Let E be the protion of the parabloid z = 4 - r^2 for r is an element-of a disk of radius 2, centered at the origin. Let F: R^3->R^3. F(x,y,z) = (xz-y, yz+x, -z^2) what is the flux over the region E (of the curl of F)?

Let E be the protion of the parabloid z = 4 - r^2 for r is an element-of a disk of radius 2, centered at the origin. Let F: R^3->R^3. F(x,y,z) = (xz-y, yz+x, -z^2) what is the flux over the region E (of the curl of F)?

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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Question

Let E be the protion of the parabloid z = 4 - r^2 for r is an element-of a disk of radius 2, centered at the origin.

Let F: R^3->R^3. F(x,y,z) = (xz-y, yz+x, -z^2)

what is the flux over the region E (of the curl of F)?

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Step 1: Firstly we will find Curl F,

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