HW2 - Physics 3122 Fall 2010 Homework Set 2 Solutions 1.32...

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Unformatted text preview: Physics 3122, Fall 2010: Homework Set 2 Solutions. 1.32 r v = xy ˆ x + 2 yz ˆ y + 3 zx ˆ z r ∇ ⋅ r v = y + 2 z + 3 x ( y + 2 z + 3 x ) dxdydz = 2 ∫ 2 ∫ 2 ∫ yx + 2 zx + 3 x 2 /2 [ ] 2 dydz 2 ∫ 2 ∫ = 2 y + 4 z + 6 [ ] dydz 2 ∫ 2 ∫ = y 2 + 4 zy + 6 y [ ] 2 dz 2 ∫ = 4 + 8 z + 12 [ ] dz 2 ∫ = 4 z + 4 z 2 + 12 z [ ] 2 = 8 + 16 + 24 [ ] = 48 r v ⋅ d r a front ∫ = 2 ydydz 2 ∫ 2 ∫ = 8 r v ⋅ d r a back ∫ = dydz 2 ∫ 2 ∫ = 0 r v ⋅ d r a right ∫ = 4 zdxdz 2 ∫ 2 ∫ = 16 r v ⋅ d r a left ∫ = dydz 2 ∫ 2 ∫ = 0 r v ⋅ d r a top ∫ = 6 xdxdy 2 ∫ 2 ∫ = 24 r v ⋅ d r a bottom ∫ = dxdz 2 ∫ 2 ∫ = r v ⋅ d r a = 8 + + 16 + + 24 + = 48 ∫ 1.33 r v = xy ˆ x + 2 yz ˆ y + 3 zx ˆ z r ∇ × r v = (0 − 2 y ) ˆ x + (0 − 3 z ) ˆ y + (0 − x ) ˆ z = − 2 y ˆ x − 3 z ˆ y − x ˆ z r ∇ × r v ⋅ ˆ x dydz 2 − z ∫ 2 ∫ = − 2 ydydz 2 − z ∫ 2 ∫ = − (2 − z ) 2 dz 2 ∫ = − (4 − 4 z + z 2 ) dz 2 ∫ = − 8/3 r v ⋅...
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HW2 - Physics 3122 Fall 2010 Homework Set 2 Solutions 1.32...

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