(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is a question about stokes theorem in general, not about a specific problem.

Directly from lecture:

"If S has no boundry (eg. if S is the boundry of a solid region) then [tex]\int\int_{S}Curl(\stackrel{\rightarrow}{F})\bullet ds = 0[/tex] "

because apparently "no boundry C exists"

However in the next example he gives S is a hemisphere or radius 1 above the XY plane; and he uses the projection of the hemesphere on the XY plane as the bondry curve C and it works out fine.

Isnt the hemisphere a boundry of a solid region? So shoudn't the integral be zero? Why can you use the boundry of the projection of S on the XY plane as the curve C?

This is hard to explain in words, if someone is so kind as to lok into this, you can see exactly what I am seeing here:

http://webcast.berkeley.edu/course_details_new.php?seriesid=2008-D-54472&semesterid=2008-D

Lecture 42, 4:00-5:00 is where he says the integral is zero, then at 9:40 he does the example with the hemesphere and it is not zero.

2. Relevant equations

[tex]\int\int_{S}Curl(\stackrel{\rightarrow}{F})\bullet ds = \int_{C}\stackrel{\rightarrow}{F}\bullet d\vec{r}[/tex]

Thanks anyone willing to look/help :)

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# Homework Help: Stokes Theorem Boundry

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