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Question: 8 b in the diagram the shaded surface s is...

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8. b) In the diagram, the shaded surface S is a right circular cylinder of height 1 and of radius 2 about the z-axis, and whose lower boundary Co is the circle of radius 2 in the r-y plane. Thus the upper boundary of S is the circle C1 of radius 2 in the plane: = 1, Note that S does not include the lower and upper disks. S is oriented by means of the unit normal n which points away from the #-axis. Consider the vector field 꾜 defined by y.a(-s,s,sin(r)) (i) Cornpute ▽ × 꾜. (i) Parameterise Co and Cr so that they are positively oriented with respect to the orien tation on S (i) By using Stokes Theorem, or otherwise, evaluate Ci (0,-2,0) S Co
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