This question concerns the vector field F= -ry'i – ryj+ z(1² + y°) k. (a) Calculate the divergence of F. Use the divergence theorem to show that the flux of F over any closed surface is equal to zero. (b) A cylinder of height h and radius R has its base in the ry-plane and its axis of symmetry along the z-axis, as shown in the diagram below. h Calculate the flux of F over the curved portion S of the surface of the cylinder by using the result of part (a) to relate the flux of F over S to the flux of F over the flat top surface T and the flux of F over the flat bottom surface B. (Hint: Calculating the flux of F over T and B is easier in cylindrical coordinates.)
This question concerns the vector field F= -ry'i – ryj+ z(1² + y°) k. (a) Calculate the divergence of F. Use the divergence theorem to show that the flux of F over any closed surface is equal to zero. (b) A cylinder of height h and radius R has its base in the ry-plane and its axis of symmetry along the z-axis, as shown in the diagram below. h Calculate the flux of F over the curved portion S of the surface of the cylinder by using the result of part (a) to relate the flux of F over S to the flux of F over the flat top surface T and the flux of F over the flat bottom surface B. (Hint: Calculating the flux of F over T and B is easier in cylindrical coordinates.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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