I look at the curl as how much it causes a stick to rotate. So like suppose we have the force field F = (y,0,0) Then we see the curl is nonzero, because the force in the x direction is increasing as we move perpendicular to the direction of the x-axis. Therefore suppose we place a twig with one end fixed a the x-axis and y=0 and the other end at same x but at y=1. Then there would be a net torque on the twig explaining why the curl must be nonzero. I have always had this "twig-picture" of the curl, but I'm starting to think it's wrong to think of it like that. Because I think that you could find vector fields with zero curl where you could still place twigs and get rotation. As an example look at the dipole of two charges on the picture attached. Definately. If you placed a twig with ends at the two green dots, you would get rotation since the horizontal force gets bigger the closer you get to the two charges. However, the curl still happens to be zero. What is wrong with my arguments here? And what is the curl really a measure of? And how long should you make your twig?