The value ofby Stoke’s theorem, whereand C is the boundary of thetriangle with vertices at ( 0 ,0 , 0 ) , ( 1 , 0 , 0 ) and ( 1 ,1 , 0 ) isa)1/2b)1/3c)1/4d)1/5Correct answer is option 'B'. Can you explain this answer?

Question

The value ofby Stoke&rsquo;s theorem, whereand C is the boundary of thetriangle with vertices at ( 0 ,0 , 0 ) , ( 1 , 0 , 0 ) and ( 1 ,1 , 0 ) isa)1/2b)1/3c)1/4d)1/5Correct answer is option 'B'. Can you explain this answer?

Answer

We have, curl

Also we note that z coordinate of each vertex of the triangle is zero.
or The triangle lies in the xy-plane. So,

So, curl

In the figure, we have only considered the xy-plane. So, by Stoke’s Theorem

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