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3) Consider the half sphere shaped object bounded by z = v V1-x² – y? and z= 0. The object is exposed to a field F = (1– z)k. Evaluate $(F.n) dS, where is the outer unit normal to - 7 S the surface and S represents the surface of the object, i. By surface integration, ii. Using the divergence theorem of Gauss. Compare the two solution methods. Hint: Making use of spherical coordinates in part i will ease the solution.

3) Consider the half sphere shaped object bounded by z = v V1-x² – y? and z= 0. The object is exposed to a field F = (1– z)k. Evaluate $(F.n) dS, where is the outer unit normal to - 7 S the surface and S represents the surface of the object, i. By surface integration, ii. Using the divergence theorem of Gauss. Compare the two solution methods. Hint: Making use of spherical coordinates in part i will ease the solution.

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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3) Consider the half sphere shaped object bounded by z = v V1-x² – y? and z= 0. The object is exposed to a field F = (1– z)k. Evaluate $(F.n) dS, where is the outer unit normal to - 7 S the surface and S represents the surface of the object, i. By surface integration, ii. Using the divergence theorem of Gauss. Compare the two solution methods. Hint: Making use of spherical coordinates in part i will ease the solution.
Transcribed Image Text:3) Consider the half sphere shaped object bounded by z = v V1-x² – y? and z= 0. The object is exposed to a field F = (1– z)k. Evaluate $(F.n) dS, where is the outer unit normal to - 7 S the surface and S represents the surface of the object, i. By surface integration, ii. Using the divergence theorem of Gauss. Compare the two solution methods. Hint: Making use of spherical coordinates in part i will ease the solution.
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