Question 7This question concerns the vector fieldF = -ry?i – x²yj+ z(x² + y?) k.(a) Calculate the divergence of F. Use the divergence theorem to show thatthe 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 itsaxis of symmetry along the z-axis, as shown in the diagram below.hRCalculate the flux of F over the curved portion S of the surface of thecylinder by using the result of part (a) to relate the flux of F over S tothe flux of F over the flat top surface T and the flux of F over the flatbottom surface B.(Hint: Calculating the flux of F over T and B is easier in cylindricalcoordinates.)

Given: The vector filed F=-xy2i-x2yj+zx2+y2k

Question 7 This question concerns the vector field F = -ry?i – a²yj + z(x² + y³) 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 R Y 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.)

Question 7 This question concerns the vector field F = -ry?i – a²yj + z(x² + y³) 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 R Y 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.)

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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