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Unformatted text preview: ECE 3030: Electromagnetic Fields and Waves Fall 2009 WORKSHOP 5 INSTRUCTOR NOTES: Virtual Work and Plane Waves Reminder: Give students the indicated items. Date: Thursday 10/1 1. Problem 8.14 Apply virtual work concepts. Give the students the basic formulas: U = 1 2 CV 2 , Q = CV , and C A x = C Wa d where U is the energy, C the capacitance, W the width of the plates, a the plate overlap, A = Wa the area of the capacitor plates, and d the spacing between the plates. Remind the students that although we ignore the fringing fields in the calculations, it is, in fact, the fringing fields that cause the force. The students should do the rest, but check in their initial steps. a. The force is F =- U a + V Q a fl fl fl fl V fixed =- 1 2 C a V 2 + V C a V = 1 2 C a V 2 F = 1 2 W d V 2 = 1 2 CV 2 a b. I ( t ) = d Q d t = d( CV ) d t = V d C d t = W d V d a d t c. The work done by the source is t f Z t i V I ( t )d t = V t f Z t i W d V d a d t d t...
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