homework2

# Engineering Electromagnetics with CD (McGraw-Hill Series in Electrical Engineering)

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EE 151 Caltech Electromagnetic Engineering Spring ‘05 Homework 2 Due Tuesday, April 12 th in class 1. (a) (1) The width of the region containing ε R1 in Fig. 1 is 1.2 m. Find ε R1 if ε R2 = 2.5 and the total capacitance is 60 nF. (2) Find the width of each region (containing ε R1 and ε R2 ) if C total = 80 nF, ε R2 = 3 ε R1 , and C 1 = 2 C 2 . (b) For the same system as in part (a) , use Femlab to plot the E and D fields. Based on your simulation, answer the following questions: (1) At the interface of the two dielectric materials, is there any discontinuity of the E and D fields? Is there any net charge at the interface? (2) Which side of the capacitor has higher fringe field? (3) Taking into account the fringe fields, is the capacitance higher or lower than what you calculate in part (a) ? Explain. 2 m ε R1 2 m ε R2 2 mm Conducting plates Figure 1

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