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Let S be the disk enclosed by the curve C: r(t) = (cos q cos t, sint, sin p cos t), for 0sts2a, where 0sp s; is a fixed angle. By introducing he variable r, this surface can be parameterized as S= {(r cos p cos t,rsin t,rsin p cos t): 0srs1, 0st<2x} with the normal vector n= {-rsinq,0,r cos q) . Use Stokes' Theorem and a surface integral to find the circulation on C of the vector field F = (-y,x, 0) as a function of p. For what value of o is the circulation a maximum? The circulation on C is 27 cos q. (Type an exact answer, using x as needed.) The circulation is a maximum for p = 0. (Type an exact answer, using n as needed.)

Let S be the disk enclosed by the curve C: r(t) = (cos q cos t, sint, sin p cos t), for 0sts2a, where 0sp s; is a fixed angle. By introducing he variable r, this surface can be parameterized as S= {(r cos p cos t,rsin t,rsin p cos t): 0srs1, 0st<2x} with the normal vector n= {-rsinq,0,r cos q) . Use Stokes' Theorem and a surface integral to find the circulation on C of the vector field F = (-y,x, 0) as a function of p. For what value of o is the circulation a maximum? The circulation on C is 27 cos q. (Type an exact answer, using x as needed.) The circulation is a maximum for p = 0. (Type an exact answer, using n as needed.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Let S be the disk enclosed by the curve C: r(t) = (cos p cos t, sint, sin p cos t), for 0st<2n, where 0<ps is a fixed angle. By introducing the variable r, this surface can be parameterized as S= {(r cos p cos t,rsin t,r sin p cos t): 0srs1, 0st< 2x} with the normal vector n= (-rsin o,0,r cos p). Use Stokes' Theorem and a surface integral to find the circulation on C of the vector field F = (-y,x, 0) as a function of p. For what value of p is the circulation a maximum? The circulation on C is 2n cos o. (Type an exact answer, using n as needed.) The circulation is a maximum for p = 0. (Type an exact answer, using n as needed.)
Transcribed Image Text:Let S be the disk enclosed by the curve C: r(t) = (cos p cos t, sint, sin p cos t), for 0st<2n, where 0<ps is a fixed angle. By introducing the variable r, this surface can be parameterized as S= {(r cos p cos t,rsin t,r sin p cos t): 0srs1, 0st< 2x} with the normal vector n= (-rsin o,0,r cos p). Use Stokes' Theorem and a surface integral to find the circulation on C of the vector field F = (-y,x, 0) as a function of p. For what value of p is the circulation a maximum? The circulation on C is 2n cos o. (Type an exact answer, using n as needed.) The circulation is a maximum for p = 0. (Type an exact answer, using n as needed.)
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