Evaluate S (☑× F) .d.S where S is the open hemispherical surface x² + y² + z² = a², with 0, and F(r) = (1 − ay) e₁ + 2y² e̱2 + (x² + 1) €3 - By direct evaluation. Take the vector element of area dS to point away from the origin. By using the divergence theorem applied to the vector field × F. (Recall that the divergence theorem applies to a closed surface.) (ii) (iii) By using Stokes' theorem applied to the vector field F.
Evaluate S (☑× F) .d.S where S is the open hemispherical surface x² + y² + z² = a², with 0, and F(r) = (1 − ay) e₁ + 2y² e̱2 + (x² + 1) €3 - By direct evaluation. Take the vector element of area dS to point away from the origin. By using the divergence theorem applied to the vector field × F. (Recall that the divergence theorem applies to a closed surface.) (ii) (iii) By using Stokes' theorem applied to the vector field 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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Transcribed Image Text:Evaluate
S
with 0, and
× F) dS where S is the open hemispherical surface x² + y² + z² = a²,
F(r) = (1 − ay) e₁ + 2y² e̱2 + (x² + 1) €3
-
By direct evaluation. Take the vector element of area dS to point away from
the origin.
By using the divergence theorem applied to the vector field × F.
(Recall that the divergence theorem applies to a closed surface.)
(ii)
(iii)
By using Stokes' theorem applied to the vector field F.
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