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Unformatted text preview: ECE 3030: Electromagnetic Fields and Waves Fall 2009 WORKSHOP 6 INSTRUCTOR NOTES: Anisotropic Plates Reminder: A difficult subject! Date: Thursday 10/8 1. Review highlights of Prelim 1? Solutions posted. 2. Problem 10.3 A plane wave propagates in the negative x direction in a dielectric with ε = 2 ε . The wave is left circularly polarized, its fre- quency is 2 GHz, and the complex amplitude of ~ E is 1 V/m. Give the complete complex expressions for ~ E and ~ H as functions of space and time such that ~ E is in the positive z direction at x = t = 0. Solution: From the information given k =- ω c √ 2 a x = ⇒ - k · r = + ω c √ 2 x (1) since ² = 2 ² . The total electric field may be written as E = E [ j ˆ a y + ˆ a z ] e j ( ωt + kx ) (2) with ω = 4 π × 10 9 s- 1 . From (2) we can see that the instantaneous value of E (the real part of (2)) at the origin will be in the z direction at t = 0 and then will rotate to the negative y-direction (which is also perpendicular to k ) when ωt = π/ 2. So E remains perpendicular to the k-vector and rotates in the left hand sense, for propagation in the negative x direction. (Draw yourself a sketch of < [ E ] if you don’t see this.) Since | E · E * | = 2 E 2 o , E o = 1 √ 2 V/m and so the full complex expression for E becomes...
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