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7. Use the divergence theorem to calculate the outward flux of F through the closed surface S. (a) F² = r²i + y² j + z2k and S is the region cut from the solid cylinder r² + y²

7. Use the divergence theorem to calculate the outward flux of F through the closed surface S. (a) F² = r²i + y² j + z2k and S is the region cut from the solid cylinder r² + y²

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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7. Use the divergence theorem to calculate the outward flux of F through the closed surface S. (a) F² = r²i + y² j + z2k and S is the region cut from the solid cylinder r² + y² <a² by the planes z = 0 and z = 1. (b) ♬³ = r²ì – 2ryj + 3rzk and S is the region cut from the first octant by the sphere r² + y² + 2² = 4. - (c) F = 2zzi+yj - z2k and S is the wedge cut from the first octant by the plane z = y and the elliptical cylinder 2+4y² = 16. (d) Fit and S is the region 1 ≤ r² + y² + z² ≤ 4.
Transcribed Image Text:7. Use the divergence theorem to calculate the outward flux of F through the closed surface S. (a) F² = r²i + y² j + z2k and S is the region cut from the solid cylinder r² + y² <a² by the planes z = 0 and z = 1. (b) ♬³ = r²ì – 2ryj + 3rzk and S is the region cut from the first octant by the sphere r² + y² + 2² = 4. - (c) F = 2zzi+yj - z2k and S is the wedge cut from the first octant by the plane z = y and the elliptical cylinder 2+4y² = 16. (d) Fit and S is the region 1 ≤ r² + y² + z² ≤ 4.
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