# What is the physical cause that circulation on a closed surface is zero?

This is quoted from Feynman's Lectures:

We would like to see what happens when the loop shrinks down to a point, so that surface boundary disappears - the surface becomes closed. Now, if the vector $\mathbf{C}$ is everywhere finite, the line integral around the loop must go to zero as we shrink the loop. According to Stokes' theorem, the surface integral of $(\nabla \times \mathbf{C})_n$ must also vanish.

Mathematically, from Stokes' theorem, it can be inferred that

$$\int_{\text{any closed surface}} (\nabla \times \mathbf{C}) \cdot n \cdot da = 0.$$ But physically, what is going on that is making the circulation zero in the closed surface?

• Your equation is a mathematical theorem. It seems to make little sense to try to explain why it is true from experience. Aren't you looking for examples of its use in physics, instead? Commented Apr 5, 2015 at 13:05
• @Ján Lalinský: Yes, sir. Actually I want the reason.
– user36790
Commented Apr 5, 2015 at 13:09