 - EE 101 Homework 3 Due date Q1 Suppose...

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EE 101 Homework 3 Due date: Oct 29, 2009 Q1. Suppose that a parallel plate capacitor has rectangular plates but the plates are not exactly parallel. The separation at one edge is d a and d + a at the other edge where a « d . Show that the capacitance is given approximately by g ≈ G ± ² ³ ´1 + µ · where A is the area of the plates. ( 12 points ) (Hints: You need to consider the differential capacitance ³g = G ± ¸³¹ º , º = µ » ¹ + ³ where l is the depth of the plate, s is the separation of the plates at the differential element’s location. Then, integration of this differential element over – w to w gives you the result. In addition, you need to use the approximation, 1 / (1 + x ) ≈ 1 – x + x 2 .) Q2. Assume a point charge Q above an infinite conducting plane at y = 0. a) Prove that the potential V ( x , y , z ) at any point (except at the location of the point charge) on the upper-half space ( y > 0) satisfies Laplace’s equation if the conducting

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20095ee101_1_HW3 - EE 101 Homework 3 Due date Q1 Suppose...

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