a) Compute the flux of the vector field F = (-2, 3, z³) across the disk in the xy- plane of radius 2, oriented with upward pointing normal vectors. Explain the result. - b) Is the flux across the top hemisphere of the sphere x² + y² + ² 4 oriented with outward pointing normal vectors equal to the flux across the disk just computed in part a)? Explain your reasoning.
a) Compute the flux of the vector field F = (-2, 3, z³) across the disk in the xy- plane of radius 2, oriented with upward pointing normal vectors. Explain the result. - b) Is the flux across the top hemisphere of the sphere x² + y² + ² 4 oriented with outward pointing normal vectors equal to the flux across the disk just computed in part a)? Explain your reasoning.
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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Transcribed Image Text:a) Compute the flux of the vector field F = (-2, 3, z3³) across the disk in the xy-
plane of radius 2, oriented with upward pointing normal vectors. Explain the result.
b) Is the flux across the top hemisphere of the sphere x² + y² + z² 4 oriented
with outward pointing normal vectors equal to the flux across the disk just computed
in part a)? Explain your reasoning.
-
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