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4. Let F = (0, -2z, 2), and let S be the part of the sphere x² + y² + z² = 1 where z ≥ 1/2. (a) Evaluate I = ffs FdS directly as a surface integral. (b) Verify that F = curl G, where G = (0, 2r, 2xz), and evaluate I using Stokes' Theorem.

4. Let F = (0, -2z, 2), and let S be the part of the sphere x² + y² + z² = 1 where z ≥ 1/2. (a) Evaluate I = ffs FdS directly as a surface integral. (b) Verify that F = curl G, where G = (0, 2r, 2xz), and evaluate I using Stokes' Theorem.

Advanced Engineering Mathematics
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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4. Let F = (0, -2z, 2), and let S be the part of the sphere x² + y² + z² = 1 where z ≥ 1/2. (a) Evaluate I = ffs FdS directly as a surface integral. (b) Verify that F = curl G, where G = (0, 2r, 2xz), and evaluate I using Stokes' Theorem.
Transcribed Image Text:4. Let F = (0, -2z, 2), and let S be the part of the sphere x² + y² + z² = 1 where z ≥ 1/2. (a) Evaluate I = ffs FdS directly as a surface integral. (b) Verify that F = curl G, where G = (0, 2r, 2xz), and evaluate I using Stokes' Theorem.
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