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2_13 - PHY 5346 HW Set 5 Solutions Kimel 1 2.13 The system...

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PHY 5346 HW Set 5 Solutions – Kimel 1. 2.13 The system is pictured in the following figure: a) Notice from the figure, fi _ , ? d = fi _ , d ; thus from Eq. (2.71) in the text, fi _ , d = a 0 + > n = 1 K a n _ n cos n d X ? ^ /2 3 ^ /2 fi b , d = 2 ^ a 0 = ^ V 1 + ^ V 2 a 0 = V 1 + V 2 2 Using X ? ^ /2 3 ^ /2 cos m d cos n d d d = N nm ^ Applying this to fi , only odd terms m contribute in the sum and a m = 2 V 1 ? V 2 ^ mb m ? 1 m ? 1 2 Thus fi _ , d = V 1 + V 2 2 + 2 V 1 ? V 2 ^ Im > m odd i m _ m e im d mb m Using 2 > m odd x m m = ln 1 + x 1 ? x and Im ln A + iB = tan ? 1 B / A we get fi _ , d = V 1 + V 2 2 + V 1 ? V 2 ^ tan ? 1 2 _ b cos
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