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2_2 - PHY 5346 HW Set 2 Solutions Kimel 5 2.2 The system is...

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PHY 5346 HW Set 2 Solutions – Kimel 5. 2.2 The system is described by a) Using the method of images d x 3 = 1 4 ^ P 0 q | x 3 ? y 3 | + q v | x 3 ? y 3 v | with y v = a 2 y , and q v = ? q a y b) a = ? P 0 / / n d | x = a = +P 0 / / x d | x = a a = P 0 1 4 ^ P 0 / / x q x 2 + y 2 ? 2 xy cos L 1/2 + q v x 2 + y v 2 ? 2 xy v cos L 1/2 a = ? q 1 4 ^ a 1 ? y 2 a 2 y 2 + a 2 ? 2 ay cos L 3/2 Note q induced = a 2 X a d I = ? q 1 4 ^ a 2 2 ^ a 1 ? y 2 a 2 X ? 1 1 dx y 2 + a 2 ? 2 ayx 3/2 , where x = cos L q induced = ? q 2 a a 2 ? y 2 2 a a 2 ? y 2 = ? q c) | F | = qq v 4 ^ P 0 y v ? y 2 = 1 4 ^ P 0 q 2 ay a 2 ? y 2 , the force is attractive, to the right. d) If the conductor were fixed at a different potential, or equivalently if extra charge were put on
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