P30_027 - 27. We use Eq. 30-15 and the superposition of...

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27. We use Eq. 30-15 and the superposition of forces: ~ F 4 = ~ F 14 + ~ F 24 + ~ F 34 . With θ =45 , the situation is as shown below: y x 12 3 4 ~ F 41 ~ F 42 ~ F 43 θ θ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The components of ~ F 4 are given by F 4 x = F 43 F 42 cos θ = µ 0 i 2 2 πa µ 0 i 2 cos 45 2 2 = 3 µ 0 i 2 4 and F 4 y = F 41 F 42 sin θ = µ 0 i 2 2 µ 0 i 2 sin 45 2 2 = µ 0 i 2 4 . Thus, F 4 =( F 2 4 x + F 2 4 y ) 1 / 2 = " µ 3 µ 0 i 2 4 2 + µ µ 0 i 2 4 2 # 1 / 2 =
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