Module 1 : A Crash Course in Vectors
Lecture 5 : Curl of a Vector - Stoke's Theorem
   
  Let us calculate the surface integral of the curl of the field over two surfaces bound by the circular curve.
(i)
On the circular surface bound by the curve in the x-y plane, the outward normal is along $\hat k$ (right hand rule). Thus
 
\begin{displaymath}\int_S (\nabla\times\vec F)\cdot(\hat k dS)= \int_S dS = \pi R^2\end{displaymath}

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