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Question: let d be the unit disc in r3 which is...

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Let D be the unit disc in R3 which is centred at the origin and which lies in the ry-plane, i.e. the plane z = 0· Let S be the upper half of the unit sphere in R3 which is also centred at the origin. Thus θD = aS = C, where C := {(z, y, 0) : 2,2 + уг = 1). Define a vector field w by r, у z) (-2y..rsin(z) + V1 + e», 0 (i) Calculate ▽ x w. (i) Choose a unit normal n to D and calculate t x (V xw). n dA ii) Choose a unit tangent t to C. Using Stokes theorem or otherwise, evaluate the circulation w tds iv) Let N be the unit normal to S which points away from the origin and calculate the flux
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