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EE101 HW1S - Problem 1 In cylindrical coordinate system v=...

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Problem 1. In cylindrical coordinate system: ± 2 r v T π φ = K where 2 T π ω = So ± v r ω φ = K Then transform it into spherical coordinate: ± sin v R ω θφ = K Problem 2. In cylindrical coordinate system ± 2 v r ω φ = K by applying the curl in cylindrical coordinate using the formula on page 13 in lecture note => 3 v z r ω ∇× = K ± Then convert P1, P2, P3 into cylindrical coordinate system => , 1 (0,0,0) P = 2 (0, /3, / 2) o P R π = , 3 ( 3 / 4, /3, / 4) o o P R R π = in cylindrical coordinate (r, φ , z). Then by noticing that the amplitude of the curl of this vector field is only proportional to r, the rank should be P3>P2=P1 Problem 3. a. at R=R m R S v ds K v o = l l 2 2 0 0 sin ( sin ) 9 o o R R R d d π π R θ θ θ φ ∫ ∫ = 2 3 2 0 0 sin 9 o R d d π π θ θ φ ∫ ∫ = 2 3 9 o R π
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