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Let S be the upper half of the unit sphere X+y+z<=1with outward-pointing normal vector (so Z20). .2 Suppose F= (y, x, x²+y?). Find the flux of curl(F) through S using a surface integral. Hint: You are asked to compute: . curl(F)-as = JJ curl(F)•n dS = .curUF) N dudv. For N, you can use N=(cosesin²o, sin@sin²ø, cosøsinø ) which comes from G(u,v)=G(@,4)=where Osos2n and 0<0Sa/2. See if you get Curl (F)=<2sin@sinø, –2cos@sinø, 0).

Let S be the upper half of the unit sphere X+y+z<=1with outward-pointing normal vector (so Z20). .2 Suppose F= (y, x, x²+y?). Find the flux of curl(F) through S using a surface integral. Hint: You are asked to compute: . curl(F)-as = JJ curl(F)•n dS = .curUF) N dudv. For N, you can use N=(cosesin²o, sin@sin²ø, cosøsinø ) which comes from G(u,v)=G(@,4)=where Osos2n and 0<0Sa/2. See if you get Curl (F)=<2sin@sinø, –2cos@sinø, 0).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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QUESTION 1 Let S be the upper half of the unit sphere x+y²+z=1 with outward-pointing normal vector (so Z>0). Suppose F = <y, x, x²+y²). Find the flux of curl(F) through S using a surface integral. Hint: You are asked to compute: J| curl(F) ds = | curl (F) n ds= || curl(F)·N dudv. %3D S. S. For N, you can use N=(cos@sin²q,'sin@sin²ø, cosøsino)which comes from G(u,v)=G(0,4)=(cos@sinø, sin@sing, cosø>=<x,y,z>where Os@s2M and0søST/2. See if you get Cur (F)=(2sin@sinø, –2cos@sinø, 0).
Transcribed Image Text:QUESTION 1 Let S be the upper half of the unit sphere x+y²+z=1 with outward-pointing normal vector (so Z>0). Suppose F = <y, x, x²+y²). Find the flux of curl(F) through S using a surface integral. Hint: You are asked to compute: J| curl(F) ds = | curl (F) n ds= || curl(F)·N dudv. %3D S. S. For N, you can use N=(cos@sin²q,'sin@sin²ø, cosøsino)which comes from G(u,v)=G(0,4)=(cos@sinø, sin@sing, cosø>=<x,y,z>where Os@s2M and0søST/2. See if you get Cur (F)=(2sin@sinø, –2cos@sinø, 0).
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