Let be the curve given by the intersection of the plane z = 2 and the cone z = √² + y² counter- clockwise oriented as viewed from above. Let the vector field F = (x²-y, 4z, 1²). Use Stokes' theorem to find the circulation of F around by integrating over (i) the surface of the cone (ii) the flat disk of radius 2 centered on the z-axis and lying in the plane z = 2.
Let be the curve given by the intersection of the plane z = 2 and the cone z = √² + y² counter- clockwise oriented as viewed from above. Let the vector field F = (x²-y, 4z, 1²). Use Stokes' theorem to find the circulation of F around by integrating over (i) the surface of the cone (ii) the flat disk of radius 2 centered on the z-axis and lying in the plane z = 2.
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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![Let be the curve given by the intersection of the plane z = 2 and the cone z = √² + y2 counter-
clockwise oriented as viewed from above. Let the vector field F = (x²-y, 4z, 2²). Use Stokes' theorem
to find the circulation of F around by integrating over
(i) the surface of the cone
(ii) the flat disk of radius 2 centered on the z-axis and lying in the plane z = 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F741f6be6-8829-482d-8847-4d6abe7c76ed%2F537bf6b0-c0b2-4a2d-8bfc-e00080681a18%2F8gk1rv8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let be the curve given by the intersection of the plane z = 2 and the cone z = √² + y2 counter-
clockwise oriented as viewed from above. Let the vector field F = (x²-y, 4z, 2²). Use Stokes' theorem
to find the circulation of F around by integrating over
(i) the surface of the cone
(ii) the flat disk of radius 2 centered on the z-axis and lying in the plane z = 2.
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