1. Evaluate circulation in HW5 problem 1 with Stokes' theorem as follows: i) Find the normal to the surface according to path direction and equation of the surface. ii) Find curl of F. iii) Find circulation with results from i) and ii). iv) Based on results from ii) and iii), can F be expressed as the gradient of a scalar? Explain.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Given a vector field F = a,xy - a,2x, find its circulation around the path
OABO shown in Fig. 2-22.
SOLUTION
Let us split the circulation integral into three parts.
² = f*^ F · € + S² F · ª² + Sº° F · a
F.de
F.dl.
F.de =
JOABO
Along path OA: y=0, F = -a,2x, df = a,dx, F.de = 0.
SF-de
F.de = 0.
FIGURE 2-22 Path for line integral (Examples 2-14 and 2-16).
34
B
A
·x
Transcribed Image Text:Given a vector field F = a,xy - a,2x, find its circulation around the path OABO shown in Fig. 2-22. SOLUTION Let us split the circulation integral into three parts. ² = f*^ F · € + S² F · ª² + Sº° F · a F.de F.dl. F.de = JOABO Along path OA: y=0, F = -a,2x, df = a,dx, F.de = 0. SF-de F.de = 0. FIGURE 2-22 Path for line integral (Examples 2-14 and 2-16). 34 B A ·x
1. Evaluate circulation in HW5 problem 1 with Stokes' theorem as follows: i) Find the normal to the surface according to
path direction and equation of the surface. ii) Find curl of F. iii) Find circulation with results from i) and ii). iv) Based
on results from ii) and iii), can F be expressed as the gradient of a scalar? Explain.
Transcribed Image Text:1. Evaluate circulation in HW5 problem 1 with Stokes' theorem as follows: i) Find the normal to the surface according to path direction and equation of the surface. ii) Find curl of F. iii) Find circulation with results from i) and ii). iv) Based on results from ii) and iii), can F be expressed as the gradient of a scalar? Explain.
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