Force between loops

Question

It is physics (force between loops) but the highlighted term is equal to zero and I don't understand it. It is from Stokes' theorem but I don't understand it.

Answer 1

$\int \vec{dl}.\nabla f = \int\int curl(\nabla f)da =0 $ since the curl of a gradient is always $0$. Here I used $f$ for $\dfrac{1}{r_{12}}$